From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/blueball.gif | Bin 0 -> 398 bytes src/slalib/sun67.htx/change_begin.gif | Bin 0 -> 133 bytes src/slalib/sun67.htx/change_begin_right.gif | Bin 0 -> 128 bytes src/slalib/sun67.htx/change_delete.gif | Bin 0 -> 257 bytes src/slalib/sun67.htx/change_delete_right.gif | Bin 0 -> 257 bytes src/slalib/sun67.htx/change_end.gif | Bin 0 -> 135 bytes src/slalib/sun67.htx/change_end_right.gif | Bin 0 -> 127 bytes src/slalib/sun67.htx/contents.xbm | 12 + src/slalib/sun67.htx/contents_motif.gif | Bin 0 -> 225 bytes src/slalib/sun67.htx/cross_ref_motif.gif | Bin 0 -> 78 bytes src/slalib/sun67.htx/foot_motif.gif | Bin 0 -> 87 bytes src/slalib/sun67.htx/footnode.html | 224 ++ src/slalib/sun67.htx/greenball.gif | Bin 0 -> 398 bytes src/slalib/sun67.htx/icons.html | 42 + src/slalib/sun67.htx/image.gif | Bin 0 -> 195 bytes 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259 bytes src/slalib/sun67.htx/next_motif.gif | Bin 0 -> 172 bytes src/slalib/sun67.htx/next_motif_gr.gif | Bin 0 -> 172 bytes src/slalib/sun67.htx/node1.html | 65 + src/slalib/sun67.htx/node10.html | 75 + src/slalib/sun67.htx/node100.html | 110 + src/slalib/sun67.htx/node101.html | 132 + src/slalib/sun67.htx/node102.html | 149 ++ src/slalib/sun67.htx/node103.html | 170 ++ src/slalib/sun67.htx/node104.html | 208 ++ src/slalib/sun67.htx/node105.html | 166 ++ src/slalib/sun67.htx/node106.html | 207 ++ src/slalib/sun67.htx/node107.html | 188 ++ src/slalib/sun67.htx/node108.html | 156 ++ src/slalib/sun67.htx/node109.html | 168 ++ src/slalib/sun67.htx/node11.html | 102 + src/slalib/sun67.htx/node110.html | 200 ++ src/slalib/sun67.htx/node111.html | 104 + src/slalib/sun67.htx/node112.html | 107 + src/slalib/sun67.htx/node113.html | 109 + src/slalib/sun67.htx/node114.html | 107 + src/slalib/sun67.htx/node115.html | 115 + src/slalib/sun67.htx/node116.html | 116 + 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src/slalib/sun67.htx/node138.html | 116 + src/slalib/sun67.htx/node139.html | 117 + src/slalib/sun67.htx/node14.html | 112 + src/slalib/sun67.htx/node140.html | 148 ++ src/slalib/sun67.htx/node141.html | 107 + src/slalib/sun67.htx/node142.html | 108 + src/slalib/sun67.htx/node143.html | 133 + src/slalib/sun67.htx/node144.html | 310 +++ src/slalib/sun67.htx/node145.html | 279 +++ src/slalib/sun67.htx/node146.html | 255 ++ src/slalib/sun67.htx/node147.html | 278 +++ src/slalib/sun67.htx/node148.html | 256 ++ src/slalib/sun67.htx/node149.html | 135 + src/slalib/sun67.htx/node15.html | 230 ++ src/slalib/sun67.htx/node150.html | 202 ++ src/slalib/sun67.htx/node151.html | 111 + src/slalib/sun67.htx/node152.html | 145 ++ src/slalib/sun67.htx/node153.html | 120 + src/slalib/sun67.htx/node154.html | 131 + src/slalib/sun67.htx/node155.html | 110 + src/slalib/sun67.htx/node156.html | 323 +++ src/slalib/sun67.htx/node157.html | 203 ++ src/slalib/sun67.htx/node158.html | 102 + src/slalib/sun67.htx/node159.html | 145 ++ src/slalib/sun67.htx/node16.html | 121 + src/slalib/sun67.htx/node160.html | 98 + src/slalib/sun67.htx/node161.html | 93 + src/slalib/sun67.htx/node162.html | 93 + src/slalib/sun67.htx/node163.html | 166 ++ src/slalib/sun67.htx/node164.html | 184 ++ src/slalib/sun67.htx/node165.html | 176 ++ src/slalib/sun67.htx/node166.html | 428 ++++ src/slalib/sun67.htx/node167.html | 232 ++ src/slalib/sun67.htx/node168.html | 276 +++ src/slalib/sun67.htx/node169.html | 275 +++ src/slalib/sun67.htx/node17.html | 205 ++ src/slalib/sun67.htx/node170.html | 111 + src/slalib/sun67.htx/node171.html | 115 + src/slalib/sun67.htx/node172.html | 101 + src/slalib/sun67.htx/node173.html | 121 + src/slalib/sun67.htx/node174.html | 126 + src/slalib/sun67.htx/node175.html | 129 + src/slalib/sun67.htx/node176.html | 100 + src/slalib/sun67.htx/node177.html | 152 ++ src/slalib/sun67.htx/node178.html | 111 + src/slalib/sun67.htx/node179.html | 107 + src/slalib/sun67.htx/node18.html | 135 + src/slalib/sun67.htx/node180.html | 184 ++ src/slalib/sun67.htx/node181.html | 122 + src/slalib/sun67.htx/node182.html | 201 ++ src/slalib/sun67.htx/node183.html | 109 + src/slalib/sun67.htx/node184.html | 117 + src/slalib/sun67.htx/node185.html | 168 ++ src/slalib/sun67.htx/node186.html | 144 ++ src/slalib/sun67.htx/node187.html | 378 +++ src/slalib/sun67.htx/node188.html | 220 ++ src/slalib/sun67.htx/node189.html | 160 ++ src/slalib/sun67.htx/node19.html | 160 ++ src/slalib/sun67.htx/node190.html | 137 ++ src/slalib/sun67.htx/node191.html | 91 + src/slalib/sun67.htx/node192.html | 95 + src/slalib/sun67.htx/node193.html | 93 + src/slalib/sun67.htx/node194.html | 91 + src/slalib/sun67.htx/node195.html | 114 + src/slalib/sun67.htx/node196.html | 137 ++ src/slalib/sun67.htx/node197.html | 171 ++ src/slalib/sun67.htx/node198.html | 167 ++ src/slalib/sun67.htx/node199.html | 174 ++ src/slalib/sun67.htx/node2.html | 85 + src/slalib/sun67.htx/node20.html | 320 +++ src/slalib/sun67.htx/node200.html | 168 ++ src/slalib/sun67.htx/node201.html | 215 ++ src/slalib/sun67.htx/node202.html | 254 ++ src/slalib/sun67.htx/node203.html | 187 ++ src/slalib/sun67.htx/node204.html | 127 + src/slalib/sun67.htx/node205.html | 92 + src/slalib/sun67.htx/node206.html | 125 + src/slalib/sun67.htx/node207.html | 119 + src/slalib/sun67.htx/node208.html | 92 + src/slalib/sun67.htx/node209.html | 147 ++ src/slalib/sun67.htx/node21.html | 264 ++ src/slalib/sun67.htx/node210.html | 177 ++ src/slalib/sun67.htx/node211.html | 232 ++ src/slalib/sun67.htx/node212.html | 171 ++ src/slalib/sun67.htx/node213.html | 181 ++ src/slalib/sun67.htx/node214.html | 189 ++ src/slalib/sun67.htx/node215.html | 87 + src/slalib/sun67.htx/node216.html | 110 + src/slalib/sun67.htx/node217.html | 92 + src/slalib/sun67.htx/node218.html | 91 + src/slalib/sun67.htx/node219.html | 184 ++ src/slalib/sun67.htx/node22.html | 119 + src/slalib/sun67.htx/node220.html | 96 + src/slalib/sun67.htx/node221.html | 158 ++ src/slalib/sun67.htx/node222.html | 113 + src/slalib/sun67.htx/node223.html | 139 ++ src/slalib/sun67.htx/node224.html | 617 +++++ src/slalib/sun67.htx/node225.html | 143 ++ src/slalib/sun67.htx/node226.html | 212 ++ src/slalib/sun67.htx/node227.html | 230 ++ src/slalib/sun67.htx/node228.html | 696 ++++++ src/slalib/sun67.htx/node229.html | 65 + src/slalib/sun67.htx/node23.html | 278 +++ src/slalib/sun67.htx/node24.html | 213 ++ src/slalib/sun67.htx/node25.html | 103 + src/slalib/sun67.htx/node26.html | 123 + src/slalib/sun67.htx/node27.html | 122 + src/slalib/sun67.htx/node28.html | 128 + src/slalib/sun67.htx/node29.html | 140 ++ src/slalib/sun67.htx/node3.html | 76 + src/slalib/sun67.htx/node30.html | 103 + src/slalib/sun67.htx/node31.html | 114 + src/slalib/sun67.htx/node32.html | 115 + src/slalib/sun67.htx/node33.html | 128 + src/slalib/sun67.htx/node34.html | 129 + src/slalib/sun67.htx/node35.html | 142 ++ src/slalib/sun67.htx/node36.html | 122 + src/slalib/sun67.htx/node37.html | 121 + src/slalib/sun67.htx/node38.html | 99 + src/slalib/sun67.htx/node39.html | 114 + src/slalib/sun67.htx/node4.html | 131 + src/slalib/sun67.htx/node40.html | 125 + src/slalib/sun67.htx/node41.html | 125 + src/slalib/sun67.htx/node42.html | 122 + src/slalib/sun67.htx/node43.html | 229 ++ src/slalib/sun67.htx/node44.html | 109 + src/slalib/sun67.htx/node45.html | 103 + src/slalib/sun67.htx/node46.html | 123 + src/slalib/sun67.htx/node47.html | 157 ++ src/slalib/sun67.htx/node48.html | 110 + src/slalib/sun67.htx/node49.html | 103 + src/slalib/sun67.htx/node5.html | 83 + src/slalib/sun67.htx/node50.html | 166 ++ src/slalib/sun67.htx/node51.html | 99 + src/slalib/sun67.htx/node52.html | 115 + src/slalib/sun67.htx/node53.html | 145 ++ src/slalib/sun67.htx/node54.html | 127 + src/slalib/sun67.htx/node55.html | 200 ++ src/slalib/sun67.htx/node56.html | 146 ++ src/slalib/sun67.htx/node57.html | 118 + src/slalib/sun67.htx/node58.html | 112 + src/slalib/sun67.htx/node59.html | 117 + src/slalib/sun67.htx/node6.html | 116 + src/slalib/sun67.htx/node60.html | 107 + src/slalib/sun67.htx/node61.html | 152 ++ src/slalib/sun67.htx/node62.html | 154 ++ src/slalib/sun67.htx/node63.html | 106 + src/slalib/sun67.htx/node64.html | 115 + src/slalib/sun67.htx/node65.html | 117 + src/slalib/sun67.htx/node66.html | 122 + src/slalib/sun67.htx/node67.html | 121 + src/slalib/sun67.htx/node68.html | 93 + src/slalib/sun67.htx/node69.html | 93 + src/slalib/sun67.htx/node7.html | 76 + src/slalib/sun67.htx/node70.html | 114 + src/slalib/sun67.htx/node71.html | 129 + src/slalib/sun67.htx/node72.html | 100 + src/slalib/sun67.htx/node73.html | 131 + src/slalib/sun67.htx/node74.html | 125 + src/slalib/sun67.htx/node75.html | 125 + src/slalib/sun67.htx/node76.html | 109 + src/slalib/sun67.htx/node77.html | 117 + src/slalib/sun67.htx/node78.html | 168 ++ src/slalib/sun67.htx/node79.html | 144 ++ src/slalib/sun67.htx/node8.html | 85 + src/slalib/sun67.htx/node80.html | 111 + src/slalib/sun67.htx/node81.html | 137 ++ src/slalib/sun67.htx/node82.html | 91 + src/slalib/sun67.htx/node83.html | 95 + src/slalib/sun67.htx/node84.html | 93 + src/slalib/sun67.htx/node85.html | 145 ++ src/slalib/sun67.htx/node86.html | 124 + src/slalib/sun67.htx/node87.html | 97 + src/slalib/sun67.htx/node88.html | 106 + src/slalib/sun67.htx/node89.html | 140 ++ src/slalib/sun67.htx/node9.html | 75 + src/slalib/sun67.htx/node90.html | 106 + src/slalib/sun67.htx/node91.html | 330 +++ src/slalib/sun67.htx/node92.html | 91 + src/slalib/sun67.htx/node93.html | 91 + src/slalib/sun67.htx/node94.html | 110 + src/slalib/sun67.htx/node95.html | 91 + src/slalib/sun67.htx/node96.html | 91 + src/slalib/sun67.htx/node97.html | 98 + src/slalib/sun67.htx/node98.html | 111 + src/slalib/sun67.htx/node99.html | 105 + src/slalib/sun67.htx/orangeball.gif | Bin 0 -> 398 bytes src/slalib/sun67.htx/pinkball.gif | Bin 0 -> 398 bytes src/slalib/sun67.htx/previous_group_motif.gif | Bin 0 -> 303 bytes src/slalib/sun67.htx/previous_group_motif_gr.gif | Bin 0 -> 303 bytes src/slalib/sun67.htx/previous_motif.gif | Bin 0 -> 220 bytes src/slalib/sun67.htx/previous_motif_gr.gif | Bin 0 -> 220 bytes src/slalib/sun67.htx/purpleball.gif | Bin 0 -> 398 bytes src/slalib/sun67.htx/redball.gif | Bin 0 -> 398 bytes src/slalib/sun67.htx/source.gif | Bin 0 -> 979 bytes src/slalib/sun67.htx/sun67.css | 10 + src/slalib/sun67.htx/sun67.html | 610 +++++ src/slalib/sun67.htx/up_motif.gif | Bin 0 -> 145 bytes src/slalib/sun67.htx/up_motif_gr.gif | Bin 0 -> 145 bytes src/slalib/sun67.htx/whiteball.gif | Bin 0 -> 275 bytes src/slalib/sun67.htx/yellowball.gif | Bin 0 -> 398 bytes 601 files changed, 44518 insertions(+) create mode 100644 src/slalib/sun67.htx/blueball.gif create mode 100644 src/slalib/sun67.htx/change_begin.gif create mode 100644 src/slalib/sun67.htx/change_begin_right.gif create mode 100644 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+
...SLALIB +
The name isn't an acronym; +it just stands for ``Subprogram Library A''. +
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...papers; +
One frame not included in +Figure 1 is that of the Hipparcos catalogue. This is currently the +best available implementation in the optical of the International +Celestial Reference System (ICRS), which is based on extragalactic +radio sources observed by VLBI. The distinction between FK5 J2000 +and Hipparcos coordinates only becomes important when accuracies of +50 mas or better are required. More details are given in +Section 4.14. +
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...equinox. +
With +the introduction of the International Celestial Reference System (ICRS), the +connection between (i) star coordinates and (ii) the Earth's orientation +and orbit has been broken. However, the orientation of the +International Celestial Reference Frame (ICRF) axes was, for convenience, +chosen to match J2000 FK5, and for most practical purposes ICRF coordinates +(for example entries in the Hipparcos catalogue) can be regarded as +synonymous with J2000 FK5. See Section 4.14 for further details. +
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...used. +
An equinox is, however, not required for coordinates +in the International Celestial Reference System. Such coordinates must +be labelled simply ``ICRS'', or the specific catalogue can be mentioned, +such as ``Hipparcos''; constructions such as ``Hipparcos, J2000'' are +redundant and misleading. +
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...catalogues. +
This was +true until the inception of the International Celestial Reference +System, which is based on the idea of axes locked into the +distant background. The coordinates +of the extragalactic sources which realize these +axes have no individual significance; there is a ``no net rotation'' +condition which has to be satisfied each time any revisions take +place. +
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+SLALIB -- Positional Astronomy Library +
+Starlink User Note 67 +
+P. T. Wallace +
+12 October 1999 +
+E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/greenball.gif b/src/slalib/sun67.htx/greenball.gif new file mode 100644 index 0000000..2ffbb22 Binary files /dev/null and b/src/slalib/sun67.htx/greenball.gif differ diff --git a/src/slalib/sun67.htx/icons.html b/src/slalib/sun67.htx/icons.html new file mode 100644 index 0000000..d6b38c3 --- /dev/null +++ b/src/slalib/sun67.htx/icons.html @@ -0,0 +1,42 @@ + +
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+ 14 hyphenation exceptions out of 607 + 21i,13n,21p,242b,498s stack positions out of 300i,40n,60p,3000b,4000s + +Output written on images.dvi (330 pages, 51052 bytes). diff --git a/src/slalib/sun67.htx/images.pl b/src/slalib/sun67.htx/images.pl new file mode 100644 index 0000000..498f422 --- /dev/null +++ b/src/slalib/sun67.htx/images.pl @@ -0,0 +1,1686 @@ +# LaTeX2HTML 97.1 (release) (July 13th, 1997) +# Associate images original text with physical files. + + +$key = q/{_inline}1hspace-0.05em^'hspace-0.1em'hspace-0.4em.74{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.74$|; + +$key = q/{_inline}cosdeltaE{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\cos \delta E$|; + +$key = q/{_inline}0^rmshspace-0.3em.03{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.03$|; + +$key = q/{_inline}0leqx<1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0 \leq x < 1$|; + +$key = q/{_inline}zeta=80^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta=80^\circ$|; + +$key = q/{_inline}-75^circ,59^',27^''.2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-75^{\circ}\,59^{'}\,27^{''}.2$|; + +$key = q/{_inline}150hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$150\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}2hspace-0.05em^'hspace-0.1em'hspace-0.4em.3{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$2\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$|; + +$key = q/{_inline}1hspace-0.05em^'hspace-0.1em'hspace-0.4em.6{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$|; + +$key = q/{displaymath}zeta_vacapproxzeta_obs+Atanzeta_obs+Btan^3zeta_obs{displaymath}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|\begin{displaymath} +\zeta _{vac} \approx \zeta _{obs} + + A \tan \zeta _{obs} + + B \tan ^{3}\zeta _{obs} \end{displaymath}|; + +$key = q/{_inline}1000times20{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1000\times20$|; + +$key = q/{_inline}times3602pi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times 360/2\pi$|; + +$key = q/{_inline}21hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$21\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}12^h,07^m,58^s.09{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$12^{h}\,07^{m}\,58^{s}.09$|; + +$key = q/{_inline}81^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$81^\circ$|; + +$key = q/{_inline}omega{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\omega$|; + +$key = q/{_inline}30^rmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$30^{\rm m}$|; + +$key = q/{_inline}89^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$89^\circ$|; + +$key = q/{displaymath}zeta_obsapproxzeta_vac-fracAtanzeta_vac+Btan^3zeta_vac1+(A+3Btan^2zeta_vac)sec^2zeta_vac{displaymath}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|\begin{displaymath} +\zeta _{obs} \approx \zeta _{vac} + - \frac{A \tan \zeta _{va... + ... + {1 + ( A + 3 B \tan ^{2}\zeta _{vac} ) \sec ^{2}\zeta _{vac}}\end{displaymath}|; + +$key = q/{_inline}1^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1^\circ$|; + +$key = q/{_inline}=Deltapsicosepsilon{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$=\Delta\psi\cos\epsilon$|; + +$key = q/{_inline}(3times3){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$(3\times3)$|; + +$key = q/{_inline}epsilon{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\epsilon$|; + +$key = q/{_inline}290^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$290^\circ$|; + +$key = q/{_inline}+1^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$+1^{\circ}$|; + +$key = q/{_inline}20,murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$20\,\mu{\rm m}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.6{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$|; + +$key = q/{_inline}7hspace-0.05em^'hspace-0.1em'hspace-0.4em.1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$7\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$|; + +$key = q/{_inline}C_3!=!-10.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$C_3\!=\!-10.0$|; + +$key = q/{_inline}~sinalpha+({_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\sin \alpha + + ($|; + +$key = q/{_inline}xi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\xi$|; + +$key = q/{_inline}1100hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1100\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}[lambda,phi]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\lambda,\phi]$|; + +$key = q/{_inline}30hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$30\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}1.0027379cdots{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1.0027379\cdots$|; + +$key = q/{_inline}90^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$90^{\circ}$|; + +$key = q/{_inline}14hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$14\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}rho=r(1+cr^2){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\rho = r (1 + c r^{2})$|; + +$key = q/{_inline}pmn{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm n$|; + +$key = q/{_inline}bfD{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\bf D}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.24{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.24$|; + +$key = q/{_inline}0^rmshspace-0.3em.015869{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.015869$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.43549{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.43549$|; + +$key = q/{_inline}[,Deltax,Deltay,Deltaz,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,\Delta x,\Delta y, \Delta z\,]$|; + +$key = q/{_inline}86hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$86\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}(0leqe<1){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$( 0 \leq e < 1 )$|; + +$key = q/{_inline}0^rmh{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm h}$|; + +$key = q/{_inline}~cosalpha-{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\cos \alpha + -$|; + +$key = q/{_inline}[theta,phi,dottheta,dotphi]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\theta,\phi,\dot{\theta},\dot{\phi}]$|; + +$key = q/{_inline}1hspace-0.05em^'hspace-0.1em'hspace-0.4em.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0$|; + +$key = q/{_inline}nu=rho_wrho_s{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\nu=\rho_w/\rho_s$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.3{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$|; + +$key = q/{_inline}varpi=Omega+omega{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\varpi = \Omega + \omega$|; + +$key = q/{_inline}6hspace-0.05em^'hspace-0.1em'hspace-0.4em.1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$6\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$|; + +$key = q/{_inline}mu_delta,=+{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\mu_\delta\,=+$|; + +$key = q/{_inline}920hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$920\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}b^I!I=0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$b^{I\!I}=0$|; + +$key = q/{_inline}x'=x_1+rmXZ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$x' = x_{1} + {\rm XZ}$|; + +$key = q/{_inline}mu_alpha={_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\mu_\alpha=$|; + +$key = q/{_inline}rmbfr_0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\rm \bf r}_0$|; + +$key = q/{_inline}zeta_vac{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta _{vac}$|; + +$key = q/{_inline}86^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$86^\circ$|; + +$key = q/{_inline}y'''=+x''sinrmPERP2+y''cosrmPERP2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$|; + +$key = q/{_inline}C_2!=!-2.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$C_2\!=\!-2.0$|; + +$key = q/{_inline}0.0065^circm^-1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0.0065^\circ m^{-1}$|; + +$key = q/{_inline}alpha=18^rmh,delta=+30^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\alpha=18^{\rm h},\delta=+30^{\circ}$|; + +$key = q/{_inline}[mu_alpha,mu_delta]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\mu_\alpha,\mu_\delta]$|; + +$key = q/{_inline}5^rmh,25^rmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$5^{\rm h}\,25^{\rm m}$|; + +$key = q/{figure}centertabular|cccccc|hline&&&&&hspace5em&hspace5em&hspace5em&hspace5em&halloftheprecessionandE-termscorrectionsaresuperfluous.{figure}MSF=1.5;FSF=1;AAT;/; +$cached_env_img{$key} = q|\begin{figure} +\begin{center} +\begin{tabular} +{\vert cccccc\vert} \hline +& & & &... + ...2000, all of the precession and E-terms corrections +are superfluous.\end{figure}|; + +$key = q/{_inline}~sinalpha-{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\sin \alpha + -$|; + +$key = q/{_inline}equiv123{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\equiv123$|; + +$key = q/{_inline}3hspace-0.05em^'hspace-0.1em'hspace-0.4em.7{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.7$|; + +$key = q/{_inline}12^circ,34^',56^''.7{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$12^{\circ}\,34^{'}\,56^{''}.7$|; + +$key = q/{_inline}y'=y_1+rmYZ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$y' = y_{1} + {\rm YZ}$|; + +$key = q/{_inline}+0hspace-0.05em^'hspace-0.1em'hspace-0.4em.103{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$+0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.103$|; + +$key = q/{_inline}=93^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$=93^\circ$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.0001{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0001$|; + +$key = q/{_inline}[x_e,y_e,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[x_{e},y_{e}\,]$|; + +$key = q/{_inline}[,0,,1,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,0,\,1\,]$|; + +$key = q/{_inline}20hspace-0.05em^'hspace-0.1em'hspace-0.4em.5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$|; + +$key = q/{_inline}theta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\theta$|; + +$key = q/{_inline}zeta<80^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta<80^{\circ}$|; + +$key = q/{_inline}0^rmshspace-0.3em.000340{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.000340$|; + +$key = q/{_inline}deltaEcosE{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\delta E \cos E$|; + +$key = q/{_inline}[x_m,y_m,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[x_{m},y_{m}\,]$|; + +$key = q/{_inline}-0hspace-0.05em^'hspace-0.1em'hspace-0.4em.06{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.06$|; + +$key = q/{_inline}340hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$340\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}l^I!I,b^I!I{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$l^{I\!I},b^{I\!I}$|; + +$key = q/{_inline}20^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$20^\circ$|; + +$key = q/{_inline}_j)]cdot({_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$_{j})] + \cdot ($|; + +$key = q/{_inline}times{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times$|; + +$key = q/{_inline}20hspace-0.05em^'hspace-0.1em'hspace-0.4em.49552{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.49552$|; + +$key = q/{_inline}tan^3zeta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\tan^{3} \zeta$|; + +$key = q/{_inline}E=90^circ-zeta_true{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$E=90^\circ-\zeta_{true}$|; + +$key = q/{_inline}83^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$83^\circ$|; + +$key = q/{_inline}0^rmshspace-0.3em.9{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.9$|; + +$key = q/{_inline}(0leqeleq10){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$( 0 \leq e \leq 10 )$|; + +$key = q/{_inline}17hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$17\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}0.4,murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0.4\,\mu{\rm m}$|; + +$key = q/{_inline}3^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$3^{\circ}$|; + +$key = q/{_inline}20^rms{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$20^{\rm s}$|; + +$key = q/{_inline}1hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}zeta=70^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta=70^\circ$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.001{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.001$|; + +$key = q/{_inline}DeltarmT{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta {\rm T}$|; + +$key = q/{_inline}pm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm$|; + +$key = q/{_inline}C_1!=!+50.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$C_1\!=\!+50.0$|; + +$key = q/{_inline}l^I!I=90^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$l^{I\!I}=90^{\circ}$|; + +$key = q/{_inline}50^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$50^\circ$|; + +$key = q/{_inline}[,theta,phi~]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,\theta,\phi~]$|; + +$key = q/{_inline}x!pm!n{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$x\!\pm\!n$|; + +$key = q/{_inline}mu_delta={_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\mu_\delta=$|; + +$key = q/{_inline}3times3{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$3\times3$|; + +$key = q/{_inline}50hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$50\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}1.0,murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1.0\,\mu{\rm m}$|; + +$key = q/{_inline}92^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$92^\circ$|; + +$key = q/{_inline}18hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$18\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}0.7,murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0.7\,\mu{\rm m}$|; + +$key = q/{_inline}timesn{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times n$|; + +$key = q/{_inline}rmMJD=(rmJD-2400000.5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\rm MJD} = ({\rm JD} - 2400000.5$|; + +$key = q/{_inline}0^circhspace-0.37em.hspace0.02em5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$|; + +$key = q/{_inline}tan^-14{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\tan^{-1} 4$|; + +$key = q/{_inline}0^rmshspace-0.3em.01{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.01$|; + +$key = q/{_inline}100hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$100\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}2hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$2\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}[,xi,eta,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,\xi,\eta\,]$|; + +$key = q/{_inline}00^h,00^m,00^s.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$00^{h}\,00^{m}\,00^{s}.0$|; + +$key = q/{_inline}0!-!pi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\!-\!\pi$|; + +$key = q/{_inline}280^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$280^\circ$|; + +$key = q/{_inline}beta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\beta$|; + +$key = q/{_inline}0^rmshspace-0.3em.000083{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.000083$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.00510{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00510$|; + +$key = q/{_inline}zeta=87^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta = 87^{\circ}$|; + +$key = q/{_inline}90^circ-delta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$90^\circ-\delta$|; + +$key = q/{_inline}2murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$2\mu{\rm m}$|; + +$key = q/{_inline}{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$<{\bf V1}+{\bf D}\gt$|; + +$key = q/{_inline}5hspace-0.05em^'hspace-0.1em'hspace-0.4em.8{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$5\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$|; + +$key = q/{_inline}25^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$25^\circ$|; + +$key = q/{_inline}80^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$80^\circ$|; + +$key = q/{_inline}pmpi2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm\pi/2$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.01{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$|; + +$key = q/{_inline}rho{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\rho$|; + +$key = q/{_inline}152pi=2.3873241463784300365{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$15/{2\pi} = 2.3873241463784300365$|; + +$key = q/{_inline}2pi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$2\pi$|; + +$key = q/{_inline}43hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$43\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}sim20{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\sim20$|; + +$key = q/{_inline}[,alpha,delta,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,\alpha,\delta\,]$|; + +$key = q/{_inline}dotalpha{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\dot{\alpha}$|; + +$key = q/{_inline}0^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\circ}$|; + +$key = q/{_inline}88^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$88^\circ$|; + +$key = q/{_inline}bfV1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\bf V1}$|; + +$key = q/{_inline}tan^-11{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\tan^{-1} 1$|; + +$key = q/{_inline}0^circhspace-0.37em.hspace0.02em2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}2$|; + +$key = q/{_inline}-19^circ,44^',37^''.1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-19^{\circ}\,44^{'}\,37^{''}.1$|; + +$key = q/{_inline}cdot~[diag(1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\cdot~[diag(1/$|; + +$key = q/{_inline}alpha=0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\alpha=0$|; + +$key = q/{_inline}~cosalpha)sindelta-{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\cos \alpha ) \sin \delta + -$|; + +$key = q/{_inline}zeta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta$|; + +$key = q/{_inline}3hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$3\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}tanzeta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\tan \zeta$|; + +$key = q/{_inline}0^rmshspace-0.3em.000105{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.000105$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.4{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$|; + +$key = q/{_inline}~sinalpha)secdelta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\sin \alpha ) \sec \delta $|; + +$key = q/{_inline}-1^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-1^{\circ}$|; + +$key = q/{_inline}times10^-5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times10^{-5}$|; + +$key = q/{_inline}C_4!=!+25.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$C_4\!=\!+25.0$|; + +$key = q/{_inline}60hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$60\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}76^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$76^\circ$|; + +$key = q/{_inline}x'''=+x''cosrmPERP2+y''sinrmPERP2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$|; + +$key = q/{_inline}deltaE{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\delta E$|; + +$key = q/{_inline}times2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times 2 / $|; + +$key = q/{_inline}zeta_obs{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta_{obs}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$|; + +$key = q/{_inline}4hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$4\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}0^rmshspace-0.3em.0016{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.0016$|; + +$key = q/{_inline}zeta=84^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta=84^\circ$|; + +$key = q/{_inline}100mum{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$100\mu m$|; + +$key = q/{_inline}sigma=5.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\sigma=5.0$|; + +$key = q/{_inline}circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\circ}$|; + +$key = q/{_inline}[x_1,y_1,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[x_{1},y_{1}\,]$|; + +$key = q/{_inline}L=varpi+M{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$L = \varpi + M$|; + +$key = q/{_inline}16^h,09^m,55^s.13{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$16^{h}\,09^{m}\,55^{s}.13$|; + +$key = q/{_inline}times(2pi86400)^2times(3602pi){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times (2\pi/86400)^2 \times (360/2\pi)$|; + +$key = q/{_inline}xi,eta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\xi,\eta$|; + +$key = q/{_inline}Deltazeta=atanzeta+btan^3zeta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$|; + +$key = q/{_inline}23^circhspace-0.37em.hspace0.02em5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$23^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$|; + +$key = q/{_inline}rightarrow{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\rightarrow$|; + +$key = q/{_inline}pmn.nxpmn{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm n.n x \pm n$|; + +$key = q/{_inline}cdot{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\cdot$|; + +$key = q/{_inline}85^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$85^\circ$|; + +$key = q/{_inline}45hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$45\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}pm3{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm3$|; + +$key = q/{_inline}0^rmshspace-0.3em.0013{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.0013$|; + +$key = q/{_inline}zeta<70^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta<70^{\circ}$|; + +$key = q/{_inline}tan^5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\tan^5$|; + +$key = q/{_inline}5hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$5\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}~sinalpha+{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\sin \alpha + +$|; + +$key = q/{_inline}620hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$620\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}ntimesn{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$n \times n$|; + +$key = q/{_inline}Deltazeta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta \zeta$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.00125{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00125$|; + +$key = q/{_inline}10^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$10^{\circ}$|; + +$key = q/{_inline}varpi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\varpi$|; + +$key = q/{_inline}lambda,beta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\lambda,\beta$|; + +$key = q/{_inline}0.3,murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0.3\,\mu{\rm m}$|; + +$key = q/{_inline}pm100{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm100$|; + +$key = q/{_inline}1900hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1900\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}times10^-10{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times10^{-10}$|; + +$key = q/{_inline}M_odot=1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$M_\odot = 1$|; + +$key = q/{_inline}Deltaalpha{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta\alpha$|; + +$key = q/{displaymath}Deltazeta=Fleft(frac0^circhspace-0.37em.hspace0.02em55445-0^circhsp-0.37em.hspace0.02em00202E^21+0.28385E+0.02390E^2right){displaymath}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|\begin{displaymath} +\Delta \zeta = F \left( + \frac{0^\circ\hspace{-0.37em}.\hspa... + ...hspace{0.02em}00202 E^2} + {1 + 0.28385 E +0.02390 E^2} \right) \end{displaymath}|; + +$key = q/{_inline}times(2pi86400)times(3602pi){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\times (2\pi/86400) \times (360/2\pi)$|; + +$key = q/{_inline}zeta<45^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta<45^{\circ}$|; + +$key = q/{_inline}[,Az,El~]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,Az,El~]$|; + +$key = q/{_inline}6hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$6\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}^Tcdot{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$^{T}\cdot$|; + +$key = q/{_inline}3hspace-0.05em^'hspace-0.1em'hspace-0.4em.2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$|; + +$key = q/{_inline}[x_p,y_p,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[x_{p},y_{p}\,]$|; + +$key = q/{_inline}[x_2,y_2,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[x_{2},y_{2}\,]$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.00158{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00158$|; + +$key = q/{_inline}x_2=+x'''cosrmORIENT+y'''sinrmORIENT{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$x_{2} = + x''' \cos {\rm ORIENT} + + y''' \sin {\rm ORIENT}$|; + +$key = q/{_inline}61^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$61^\circ$|; + +$key = q/{_inline}y_2=-x'''sinrmORIENT+y'''cosrmORIENT{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$y_{2} = - x''' \sin {\rm ORIENT} + + y''' \cos {\rm ORIENT}$|; + +$key = q/{_inline}82^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$82^\circ$|; + +$key = q/{_inline}0!-!2pi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\!-\!2\pi$|; + +$key = q/{_inline}71hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$71\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.05{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.05$|; + +$key = q/{_inline}sqrt1-left|mboxbfvright|^2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\sqrt{1-\left\vert\mbox{\bf v}\right\vert^2}$|; + +$key = q/{_inline}murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\mu{\rm m}$|; + +$key = q/{_inline}alpha,deltarightarrowlambda,beta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\alpha,\delta\rightarrow\lambda,\beta$|; + +$key = q/{displaymath}h=theta-alpha{displaymath}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|\begin{displaymath} +h = \theta - \alpha \end{displaymath}|; + +$key = q/{_inline}2^circhspace-0.37em.hspace0.02em4{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$2^{\circ} + \hspace{-0.37em}.\hspace{0.02em}4$|; + +$key = q/{_inline}1hspace-0.05em^'hspace-0.1em'hspace-0.4em.85{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.85$|; + +$key = q/{_inline}+pi2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$+\pi/2$|; + +$key = q/{_inline}sim!76^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\sim\!76^\circ$|; + +$key = q/{_inline}[,x,y,z,dotx,doty,dotz,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$|; + +$key = q/{_inline}6.5^circKkm^-1{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$6.5^\circ K km^{-1}$|; + +$key = q/{_inline}270^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$270^\circ$|; + +$key = q/{_inline}7hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$7\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}tandeltaEapproxdeltaE{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\tan \delta E\approx\delta E}$|; + +$key = q/{_inline}cdots{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\cdots$|; + +$key = q/{_inline}1hspace-0.05em^'hspace-0.1em'hspace-0.4em.5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.8{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$|; + +$key = q/{_inline}(1-deltaE^22){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$(1-\delta E^2 /2)$|; + +$key = q/{_inline}mu{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\mu$|; + +$key = q/{_inline}15^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$15^\circ$|; + +$key = q/{_inline}[Deltax,Deltay,Deltaz,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\Delta x, \Delta y, \Delta z\,]$|; + +$key = q/{_inline}70^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$70^\circ$|; + +$key = q/{_inline}DeltarmT=rmET-rmUT{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta {\rm T} = {\rm ET} - {\rm UT}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.02{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.02$|; + +$key = q/{_inline}91^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$91^\circ$|; + +$key = q/{_inline}Delta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta$|; + +$key = q/{_inline}l^I!I=53^circ,b^I!I=+25^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$l^{I\!I}=53^{\circ},b^{I\!I}=+25^{\circ}$|; + +$key = q/{_inline}y''=y'rmYS{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$y'' = y' {\rm YS}$|; + +$key = q/{_inline}bfV2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\bf V2}$|; + +$key = q/{_inline}[,0,2pi,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,0,2\pi\,]$|; + +$key = q/{_inline}mgeqn{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$m \geq n$|; + +$key = q/{_inline}360^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$360^{\circ}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.5{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$|; + +$key = q/{_inline}alpha,delta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\alpha,\delta$|; + +$key = q/{_inline}8hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$8\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}deltaEsinE{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\delta E \sin E$|; + +$key = q/{_inline}alpha={_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\alpha=$|; + +$key = q/{_inline}4hspace-0.05em^'hspace-0.1em'hspace-0.4em.9{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$4\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.9$|; + +$key = q/{_inline}45^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$45^\circ$|; + +$key = q/{_inline}3200hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$3200\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}equiv{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\equiv$|; + +$key = q/{_inline}delta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\delta$|; + +$key = q/{_inline}-26hspace-0.05em^'hspace-0.1em'hspace-0.4em.00{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-26\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00$|; + +$key = q/{_inline}psi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\psi$|; + +$key = q/{_inline}-10^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-10^\circ$|; + +$key = q/{_inline}81hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$81\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}l^I!I=137.37{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$l^{I\!I}=137.37$|; + +$key = q/{_inline}87^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$87^\circ$|; + +$key = q/{_inline}(mu-1){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$(\mu-1)$|; + +$key = q/{_inline}23^h,59^m,60^s.0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$23^{h}\,59^{m}\,60^{s}.0$|; + +$key = q/{_inline}[,x,y,z,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,x,y,z\,]$|; + +$key = q/{_inline}(1-bfDcdotbfV1){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$(1-{\bf D}\cdot{\bf V1})$|; + +$key = q/{_inline}24^h,59^m,59^s.999{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$24^{h}\,59^{m}\,59^{s}.999$|; + +$key = q/{_inline}7^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$7^\circ$|; + +$key = q/{_inline}220hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$220\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.2{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$|; + +$key = q/{_inline}dotalphacosdelta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\dot{\alpha}\cos\delta$|; + +$key = q/{_inline}9hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$9\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}h,delta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$h,\delta$|; + +$key = q/{_inline}beta~(=H_0r_0){_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\beta~(=H_0/r_0)$|; + +$key = q/{_inline}0^rmshspace-0.3em.029032{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0^{\rm s}\hspace{-0.3em}.029032$|; + +$key = q/{_inline}32^rmshspace-0.3em.184{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$32^{\rm s}\hspace{-0.3em}.184$|; + +$key = q/{_inline}10hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$10\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}alpha{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\alpha$|; + +$key = q/{_inline}nu=p_wp_s{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\nu=p_w/p_s$|; + +$key = q/{_inline}0-2pi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0-2\pi$|; + +$key = q/{_inline}[,dotx,doty,dotz,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,\dot{x},\dot{y},\dot{z}\,]$|; + +$key = q/{_inline}75^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$75^\circ$|; + +$key = q/{_inline}100,murmm{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$100\,\mu{\rm m}$|; + +$key = q/{_inline}x''=x'rmXS{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$x'' = x' {\rm XS}$|; + +$key = q/{_inline}[,x,y,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,x,y\,]$|; + +$key = q/{_inline}Deltapsi,cos,epsilon{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta\psi\,cos\,\epsilon$|; + +$key = q/{_inline}bfrmM{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\bf \rm M}$|; + +$key = q/{_inline}zeta<60^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta<60^{\circ}$|; + +$key = q/{_inline}Deltapsicosepsilon{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Delta\psi\cos\epsilon$|; + +$key = q/{_inline}zeta=83^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\zeta=83^\circ$|; + +$key = q/{_inline}mtimesn{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$m \times n$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.062{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.062$|; + +$key = q/{_inline}12pi=0.1591549430918953358{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1/{2 \pi} = 0.1591549430918953358$|; + +$key = q/{_inline}42^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$42^{\circ}$|; + +$key = q/{_inline}1000hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$1000\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}11hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$11\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +$key = q/{_inline}29^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$29^\circ$|; + +$key = q/{_inline}84^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$84^\circ$|; + +$key = q/{_inline}[,l^I!I,b^I!I,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,l^{I\!I},b^{I\!I}\,]$|; + +$key = q/{_inline}rmbfv_0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\rm \bf v}_0$|; + +$key = q/{_inline}mu_alpha=-{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\mu_\alpha=-$|; + +$key = q/{_inline}w_iigeq0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$w_{ii} \geq 0$|; + +$key = q/{_inline}sim76^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\sim 76^\circ$|; + +$key = q/{_inline}bfM{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\bf M}$|; + +$key = q/{_inline}pmpi{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\pm \pi$|; + +$key = q/{_inline}23^rmh,59^rmm,59^rms{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$23^{\rm h}\,59^{\rm m}\,59^{\rm s}$|; + +$key = q/{_inline}30^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$30^\circ$|; + +$key = q/{_inline}rmbfr_0.rmbfv_0{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|${\rm \bf r}_0.{\rm \bf v}_0$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.00066{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00066$|; + +$key = q/{_inline}-0^rmshspace-0.3em.0312{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$-0^{\rm s}\hspace{-0.3em}.0312$|; + +$key = q/{_inline}delta={_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\delta=$|; + +$key = q/{_inline}Omega{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$\Omega$|; + +$key = q/{_inline}93^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$93^\circ$|; + +$key = q/{_inline}+20^circ{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$+20^\circ$|; + +$key = q/{_inline}0hspace-0.05em^'hspace-0.1em'hspace-0.4em.50{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.50$|; + +$key = q/{_inline}~cosdelta{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$~\cos \delta $|; + +$key = q/{_inline}[,h,delta,]{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$[\,h,\delta\,]$|; + +$key = q/{_inline}92hspace-0.05em^'hspace-0.1em'{_inline}MSF=1.5;AAT;/; +$cached_env_img{$key} = q|$92\hspace{-0.05em}^{'\hspace{-0.1em}'}$|; + +1; + diff --git a/src/slalib/sun67.htx/images.tex b/src/slalib/sun67.htx/images.tex new file mode 100644 index 0000000..8881d62 --- /dev/null +++ b/src/slalib/sun67.htx/images.tex @@ -0,0 +1,2852 @@ +\batchmode +\documentclass[11pt,twoside]{article} +\makeatletter +\input{/home/user1/dec/ptw/hypertext/sun67_htx/html.sty} +\input{/home/user1/dec/ptw/hypertext/sun67_htx/star2html.sty} +\setcounter{tocdepth}{2} +\pagestyle{myheadings} + +\markright{SUN/67.45} + +\setlength {\textwidth}{160mm} + +\setlength {\textheight}{230mm} + +\setlength {\topmargin}{-5mm} + + +\setlength {\textwidth}{160mm} + + +\setlength {\textheight}{230mm} + + +\setlength {\topmargin}{-2mm} + + +\setlength {\oddsidemargin}{0mm} + + +\setlength {\evensidemargin}{0mm} + + +\setlength {\parindent}{0mm} + + +\setlength {\parskip}{\medskipamount} + + +\setlength {\unitlength}{1mm} + + +\latex{\renewcommand {\_}{{\tt\symbol{95}}}} + +\newlength {\oldspacing} + + +\newcommand{\stardoccategory} {Starlink User Note} + +\newcommand{\stardocinitials} {SUN} + +\newcommand{\stardocsource} {sun67.45} + +\newcommand{\stardocnumber} {67.45} + +\newcommand{\stardocauthors} {P.\,T.\,Wallace} + +\newcommand{\stardocdate} {12 October 1999} + +\newcommand{\stardoctitle} {SLALIB --- Positional Astronomy Library} + +\newcommand{\stardocversion} {2.4-0} + +\newcommand{\stardocmanual} {Programmer's Manual} + +\newcommand{\stardocname}{\stardocinitials /\stardocnumber} + +\newcommand{\htmladdnormallinkfoot}[2]{#1\footnote{#2}} + +\newcommand{\htmladdnormallink}[2]{#1} + +\newcommand{\htmladdimg}[1]{} + +\newenvironment{latexonly}{}{} + +\newcommand{\hyperref}[4]{#2\ref{#4}#3} + +\newcommand{\htmlref}[2]{#1} + +\newcommand{\htmlimage}[1]{} + +\newcommand{\htmladdtonavigation}[1]{} + +\newcommand{\xref}[3]{#1} + +\newcommand{\xlabel}[1]{} + +\newcommand{\latextohtml}{{\bf LaTeX}{2}{\tt{HTML}}} + +\newcommand{\latex}[1]{#1} + +\newcommand{\setunderscore}{\renewcommand {\_}{{\tt\symbol{95}}}} + +\newcommand{\latexonlytoc}[0]{\tableofcontents} + +\newcommand{\nroutines} {183} + +\newcommand{\radec} {$[\,\alpha,\delta\,]$} + +\newcommand{\hadec} {$[\,h,\delta\,]$} + +\newcommand{\xieta} {$[\,\xi,\eta\,]$} + +\newcommand{\azel} {$[\,Az,El~]$} + +\newcommand{\ecl} {$[\,\lambda,\beta~]$} + +\newcommand{\gal} {$[\,l^{I\!I},b^{I\!I}\,]$} + +\newcommand{\xy} {$[\,x,y\,]$} + +\newcommand{\xyz} {$[\,x,y,z\,]$} + +\newcommand{\xyzd} {$[\,\dot{x},\dot{y},\dot{z}\,]$} + +\newcommand{\xyzxyzd} {$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$} + +\newcommand{\degree}[2] {$#1^{\circ} + \hspace{-0.37em}.\hspace{0.02em}#2$} + +\newcommand{\arcsec}[2] {\arcseci{#1}$\hspace{-0.4em}.#2$} + +\newcommand{\arcseci}[1] {$#1\hspace{-0.05em}$\raisebox{-0.5ex} + {$^{'\hspace{-0.1em}'}$}} + +\renewcommand{\arcseci}[1] {$#1\hspace{-0.05em}^{'\hspace{-0.1em}'}$} + +\newcommand{\dms}[4] {$#1^{\circ}\,#2\raisebox{-0.5ex} + {$^{'}$}\,$\arcsec{#3}{#4}} + +\renewcommand{\dms}[4]{$#1^{\circ}\,#2^{'}\,#3^{''}.#4$} + +\newcommand{\tseci}[1] {$#1$\mbox{$^{\rm s}$}} + +\newcommand{\tsec}[2] {\tseci{#1}$\hspace{-0.3em}.#2$} + +\renewcommand{\tsec}[2] {$#1^{\rm s}\hspace{-0.3em}.#2$} + +\newcommand{\hms}[4] {$#1^{\rm h}\,#2^{\rm m}\,$\tsec{#3}{#4}} + +\renewcommand{\hms}[4] {$#1^{h}\,#2^{m}\,#3^{s}.#4$} + +\newcommand{\callhead}[1]{\goodbreak\vspace{\bigskipamount}{\large\bf{#1}}} + +\newenvironment{callset}{\begin{list}{}{\setlength{\leftmargin}{2cm} + \setlength{\parsep}{\smallskipamount}}}{\end{list}} + +\newcommand{\subp}[1]{\item\hspace{-1cm}#1\\} + +\newcommand{\subq}[2]{\item\hspace{-1cm}#1\\\hspace*{-1cm}#2\\} + +\newcommand{\name}[1]{\mbox{#1}} + +\newcommand{\fortvar}[1]{\mbox{\em #1}} + +\newcommand{\routine}[3] +{\hbadness=10000 + \vbox + { + \rule{\textwidth}{0.3mm}\\ {\Large {\bf #1} \hfill #2 \hfill {\bf #1}}\\ \setlength{\oldspacing}{\topsep} + \setlength{\topsep}{0.3ex} + \begin{description} + #3 + \end{description} + \setlength{\topsep}{\oldspacing} + } +} + +\renewcommand{\routine}[3] + { + \subsection{#1\xlabel{#1} - #2\label{#1}} + \begin{description} + #3 + \end{description} + } + +\newcommand{\action}[1] +{\item[ACTION]: #1} + +\newcommand{\call}[1] +{\item[CALL]: \hspace{0.4em}{\tt #1}} + +\renewcommand{\call}[1] + { + \item[CALL:] {\tt #1} + } + +\newcommand{\args}[2] +{ + \goodbreak + \setlength{\oldspacing}{\topsep} + \setlength{\topsep}{0.3ex} + \begin{description} + \item[#1]:\\[1.5ex] + \begin{tabular}{p{7em}p{6em}p{22em}} + #2 + \end{tabular} + \end{description} + \setlength{\topsep}{\oldspacing} +} + +\renewcommand{\args}[2] + { + \begin{description} + \item[#1:]\\ \begin{tabular}{p{7em}p{6em}l} + #2 + \end{tabular} + \end{description} + } + +\newcommand{\spec}[3] +{ + {\em {#1}} & {\bf \mbox{#2}} & {#3} +} + +\newcommand{\specel}[2] +{ + \multicolumn{1}{c}{#1} & {} & {#2} +} + +\newcommand{\anote}[1] +{ + \goodbreak + \setlength{\oldspacing}{\topsep} + \setlength{\topsep}{0.3ex} + \begin{description} + \item[NOTE]: + #1 + \end{description} + \setlength{\topsep}{\oldspacing} +} + +\renewcommand{\anote}[1] + { + \begin{description} + \item[NOTE:] + #1 + \end{description} + } + +\newcommand{\notes}[1] +{ + \goodbreak + \setlength{\oldspacing}{\topsep} + \setlength{\topsep}{0.3ex} + \begin{description} + \item[NOTES]: + #1 + \end{description} + \setlength{\topsep}{\oldspacing} +} + +\renewcommand{\notes}[1] + { + \begin{description} + \item[NOTES:] + #1 + \end{description} + } + +\newcommand{\aref}[1] +{ + \goodbreak + \setlength{\oldspacing}{\topsep} + \setlength{\topsep}{0.3ex} + \begin{description} + \item[REFERENCE]: + #1 + \end{description} + \setlength{\topsep}{\oldspacing} +} + +\newcommand{\refs}[1] +{ + \goodbreak + \setlength{\oldspacing}{\topsep} + \setlength{\topsep}{0.3ex} + \begin{description} + \item[REFERENCES]: + #1 + \end{description} + \setlength{\topsep}{\oldspacing} +} + +\newcommand{\exampleitem}{\item [EXAMPLE]:} + +\renewcommand{\exampleitem}{\item [EXAMPLE:]} + +\renewcommand{\thepage}{\roman{page}} + +\renewcommand{\latexonlytoc}[0]{} + +\renewcommand{\thepage}{\arabic{page}} +\input{/home/user1/dec/ptw/hypertext/sun67_htx/star2html.sty} + + +\makeatother +\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi +\newenvironment{tex2html_wrap}{}{} +\newbox\sizebox +\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt} +\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt} +\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt} +\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt} +\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt} +\setlength{\textwidth}{451pt} +\newwrite\lthtmlwrite +\makeatletter +\let\realnormalsize=\normalsize +\topskip=0pt +\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float +\def\@float{\let\@savefreelist\@freelist\real@float} +\def\end@float{\realend@float\global\let\@freelist\@savefreelist} +\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float +\let\@largefloatcheck=\relax +\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt} +\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize\parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}\normalsize} +\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}% +\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup}% +\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup% + \let\ifinner=\iffalse }% +\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}% + \expandafter\box\next\egroup}% +\newcommand\lthtmlmathtype[1]{\def\lthtmlmathenv{#1}}% +\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize % +:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}% +\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist + \lthtmlmathtype{#1}\lthtmlvboxmathA}% +\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox + \global\let\@freelist\@savefreelist}% +\newcommand\lthtmldisplayA[1]{\lthtmlmathtype{#1}\lthtmlvboxmathA}% +\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}% + \lthtmldisplayA{#1}\let\@eqnnum\relax}% +\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}% +\newcommand\lthtmlinlinemathA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA \vrule height1.5ex width0pt }% +\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % + \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath} +\def\lthtmlsetmath{\hbox{\vrule width.5pt\vtop{\vbox{% + \kern.5pt\kern0.75 pt\hbox{\hglue.5pt\copy\sizebox\hglue0.75 pt}\kern.5pt% + \ifdim\dp\sizebox>0pt\kern0.75 pt\fi}% + \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} +\def\centerinlinemath{\dimen1=\ht\sizebox + \ifdim\dimen1<\dp\sizebox \ht\sizebox=\dp\sizebox + \else \dp\sizebox=\ht\sizebox \fi} + +\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize\expandafter\vfill + \else\expandafter\vss\fi}% +\makeatletter + + +\begin{document} +\pagestyle{empty}\thispagestyle{empty}% +\lthtmltypeout{latex2htmlLength hsize=\the\hsize}% +\lthtmltypeout{latex2htmlLength vsize=\the\vsize}% +\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}% +\lthtmltypeout{latex2htmlLength voffset=\the\voffset}% +\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}% +\lthtmltypeout{latex2htmlLength topskip=\the\topskip}% +\lthtmltypeout{latex2htmlLength headheight=\the\headheight}% +\lthtmltypeout{latex2htmlLength headsep=\the\headsep}% +\lthtmltypeout{latex2htmlLength parskip=\the\parskip}% +\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}% +\makeatletter +\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}% +\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi% +\makeatother +\setcounter{tocdepth}{2} +\stepcounter{section} +\setcounter{page}{1} +\stepcounter{section} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline417}% +$0^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline419}% +$-1^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline528}% +$[\,\alpha,\delta\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} + +\setlength {\oldspacing}{\topsep} +% + + +\setlength {\topsep}{0.3ex} +% + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline786}% +$12^{\circ}\,34^{'}\,56^{''}.7$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + + +\setlength {\topsep}{\oldspacing} +% + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline788}% +${\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline802}% +$1/{2 \pi} = 0.1591549430918953358$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline806}% +$15/{2\pi} = 2.3873241463784300365$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline893}% +$\zeta = 87^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} + +\setlength {\parskip}{\medskipamount} +% + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1090}% +$\times 360/2\pi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1092}% +$\rightarrow$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1094}% +$\times (2\pi/86400) \times (360/2\pi)$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1098}% +$\times (2\pi/86400)^2 \times (360/2\pi)$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1102}% +$[\,0,2\pi\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1104}% +$+\pi/2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1106}% +$\pm\pi/2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1373}% +$\times 2 / $% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1375}% +$\sqrt{1-\left|\mbox{\bf v}\right|^2}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1377}% +$3\times3$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1701}% +$\Delta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1705}% +$[\,x,y\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1707}% +$\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1709}% +$90^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1711}% +$\delta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1713}% +$\alpha$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1715}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1717}% +$\zeta<70^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1721}% +$3^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1725}% +$[\,Az,El~]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1729}% +$[\,h,\delta\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1745}% +$\pm$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1747}% +$0^{\rm s}\hspace{-0.3em}.9$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1749}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2524}% +$76^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2704}% +$0.7\,\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2706}% +$0.4\,\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2708}% +$29^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2710}% +$290^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2712}% +$0.0065^\circ m^{-1}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2716}% +$15^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2718}% +$1.0\,\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2720}% +$0.3\,\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2722}% +$20\,\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2724}% +$11\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2726}% +$100\,\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2728}% +$(\mu-1)$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2867}% +$[\lambda,\phi]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline2869}% +$\pm \pi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline3016}% +$\cdots$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline3160}% +$0^{\rm h}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline3380}% +$[\,x,y,z\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline3493}% +$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline4117}% +$2\pi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline4123}% +$360^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} + +\setlength {\oldspacing}{\topsep} +% + + +\setlength {\topsep}{0.3ex} +% + + +\setlength {\topsep}{\oldspacing} +% + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5205}% +$23^{\rm h}\,59^{\rm m}\,59^{\rm s}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5954}% +$[x_{1},y_{1}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5956}% +$[x_{2},y_{2}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5962}% +$x' = x_{1} + {\rm XZ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5964}% +$y' = y_{1} + {\rm YZ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5966}% +$x'' = x' {\rm XS}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5968}% +$y'' = y' {\rm YS}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5970}% +$x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5972}% +$y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5974}% +$x_{2} = + x''' \cos {\rm ORIENT} + + y''' \sin {\rm ORIENT}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline5976}% +$y_{2} = - x''' \sin {\rm ORIENT} + + y''' \cos {\rm ORIENT}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6230}% +$h,\delta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6232}% +$0\!-\!2\pi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6347}% +$\equiv123$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6475}% +$\pm n.n x \pm n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6491}% +$x\!\pm\!n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6713}% +$^{T}\cdot$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline6717}% +${\bf \rm M}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7186}% +$\cdot$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7188}% +$n \times n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7358}% +$10\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7360}% +$3\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7362}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7364}% +$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.7$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7366}% +$2\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7368}% +$18\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7370}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.50$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7374}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.24$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7376}% +$30\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7378}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline7465}% +$\times$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8210}% +$[\,\xi,\eta\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8382}% +$20^{\rm s}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8384}% +$30^{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8386}% +$-26\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8848}% +$\alpha=0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8993}% +$\xi,\eta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline8995}% +$\alpha,\delta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline9003}% +$\xi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline9812}% +$\times10^{-5}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline9814}% +$\times10^{-10}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline9967}% +$\alpha,\delta\rightarrow\lambda,\beta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10116}% +$0^{\rm s}\hspace{-0.3em}.03$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10118}% +$0^{\rm s}\hspace{-0.3em}.01$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10191}% +$[\,l^{I\!I},b^{I\!I}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10601}% +$\Omega$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10603}% +$\varpi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10605}% +$\omega$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10625}% +${\rm \bf r}_0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10627}% +${\rm \bf v}_0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10629}% +${\rm \bf r}_0.{\rm \bf v}_0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10633}% +$\psi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10663}% +$( 0 \leq e < 1 )$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline10697}% +$( 0 \leq e \leq 10 )$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11178}% +$\Delta\psi\,cos\,\epsilon$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11337}% +$[\Delta x, \Delta y, \Delta z\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11339}% +$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.49552$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11594}% +$[\,\dot{x},\dot{y},\dot{z}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11608}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.001$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11828}% +$[x_{m},y_{m}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline11830}% +$[x_{e},y_{e}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline12099}% +$\dot{\alpha}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline12101}% +$\dot{\alpha}\cos\delta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline12103}% +$10^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline12105}% +$\Delta\alpha$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline13294}% +$l^{I\!I}=137.37$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline13534}% +$1.0027379\cdots$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline13611}% +$[\,0,\,1\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline14280}% +${\bf M}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline14410}% +$\pm n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline15250}% +$920\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline15252}% +$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.85$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline15578}% +$14\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline15582}% +$9\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline16974}% +$\rho = r (1 + c r^{2})$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline16980}% +$\rho$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} + +\setlength {\parskip}{\medskipamount} +% + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19044}% +$4\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19046}% +$5\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19048}% +$6\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19050}% +$17\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19052}% +$71\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19054}% +$81\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19056}% +$86\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19060}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19064}% +${\rm MJD} = ({\rm JD} - 2400000.5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline19834}% +$270^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline20108}% +$1\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline20114}% +$100\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline20116}% +$1000\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline20952}% +$0-2\pi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline21527}% +$[x_{p},y_{p}\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline21604}% +$0 \leq x < 1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline21862}% +$\mu$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline21866}% +$\pm3$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22333}% +$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22335}% +$\zeta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22337}% +$\Delta \zeta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22343}% +$\tan \zeta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22345}% +$\tan^{3} \zeta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22353}% +$\tan^{-1} 1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22355}% +$45^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22357}% +$\tan^{-1} 4$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22359}% +$\sim 76^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22363}% +$\zeta<80^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22365}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22367}% +$\zeta<60^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22371}% +$\zeta<45^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22628}% +$\sim\!76^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22638}% +$25^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22640}% +$50^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22642}% +$75^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22656}% +$-10^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22658}% +$+20^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22660}% +$280^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22666}% +$2\mu{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22678}% +$6.5^\circ K km^{-1}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22690}% +$7^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22698}% +$\tan^5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22702}% +$\beta~(=H_0/r_0)$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22706}% +$\beta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22933}% +$70^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22935}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.05$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22947}% +$93^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22949}% +$=93^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22955}% +$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22957}% +$80^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22959}% +$\nu=p_w/p_s$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline22961}% +$\nu=\rho_w/\rho_s$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23162}% +$30^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23164}% +$\zeta=70^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23168}% +$\zeta_{obs}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23172}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23174}% +$81^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23176}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23178}% +$82^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23180}% +$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23182}% +$83^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23186}% +$84^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23188}% +$7\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23190}% +$85^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23194}% +$86^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23196}% +$45\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23198}% +$87^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23200}% +$150\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23202}% +$88^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23204}% +$340\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23206}% +$89^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23208}% +$620\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23212}% +$1100\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23214}% +$91^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23216}% +$1900\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23220}% +$92^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23222}% +$3200\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23228}% +$\zeta=84^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23469}% +$\zeta=80^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23471}% +$\zeta=83^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath23457}% +\begin{displaymath}\Delta \zeta = F \left( + \frac{0^\circ\hspace{-0.37em}.\hspace{0.02em}55445 + - 0^\circ\hspace{-0.37em}.\hspace{0.02em}01133 E + + 0^\circ\hspace{-0.37em}.\hspace{0.02em}00202 E^2} + {1 + 0.28385 E +0.02390 E^2} \right) \end{displaymath}% +\lthtmldisplayZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23475}% +$E=90^\circ-\zeta_{true}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23495}% +$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23499}% +$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23503}% +$4\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.9$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23507}% +$5\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23511}% +$6\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23515}% +$7\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23523}% +$21\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23527}% +$43\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23531}% +$92\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23537}% +$220\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23720}% +$l^{I\!I}=90^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23722}% +$b^{I\!I}=0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23896}% +$l^{I\!I}=53^{\circ},b^{I\!I}=+25^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline23995}% +$\alpha=18^{\rm h},\delta=+30^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline24798}% +$\times n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline24800}% +$m \geq n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline24802}% +$m \times n$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline24806}% +$w_{ii} \geq 0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline25275}% +$\cdot~[diag(1/$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline25277}% +$_{j})] + \cdot ($% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} + +\setlength {\parskip}{\medskipamount} +% + +\stepcounter{subsection} + +\setlength {\parskip}{\medskipamount} +% + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline26731}% +$2^{\circ} + \hspace{-0.37em}.\hspace{0.02em}4$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline26733}% +$42^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27323}% +$0\!-\!\pi$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{section} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27383}% +$61^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27391}% +$+1^{\circ}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27397}% +$24^{h}\,59^{m}\,59^{s}.999$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27464}% +$[\,\theta,\phi~]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27478}% +$[\,\Delta x,\Delta y, \Delta z\,]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27484}% +${\bf D}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27486}% +${\bf V1}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27488}% +${\bf V2}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27490}% +$<{\bf V1}+{\bf D}>$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27492}% +$(1-{\bf D}\cdot{\bf V1})$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27494}% +$\delta E$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27498}% +${\tan \delta E\approx\delta E}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27504}% +$\delta E \cos E$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27506}% +$\delta E \sin E$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27512}% +$\cos \delta E$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27514}% +$(1-\delta E^2 /2)$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27518}% +$\equiv$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27524}% +$[\theta,\phi,\dot{\theta},\dot{\phi}]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27750}% +$\lambda,\beta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27752}% +$l^{I\!I},b^{I\!I}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlfigureA{figure27550}% +\begin{figure}\begin{center} +\begin{tabular}{|cccccc|} \hline +& & & & & \\\hspace{5em} & \hspace{5em} & \hspace{5em} & + \hspace{5em} & \hspace{5em} & \hspace{5em} \\\multicolumn{2}{|c}{\hspace{0em} +\fbox {\parbox{8.5em}{\center \vspace{-2ex} + mean $[\,\alpha,\delta\,]$, FK4, \\ any equinox + \vspace{0.5ex}}} +} & + \multicolumn{2}{c}{\hspace{0em} +\fbox {\parbox{8.5em}{\center \vspace{-2ex} + mean $[\,\alpha,\delta\,]$, FK4, + no $\mu$, any equinox + \vspace{0.5ex}}} +} & +\multicolumn{2}{c|}{\hspace{0em} +\fbox {\parbox{8.5em}{\center \vspace{-2ex} + mean $[\,\alpha,\delta\,]$, FK5, \\ any equinox + \vspace{0.5ex}}} +} \\& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\\multicolumn{2}{|c}{space motion} & \multicolumn{1}{c|}{} & & + \multicolumn{2}{c|}{space motion} \\\multicolumn{2}{|c}{-- E-terms} & + \multicolumn{2}{c}{-- E-terms} & \multicolumn{1}{c|}{} & \\\multicolumn{2}{|c}{precess to B1950} & \multicolumn{2}{c}{precess to B1950} & + \multicolumn{2}{c|}{precess to J2000} \\\multicolumn{2}{|c}{+ E-terms} & + \multicolumn{2}{c}{+ E-terms} & \multicolumn{1}{c|}{} & \\\multicolumn{2}{|c}{FK4 to FK5, no $\mu$} & + \multicolumn{2}{c}{FK4 to FK5, no $\mu$} & \multicolumn{1}{c|}{} & \\\multicolumn{2}{|c}{parallax} & \multicolumn{1}{c|}{} & & + \multicolumn{2}{c|}{parallax} \\& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\ \cline{2-5} +\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{ +\fbox {\parbox{18em}{\center \vspace{-2ex} + FK5, J2000, current epoch, geocentric + \vspace{0.5ex}}} +} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{light deflection} & \\& \multicolumn{4}{c}{annual aberration} & \\& \multicolumn{4}{c}{precession/nutation} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{ +\fbox {Apparent $[\,\alpha,\delta\,]$} +} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{Earth rotation} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{ +\fbox {Apparent $[\,h,\delta\,]$} +} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{diurnal aberration} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{ +\fbox {Topocentric $[\,h,\delta\,]$} +} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{$[\,h,\delta\,]$\ to $[\,Az,El~]$} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{ +\fbox {Topocentric $[\,Az,El~]$} +} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{refraction} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{ +\fbox {Observed $[\,Az,El~]$} +} & \\& & & & & \\& & & & & \\ \hline +\end{tabular} +\end{center} +\vspace{-0.5ex} +Star positions are published or catalogued using +one of the mean $[\,\alpha,\delta\,]$\ systems shown at +the top. The ``FK4'' systems +were used before about 1980 and are usually +equinox B1950. The ``FK5'' system, equinox J2000, is now preferred, +or rather its modern equivalent, the International Celestial Reference +Frame (in the optical, the Hipparcos catalogue). +The figure relates a star's mean $[\,\alpha,\delta\,]$\ to the actual +line-of-sight to the star. +Note that for the conventional choices of equinox, namely +B1950 or J2000, all of the precession and E-terms corrections +are superfluous. +\end{figure}% +\lthtmlfigureZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27878}% +$23^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27888}% +$\epsilon$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27890}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0001$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27892}% +$(3\times3)$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27894}% +$0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27923}% +$50\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27927}% +$12^{h}\,07^{m}\,58^{s}.09$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27929}% +$-19^{\circ}\,44^{'}\,37^{''}.1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline27959}% +$[\mu_\alpha,\mu_\delta]$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28022}% +$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28106}% +$\mu_\alpha=-$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28108}% +$0^{\rm s}\hspace{-0.3em}.015869$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28112}% +$0^{\rm s}\hspace{-0.3em}.029032$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28114}% +$~\sin \alpha + +$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28116}% +$0^{\rm s}\hspace{-0.3em}.000340$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28118}% +$~\cos \alpha ) \sin \delta + -$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28120}% +$0^{\rm s}\hspace{-0.3em}.000105$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28122}% +$~\cos \alpha + -$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28124}% +$0^{\rm s}\hspace{-0.3em}.000083$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28126}% +$~\sin \alpha ) \sec \delta $% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28128}% +$\mu_\delta\,=+$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28130}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.43549$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28134}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00510$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28136}% +$~\sin \alpha + + ($% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28138}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00158$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28140}% +$~\sin \alpha + -$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28142}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00125$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28146}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00066$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28148}% +$~\cos \delta $% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28214}% +$\alpha=$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28216}% +$16^{h}\,09^{m}\,55^{s}.13$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28218}% +$\delta=$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28220}% +$-75^{\circ}\,59^{'}\,27^{''}.2$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28222}% +$\mu_\alpha=$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28224}% +$-0^{\rm s}\hspace{-0.3em}.0312$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28228}% +$\mu_\delta=$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28230}% +$+0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.103$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28234}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.062$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28274}% +$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.74$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28276}% +$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.02$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28278}% +$20^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28282}% +$90^\circ-\delta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28386}% +$\theta$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath28366}% +\begin{displaymath}h = \theta - \alpha \end{displaymath}% +\lthtmldisplayZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28394}% +$=\Delta\psi\cos\epsilon$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28408}% +$0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath28367}% +\begin{displaymath}\zeta _{vac} \approx \zeta _{obs} + + A \tan \zeta _{obs} + + B \tan ^{3}\zeta _{obs} \end{displaymath}% +\lthtmldisplayZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28412}% +$\zeta _{vac}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28420}% +$60\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28422}% +$-0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.06$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath28368}% +\begin{displaymath}\zeta _{obs} \approx \zeta _{vac} + - \frac{A \tan \zeta _{vac} + B \tan ^{3}\zeta _{vac}} + {1 + ( A + 3 B \tan ^{2}\zeta _{vac} ) \sec ^{2}\zeta _{vac}}\end{displaymath}% +\lthtmldisplayZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28444}% +$100\mu m$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsubsection} +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28549}% +$23^{h}\,59^{m}\,60^{s}.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28551}% +$00^{h}\,00^{m}\,00^{s}.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28555}% +$\Delta\psi\cos\epsilon$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsubsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28561}% +$32^{\rm s}\hspace{-0.3em}.184$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28567}% +$0^{\rm s}\hspace{-0.3em}.0016$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28569}% +$0^{\rm s}\hspace{-0.3em}.0013$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28571}% +$\Delta {\rm T} = {\rm ET} - {\rm UT}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28573}% +$\Delta {\rm T}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28650}% +$2\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28656}% +$\pm100$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28664}% +$1^\circ$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28666}% +$8\hspace{-0.05em}^{'\hspace{-0.1em}'}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28668}% +$5^{\rm h}\,25^{\rm m}$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28728}% +$\varpi = \Omega + \omega$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28740}% +$L = \varpi + M$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28752}% +$M_\odot = 1$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28769}% +$\sim20$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28861}% +$C_1\!=\!+50.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28863}% +$C_2\!=\!-2.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28865}% +$C_3\!=\!-10.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28867}% +$C_4\!=\!+25.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28869}% +$\sigma=5.0$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline28871}% +$1000\times20$% +\lthtmlinlinemathZ +\hfill\lthtmlcheckvsize\clearpage} + +\stepcounter{section} + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\setlength {\leftmargin}{2cm} +% + + +\setlength {\parsep}{\smallskipamount} +% + + +\end{document} diff --git a/src/slalib/sun67.htx/img1.gif b/src/slalib/sun67.htx/img1.gif new file mode 100644 index 0000000..d7b5e28 Binary files /dev/null and b/src/slalib/sun67.htx/img1.gif differ diff --git a/src/slalib/sun67.htx/img10.gif b/src/slalib/sun67.htx/img10.gif new file mode 100644 index 0000000..b62f1a8 Binary files /dev/null and b/src/slalib/sun67.htx/img10.gif differ diff --git a/src/slalib/sun67.htx/img100.gif b/src/slalib/sun67.htx/img100.gif new file mode 100644 index 0000000..398505a Binary files /dev/null and b/src/slalib/sun67.htx/img100.gif differ diff --git a/src/slalib/sun67.htx/img101.gif b/src/slalib/sun67.htx/img101.gif new file mode 100644 index 0000000..f058067 Binary files /dev/null and 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+$key = q/xref_SLA_EQEQX/; +$ref_files{$key} = "$dir".q|node98.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DRANRM/; +$ref_files{$key} = "$dir".q|node69.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DBJIN/; +$ref_files{$key} = "$dir".q|node47.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_POLMO/; +$ref_files{$key} = "$dir".q|node150.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_RVLG/; +$ref_files{$key} = "$dir".q|node172.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_GMSTA/; +$ref_files{$key} = "$dir".q|node116.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DCMPF/; +$ref_files{$key} = "$dir".q|node50.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_PVOBS/; +$ref_files{$key} = "$dir".q|node158.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DMXV/; +$ref_files{$key} = "$dir".q|node64.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_FK524/; +$ref_files{$key} = "$dir".q|node106.html|; +$noresave{$key} = "$nosave"; + +1; + diff --git a/src/slalib/sun67.htx/invis_anchor.xbm b/src/slalib/sun67.htx/invis_anchor.xbm new file mode 100644 index 0000000..cc208a3 --- /dev/null +++ b/src/slalib/sun67.htx/invis_anchor.xbm @@ -0,0 +1,4 @@ +#define dot_anchor_width 1 +#define dot_anchor_height 1 +static char dot_anchor_bits[] = { + 0xfe}; diff --git a/src/slalib/sun67.htx/labels.pl b/src/slalib/sun67.htx/labels.pl new file mode 100644 index 0000000..ab31648 --- /dev/null +++ b/src/slalib/sun67.htx/labels.pl @@ -0,0 +1,1482 @@ +# LaTeX2HTML 97.1 (release) (July 13th, 1997) +# Associate labels original text with physical files. + + +$key = q/SLA_DR2TF/; +$external_labels{$key} = "$URL/" . q|node67.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_OBS/; +$external_labels{$key} = "$URL/" . q|node137.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DD2TF/; +$external_labels{$key} = "$URL/" . q|node52.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DIMXV/; +$external_labels{$key} = "$URL/" . q|node57.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_PRECL/; +$external_labels{$key} = "$URL/" . q|node154.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_EVP/; +$external_labels{$key} = "$URL/" . q|node102.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_FLOTIN/; +$external_labels{$key} = "$URL/" . q|node110.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DTP2S/; +$external_labels{$key} = "$URL/" . q|node76.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_RANGE/; +$external_labels{$key} = "$URL/" . q|node161.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_NUTC/; +$external_labels{$key} = "$URL/" . q|node134.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_TPV2C/; +$external_labels{$key} = "$URL/" . q|node186.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DTP2V/; +$external_labels{$key} = "$URL/" . q|node77.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_VDV/; +$external_labels{$key} = "$URL/" . q|node191.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_FK52H/; +$external_labels{$key} = "$URL/" . q|node107.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DVN/; +$external_labels{$key} = "$URL/" . q|node83.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_PREC/; +$external_labels{$key} = "$URL/" . q|node152.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_EQECL/; +$external_labels{$key} = "$URL/" . q|node97.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_H2E/; +$external_labels{$key} = "$URL/" . q|node118.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_AOP/; +$external_labels{$key} = "$URL/" . q|node20.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DS2C6/; +$external_labels{$key} = "$URL/" . q|node70.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DRANRM/; +$external_labels{$key} = "$URL/" . q|node69.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_PAV/; +$external_labels{$key} = "$URL/" . q|node139.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_FITXY/; +$external_labels{$key} = "$URL/" . q|node103.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_CS2C/; +$external_labels{$key} = "$URL/" . q|node38.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_CC2S/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DT/; +$external_labels{$key} = "$URL/" . q|node73.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_PDA2H/; +$external_labels{$key} = "$URL/" . q|node141.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_RVLSRD/; +$external_labels{$key} = "$URL/" . q|node173.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_EG50/; +$external_labels{$key} = "$URL/" . q|node90.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DMOON/; +$external_labels{$key} = "$URL/" . q|node62.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DJCAL/; +$external_labels{$key} = "$URL/" . q|node58.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_AMP/; +$external_labels{$key} = "$URL/" . q|node18.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_CD2TF/; +$external_labels{$key} = "$URL/" . q|node32.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_EARTH/; +$external_labels{$key} = "$URL/" . q|node86.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_OAP/; +$external_labels{$key} = "$URL/" . q|node135.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_RANDOM/; +$external_labels{$key} = "$URL/" . q|node160.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_WAIT/; +$external_labels{$key} = "$URL/" . q|node194.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_AV2M/; +$external_labels{$key} = "$URL/" . q|node25.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_NUT/; +$external_labels{$key} = "$URL/" . q|node133.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_SUBET/; +$external_labels{$key} = "$URL/" . q|node178.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_RVLSRK/; +$external_labels{$key} = "$URL/" . q|node174.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_BEAR/; +$external_labels{$key} = "$URL/" . q|node26.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_PDQ2H/; +$external_labels{$key} = "$URL/" . q|node142.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_CLYD/; +$external_labels{$key} = "$URL/" . q|node34.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_V2TP/; +$external_labels{$key} = "$URL/" . q|node190.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_INTIN/; +$external_labels{$key} = "$URL/" . q|node122.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_COMBN/; +$external_labels{$key} = "$URL/" . q|node35.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_CTF2D/; +$external_labels{$key} = "$URL/" . q|node40.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_FK45Z/; +$external_labels{$key} = "$URL/" . q|node105.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DVXV/; +$external_labels{$key} = "$URL/" . q|node84.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_S2TP/; +$external_labels{$key} = "$URL/" . q|node175.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_CALYD/; +$external_labels{$key} = "$URL/" . q|node29.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DCS2C/; +$external_labels{$key} = "$URL/" . q|node51.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DCC2S/; +$external_labels{$key} = "$URL/" . q|node49.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DAF2R/; +$external_labels{$key} = "$URL/" . q|node42.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_REFRO/; +$external_labels{$key} = "$URL/" . q|node167.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_MXM/; +$external_labels{$key} = "$URL/" . q|node131.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_CTF2R/; +$external_labels{$key} = "$URL/" . q|node41.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DC62S/; +$external_labels{$key} = "$URL/" . q|node48.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_PCD/; +$external_labels{$key} = "$URL/" . q|node140.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_OBS/; +$external_labels{$key} = "$URL/" . q|node137.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DT/; +$external_labels{$key} = "$URL/" . q|node73.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DAV2M/; +$external_labels{$key} = "$URL/" . q|node45.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_MXV/; +$external_labels{$key} = "$URL/" . q|node132.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_OAPQK/; +$external_labels{$key} = "$URL/" . q|node136.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_EL2UE/; +$external_labels{$key} = "$URL/" . q|node91.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_EULER/; +$external_labels{$key} = "$URL/" . q|node101.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_RVLSRD/; +$external_labels{$key} = "$URL/" . q|node173.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DBEAR/; +$external_labels{$key} = "$URL/" . q|node46.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_EQGAL/; +$external_labels{$key} = "$URL/" . q|node99.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_EVP/; +$external_labels{$key} = "$URL/" . q|node102.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_RANDOM/; +$external_labels{$key} = "$URL/" . q|node160.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_CR2AF/; +$external_labels{$key} = "$URL/" . q|node36.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_REFCO/; +$external_labels{$key} = "$URL/" . q|node165.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_RVLSRK/; +$external_labels{$key} = "$URL/" . q|node174.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_VDV/; +$external_labels{$key} = "$URL/" . q|node191.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_EPCO/; +$external_labels{$key} = "$URL/" . q|node94.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_FK54Z/; +$external_labels{$key} = "$URL/" . q|node108.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_M2AV/; +$external_labels{$key} = "$URL/" . q|node125.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_FK425/; +$external_labels{$key} = "$URL/" . q|node104.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DS2TP/; +$external_labels{$key} = "$URL/" . q|node71.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_AOPPA/; +$external_labels{$key} = "$URL/" . q|node21.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_GE50/; +$external_labels{$key} = "$URL/" . q|node113.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_H2E/; +$external_labels{$key} = "$URL/" . q|node118.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_AOP/; +$external_labels{$key} = "$URL/" . q|node20.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DFLTIN/; +$external_labels{$key} = "$URL/" . q|node55.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_VN/; +$external_labels{$key} = "$URL/" . q|node192.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_UNPCD/; +$external_labels{$key} = "$URL/" . q|node189.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_GMST/; +$external_labels{$key} = "$URL/" . q|node115.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_PAV/; +$external_labels{$key} = "$URL/" . q|node139.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_ALTAZ/; +$external_labels{$key} = "$URL/" . q|node17.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_DJCL/; +$external_labels{$key} = "$URL/" . q|node59.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_CC62S/; +$external_labels{$key} = "$URL/" . q|node31.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_MAPPA/; +$external_labels{$key} = "$URL/" . q|node127.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DRANGE/; +$external_labels{$key} = "$URL/" . q|node68.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_UE2PV/; +$external_labels{$key} = "$URL/" . q|node188.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DTPV2C/; +$external_labels{$key} = "$URL/" . q|node79.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DVDV/; +$external_labels{$key} = "$URL/" . q|node82.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_NUT/; +$external_labels{$key} = "$URL/" . q|node133.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_ETRMS/; +$external_labels{$key} = "$URL/" . q|node100.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_PRECES/; +$external_labels{$key} = "$URL/" . q|node153.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DAFIN/; +$external_labels{$key} = "$URL/" . q|node43.html|; +$noresave{$key} = "$nosave"; + +$key = q/SLA_PREBN/; +$external_labels{$key} = "$URL/" . q|node151.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_DH2E/; +$external_labels{$key} = "$URL/" . q|node56.html|; +$noresave{$key} = "$nosave"; + +$key = q/xref_SLA_AOPPAT/; 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b/src/slalib/sun67.htx/node1.html @@ -0,0 +1,65 @@ + + + + +Abstract + + + + + + + + + + + + +

+ +next + +up + +previous +
+ Next: INTRODUCTION +
+Up: SLALIB Positional Astronomy Library +
+ Previous: SLALIB Positional Astronomy Library +

+

+

Abstract +  +

+SLALIB is a library used by writers of positional-astronomy applications. +Most of the 183 routines are concerned with astronomical position and time, +but a number have wider trigonometrical, numerical or general applications. +

+

+ +next + +up + +previous +
+ Next: INTRODUCTION +
+Up: SLALIB Positional Astronomy Library +
+ Previous: SLALIB Positional Astronomy Library +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node10.html b/src/slalib/sun67.htx/node10.html new file mode 100644 index 0000000..4a6a393 --- /dev/null +++ b/src/slalib/sun67.htx/node10.html @@ -0,0 +1,75 @@ + + + + +New Functions + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Acknowledgements +
+Up: INTRODUCTION +
+ Previous: Future Versions +

+

+

+New Functions +

+In a package like SLALIB it is difficult to know how far to go. Is it +enough to provide the primitive operations, or should more +complicated functions be packaged? Is it worth encroaching on +specialist areas, where individual experts have all written their +own software already? To what extent should CPU efficiency be +an issue? How much support of different numerical precisions is +required? And so on. +

+In practice, almost all the routines in SLALIB are there because they were +needed for some specific application, and this is likely to remain the +pattern for any enhancements in the future. +Suggestions for additional SLALIB routines should be addressed to the +author. +

+

+ +next + +up + +previous +
+ Next: Acknowledgements +
+Up: INTRODUCTION +
+ Previous: Future Versions +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node100.html b/src/slalib/sun67.htx/node100.html new file mode 100644 index 0000000..104db1d --- /dev/null +++ b/src/slalib/sun67.htx/node100.html @@ -0,0 +1,110 @@ + + + + +SLA_ETRMS - E-terms of Aberration + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EULER - Rotation Matrix from Euler Angles +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EQGAL - J2000 to Galactic +

+

+

SLA_ETRMS - E-terms of Aberration +   +

+
+
ACTION: +
Compute the E-terms vector - the part of the annual +aberration which arises from the eccentricity of the + Earth's orbit. +

CALL: +
CALL sla_ETRMS (EP, EV) +

+

+
GIVEN: +
+
+ + + + + +
EPDBesselian epoch
+

+
RETURNED: +
+
+ + + + + +
EVD(3)E-terms as $[\Delta x, \Delta y, \Delta z\,]$
+

+
NOTE: +
Note the use of the J2000 aberration constant ( +$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.49552$ ). + This is a reflection of the fact that the E-terms embodied in + existing star catalogues were computed from a variety of + aberration constants. Rather than adopting one of the old + constants the latest value is used here. +
+

+
REFERENCES: +
+
1. +
Smith, C.A. et al., 1989. Astr.J. 97, 265. +
2. +
Yallop, B.D. et al., 1989. Astr.J. 97, 274. +
+
+ +next + +up + +previous +
+ Next: SLA_EULER - Rotation Matrix from Euler Angles +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EQGAL - J2000 to Galactic +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node101.html b/src/slalib/sun67.htx/node101.html new file mode 100644 index 0000000..e5bdda2 --- /dev/null +++ b/src/slalib/sun67.htx/node101.html @@ -0,0 +1,132 @@ + + + + +SLA_EULER - Rotation Matrix from Euler Angles + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EVP - Earth Position & Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ETRMS - E-terms of Aberration +

+

+

SLA_EULER - Rotation Matrix from Euler Angles +   +

+
+
ACTION: +
Form a rotation matrix from the Euler angles - three +successive rotations about specified Cartesian axes + (single precision). +

CALL: +
CALL sla_EULER (ORDER, PHI, THETA, PSI, RMAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
ORDERC*(*)specifies about which axes the rotations occur
PHIR1st rotation (radians)
THETAR2nd rotation (radians)
PSIR3rd rotation (radians)
+

+
RETURNED: +
+
+ + + + + +
RMATR(3,3)rotation matrix
+

+
NOTES: +
+
1. +
A rotation is positive when the reference frame rotates +anticlockwise as seen looking towards the origin from the +positive region of the specified axis. +
2. +
The characters of ORDER define which axes the three successive + rotations are about. A typical value is `ZXZ', indicating that + RMAT is to become the direction cosine matrix corresponding to + rotations of the reference frame through PHI radians about the + old z-axis, followed by THETA radians about the resulting + x-axis, + then PSI radians about the resulting z-axis. In detail: +
    +
  • The axis names can be any of the following, in any order or + combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal + axis labelling/numbering conventions apply; + the xyz ($\equiv123$) triad is right-handed. Thus, the `ZXZ' example given above + could be written `zxz' or `313' (or even `ZxZ' or `3xZ'). +
  • ORDER is terminated by length or by the first unrecognized + character. +
  • Fewer than three rotations are acceptable, in which case + the later angle arguments are ignored. +
+
3. +
Zero rotations produces a unit RMAT. +
+
+ +next + +up + +previous +
+ Next: SLA_EVP - Earth Position & Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ETRMS - E-terms of Aberration +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node102.html b/src/slalib/sun67.htx/node102.html new file mode 100644 index 0000000..d22b187 --- /dev/null +++ b/src/slalib/sun67.htx/node102.html @@ -0,0 +1,149 @@ + + + + +SLA_EVP - Earth Position & Velocity + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FITXY - Fit Linear Model to Two Sets +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EULER - Rotation Matrix from Euler Angles +

+

+

SLA_EVP - Earth Position & Velocity +   +

+
+
ACTION: +
Barycentric and heliocentric velocity and position of the Earth. +
CALL: +
CALL sla_EVP (DATE, DEQX, DVB, DPB, DVH, DPH) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DATEDTDB (formerly ET) as a Modified Julian Date +(JD-2400000.5)
DEQXDJulian Epoch (e.g. 2000D0) of mean equator and +equinox of the vectors returned. If DEQX <0, +all vectors are referred to the mean equator and +equinox (FK5) of date DATE.
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
DVBD(3)barycentric $[\,\dot{x},\dot{y},\dot{z}\,]$, AU s-1
DPBD(3)barycentric $[\,x,y,z\,]$, AU
DVHD(3)heliocentric $[\,\dot{x},\dot{y},\dot{z}\,]$, AU s-1
DPHD(3)heliocentric $[\,x,y,z\,]$, AU
+

+
NOTES: +
+
1. +
This routine is used when accuracy is more important +than CPU time, yet the extra complication of reading a +pre-computed ephemeris is not justified. The maximum + deviations from the JPL DE96 ephemeris are as follows: +
    +
  • velocity (barycentric or heliocentric): 420 mm s-1 +
  • position (barycentric): 6900 km +
  • position (heliocentric): 1600 km +
+
2. +
The routine is an adaption of the BARVEL and BARCOR + subroutines of P.Stumpff, which are described in + Astr.Astrophys.Suppl.Ser. 41, 1-8 (1980). + Most of the changes are merely cosmetic and do not affect + the results at all. However, some adjustments have been + made so as to give results that refer to the new (IAU 1976 + `FK5') equinox and precession, although the differences these + changes make relative to the results from Stumpff's original + `FK4' version are smaller than the inherent accuracy of the + algorithm. One minor shortcoming in the original routines + that has not been corrected is that slightly better + numerical accuracy could be achieved if the various polynomial + evaluations were to be so arranged that the smallest terms were + computed first. Note also that one of Stumpff's precession + constants differs by + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.001$ from the value given in the + Explanatory Supplement. +
+
+ +next + +up + +previous +
+ Next: SLA_FITXY - Fit Linear Model to Two Sets +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EULER - Rotation Matrix from Euler Angles +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node103.html b/src/slalib/sun67.htx/node103.html new file mode 100644 index 0000000..4525328 --- /dev/null +++ b/src/slalib/sun67.htx/node103.html @@ -0,0 +1,170 @@ + + + + +SLA_FITXY - Fit Linear Model to Two Sets + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FK425 - FK4 to FK5 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EVP - Earth Position & Velocity +

+

+

    +
+SLA_FITXY - Fit Linear Model to Two $[\,x,y\,]$ Sets +

+
+
ACTION: +
Fit a linear model to relate two sets of $[\,x,y\,]$ coordinates. +
CALL: +
CALL sla_FITXY (ITYPE,NP,XYE,XYM,COEFFS,J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
ITYPEItype of model: 4 or 6 (note 1)
NPInumber of samples (note 2)
XYED(2,NP)expected $[\,x,y\,]$ for each sample
XYMD(2,NP)measured $[\,x,y\,]$ for each sample
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
COEFFSD(6)coefficients of model (note 3)
JIstatus:
0 = OK
-1 = illegal ITYPE
-2 = insufficient data
-3 = singular solution
+

+
NOTES: +
+
1. +
ITYPE, which must be either 4 or 6, selects the type of model +fitted. Both allowed ITYPE values produce a model COEFFS which +consists of six coefficients, namely the zero points and, for + each of XE and YE, the coefficient of XM and YM. For ITYPE=6, + all six coefficients are independent, modelling squash and shear + as well as origin, scale, and orientation. However, ITYPE=4 + selects the solid body rotation option; the model COEFFS + still consists of the same six coefficients, but now two of + them are used twice (appropriately signed). Origin, scale + and orientation are still modelled, but not squash or shear - + the units of X and Y have to be the same. +
2. +
For NC=4, NP must be at least 2. For NC=6, NP must be at + least 3. +
3. +
The model is returned in the array COEFFS. Naming the + six elements of COEFFS a,b,c,d,e & f, + the model transforms measured coordinates + $[x_{m},y_{m}\,]$ into expected coordinates + $[x_{e},y_{e}\,]$ as follows: +
xe = a + bxm + cym
+ ye = d + exm + fym
+ For the solid body rotation option (ITYPE=4), the + magnitudes of b and f, and of c and e, are equal. The + signs of these coefficients depend on whether there is a + sign reversal between [xe,ye] and [xm,ym]; + fits are performed + with and without a sign reversal and the best one chosen. +
4. +
Error status values J=-1 and -2 leave COEFFS unchanged; + if J=-3 COEFFS may have been changed. +
5. +
See also sla_PXY, sla_INVF, sla_XY2XY, sla_DCMPF. +
+
+ +next + +up + +previous +
+ Next: SLA_FK425 - FK4 to FK5 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EVP - Earth Position & Velocity +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node104.html b/src/slalib/sun67.htx/node104.html new file mode 100644 index 0000000..0a2f9ca --- /dev/null +++ b/src/slalib/sun67.htx/node104.html @@ -0,0 +1,208 @@ + + + + +SLA_FK425 - FK4 to FK5 + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FK45Z - FK4 to FK5, no P.M. or Parallax +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FITXY - Fit Linear Model to Two Sets +

+

+

SLA_FK425 - FK4 to FK5 +   +

+
+
ACTION: +
Convert B1950.0 FK4 star data to J2000.0 FK5. +This routine converts stars from the old, Bessel-Newcomb, FK4 + system to the new, IAU 1976, FK5, Fricke system. The precepts + of Smith et al. (see reference 1) are followed, + using the implementation + by Yallop et al. (reference 2) of a matrix method + due to Standish. + Kinoshita's development of Andoyer's post-Newcomb precession is + used. The numerical constants from + Seidelmann et al. (reference 3) are used canonically. +

CALL: +
CALL sla_FK425 ( + R1950,D1950,DR1950,DD1950,P1950,V1950, + R2000,D2000,DR2000,DD2000,P2000,V2000) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
R1950DB1950.0 $\alpha$ (radians)
D1950DB1950.0 $\delta$ (radians)
DR1950DB1950.0 proper motion in $\alpha$(radians per tropical year)
DD1950DB1950.0 proper motion in $\delta$(radians per tropical year)
P1950DB1950.0 parallax (arcsec)
V1950DB1950.0 radial velocity (km s-1, +ve = moving away)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
R2000DJ2000.0 $\alpha$ (radians)
D2000DJ2000.0 $\delta$ (radians)
DR2000DJ2000.0 proper motion in $\alpha$(radians per Julian year)
DD2000DJ2000.0 proper motion in $\delta$(radians per Julian year)
P2000DJ2000.0 parallax (arcsec)
V2000DJ2000.0 radial velocity (km s-1, +ve = moving away)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
Conversion from Besselian epoch 1950.0 to Julian epoch + 2000.0 only is provided for. Conversions involving other + epochs will require use of the appropriate precession, + proper motion, and E-terms routines before and/or after FK425 + is called. +
3. +
In the FK4 catalogue the proper motions of stars within + $10^{\circ}$ of the poles do not include the differential + E-terms effect and should, strictly speaking, be handled + in a different manner from stars outside these regions. + However, given the general lack of homogeneity of the star + data available for routine astrometry, the difficulties of + handling positions that may have been determined from + astrometric fields spanning the polar and non-polar regions, + the likelihood that the differential E-terms effect was not + taken into account when allowing for proper motion in past + astrometry, and the undesirability of a discontinuity in + the algorithm, the decision has been made in this routine to + include the effect of differential E-terms on the proper + motions for all stars, whether polar or not. At epoch J2000, + and measuring on the sky rather than in terms of $\Delta\alpha$, the errors resulting from this simplification are less than + 1 milliarcsecond in position and 1 milliarcsecond per + century in proper motion. +
4. +
See also sla_FK45Z, sla_FK524, sla_FK54Z. +
+

+
REFERENCES: +
+
1. +
Smith, C.A. et al., 1989. Astr.J. 97, 265. +
2. +
Yallop, B.D. et al., 1989. Astr.J. 97, 274. +
3. +
Seidelmann, P.K. (ed), 1992. Explanatory + Supplement to the Astronomical Almanac, ISBN 0-935702-68-7. +
+
+ +next + +up + +previous +
+ Next: SLA_FK45Z - FK4 to FK5, no P.M. or Parallax +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FITXY - Fit Linear Model to Two Sets +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node105.html b/src/slalib/sun67.htx/node105.html new file mode 100644 index 0000000..dde5fc9 --- /dev/null +++ b/src/slalib/sun67.htx/node105.html @@ -0,0 +1,166 @@ + + + + +SLA_FK45Z - FK4 to FK5, no P.M. or Parallax + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FK524 - FK5 to FK4 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK425 - FK4 to FK5 +

+

+

SLA_FK45Z - FK4 to FK5, no P.M. or Parallax +   +

+
+
ACTION: +
Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero +proper motion in the FK5 frame. + This routine converts stars from the old, Bessel-Newcomb, FK4 + system to the new, IAU 1976, FK5, Fricke system, in such a + way that the FK5 proper motion is zero. Because such a star + has, in general, a non-zero proper motion in the FK4 system, + the routine requires the epoch at which the position in the + FK4 system was determined. The method is from appendix 2 of + reference 1, but using the constants of reference 4. +

CALL: +
CALL sla_FK45Z (R1950,D1950,BEPOCH,R2000,D2000) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
R1950DB1950.0 FK4 $\alpha$ at epoch BEPOCH (radians)
D1950DB1950.0 FK4 $\delta$ at epoch BEPOCH (radians)
BEPOCHDBesselian epoch (e.g. 1979.3D0)
+

+
RETURNED: +
+
+ + + + + + + + + +
R2000DJ2000.0 FK5 $\alpha$ (radians)
D2000DJ2000.0 FK5 $\delta$ (radians)
+

+
NOTES: +
+
1. +
The epoch BEPOCH is strictly speaking Besselian, but +if a Julian epoch is supplied the result will be +affected only to a negligible extent. +
2. +
Conversion from Besselian epoch 1950.0 to Julian epoch + 2000.0 only is provided for. Conversions involving other + epochs will require use of the appropriate precession, + proper motion, and E-terms routines before and/or + after FK45Z is called. +
3. +
In the FK4 catalogue the proper motions of stars within + $10^{\circ}$ of the poles do not include the differential + E-terms effect and should, strictly speaking, be handled + in a different manner from stars outside these regions. + However, given the general lack of homogeneity of the star + data available for routine astrometry, the difficulties of + handling positions that may have been determined from + astrometric fields spanning the polar and non-polar regions, + the likelihood that the differential E-terms effect was not + taken into account when allowing for proper motion in past + astrometry, and the undesirability of a discontinuity in + the algorithm, the decision has been made in this routine to + include the effect of differential E-terms on the proper + motions for all stars, whether polar or not. At epoch 2000, + and measuring on the sky rather than in terms of $\Delta\alpha$, the errors resulting from this simplification are less than + 1 milliarcsecond in position and 1 milliarcsecond per + century in proper motion. +
4. +
See also sla_FK425, sla_FK524, sla_FK54Z. +
+

+
REFERENCES: +
+
1. +
Aoki, S., et al., 1983. Astr.Astrophys., 128, 263. +
2. +
Smith, C.A. et al., 1989. Astr.J. 97, 265. +
3. +
Yallop, B.D. et al., 1989. Astr.J. 97, 274. +
4. +
Seidelmann, P.K. (ed), 1992. Explanatory + Supplement to the Astronomical Almanac, ISBN 0-935702-68-7. +
+
+ +next + +up + +previous +
+ Next: SLA_FK524 - FK5 to FK4 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK425 - FK4 to FK5 +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node106.html b/src/slalib/sun67.htx/node106.html new file mode 100644 index 0000000..8c1e64a --- /dev/null +++ b/src/slalib/sun67.htx/node106.html @@ -0,0 +1,207 @@ + + + + +SLA_FK524 - FK5 to FK4 + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FK52H - FK5 to Hipparcos +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK45Z - FK4 to FK5, no P.M. or Parallax +

+

+

SLA_FK524 - FK5 to FK4 +   +

+
+
ACTION: +
Convert J2000.0 FK5 star data to B1950.0 FK4. +This routine converts stars from the new, IAU 1976, FK5, Fricke + system, to the old, Bessel-Newcomb, FK4 system. + The precepts of Smith et al. (reference 1) are followed, + using the implementation by Yallop et al. (reference 2) + of a matrix method due to Standish. Kinoshita's development of + Andoyer's post-Newcomb precession is used. The numerical + constants from Seidelmann et al. (reference 3) are + used canonically. +

CALL: +
CALL sla_FK524 ( + R2000,D2000,DR2000,DD2000,P2000,V2000, + R1950,D1950,DR1950,DD1950,P1950,V1950) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
R2000DJ2000.0 $\alpha$ (radians)
D2000DJ2000.0 $\delta$ (radians)
DR2000DJ2000.0 proper motion in $\alpha$(radians per Julian year)
DD2000DJ2000.0 proper motion in $\delta$(radians per Julian year)
P2000DJ2000.0 parallax (arcsec)
V2000DJ2000 radial velocity (km s-1, +ve = moving away)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
R1950DB1950.0 $\alpha$ (radians)
D1950DB1950.0 $\delta$ (radians)
DR1950DB1950.0 proper motion in $\alpha$(radians per tropical year)
DD1950DB1950.0 proper motion in $\delta$(radians per tropical year)
P1950DB1950.0 parallax (arcsec)
V1950Dradial velocity (km s-1, +ve = moving away)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
Note that conversion from Julian epoch 2000.0 to Besselian + epoch 1950.0 only is provided for. Conversions involving + other epochs will require use of the appropriate precession, + proper motion, and E-terms routines before and/or after + FK524 is called. +
3. +
In the FK4 catalogue the proper motions of stars within + $10^{\circ}$ of the poles do not include the differential + E-terms effect and should, strictly speaking, be handled + in a different manner from stars outside these regions. + However, given the general lack of homogeneity of the star + data available for routine astrometry, the difficulties of + handling positions that may have been determined from + astrometric fields spanning the polar and non-polar regions, + the likelihood that the differential E-terms effect was not + taken into account when allowing for proper motion in past + astrometry, and the undesirability of a discontinuity in + the algorithm, the decision has been made in this routine to + include the effect of differential E-terms on the proper + motions for all stars, whether polar or not. At epoch 2000, + and measuring on the sky rather than in terms of $\Delta\alpha$, the errors resulting from this simplification are less than + 1 milliarcsecond in position and 1 milliarcsecond per + century in proper motion. +
4. +
See also sla_FK425, sla_FK45Z, sla_FK54Z. +
+

+
REFERENCES: +
+
1. +
Smith, C.A. et al., 1989. Astr.J. 97, 265. +
2. +
Yallop, B.D. et al., 1989. Astr.J. 97, 274. +
3. +
Seidelmann, P.K. (ed), 1992. Explanatory + Supplement to the Astronomical Almanac, ISBN 0-935702-68-7. +
+
+ +next + +up + +previous +
+ Next: SLA_FK52H - FK5 to Hipparcos +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK45Z - FK4 to FK5, no P.M. or Parallax +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node107.html b/src/slalib/sun67.htx/node107.html new file mode 100644 index 0000000..e63af95 --- /dev/null +++ b/src/slalib/sun67.htx/node107.html @@ -0,0 +1,188 @@ + + + + +SLA_FK52H - FK5 to Hipparcos + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FK54Z - FK5 to FK4, no P.M. or Parallax +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK524 - FK5 to FK4 +

+

+

SLA_FK52H - FK5 to Hipparcos +   +

+
+
ACTION: +
Transform an FK5 (J2000) position and proper motion +into the frame of the Hipparcos catalogue. +

CALL: +
CALL sla_FK52H (R5,D5,DR5,DD5,RH,DH,DRH,DDH) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
R5DJ2000.0 FK5 $\alpha$ (radians)
D5DJ2000.0 FK5 $\delta$ (radians)
DR5DJ2000.0 FK5 proper motion in $\alpha$(radians per Julian year)
DD5DJ2000.0 FK5 proper motion in $\delta$(radians per Julian year)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
RHDHipparcos $\alpha$ (radians)
DHDHipparcos $\delta$ (radians)
DRHDHipparcos proper motion in $\alpha$(radians per Julian year)
DDHDHipparcos proper motion in $\delta$(radians per Julian year)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
The FK5 to Hipparcos + transformation consists of a pure rotation and spin; + zonal errors in the FK5 catalogue are not taken into account. +
3. +
The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin + values are as follows (see reference): +


+
+
+

             + + + + + + + + + + + + + + + + + + + + + +
 orientation   spin   
x-19.9     -0.30  
y-9.1     +0.60  
z+22.9     +0.70  
 mas      mas/y 
+


+
+
+
+

+These orientation and spin components are interpreted as + axial vectors. An axial vector points at the pole of + the rotation and its length is the amount of rotation in radians. +

4. +
See also sla_FK5HZ, sla_H2FK5, sla_HFK5Z. +
+

+
REFERENCE: +
Feissel, M. & Mignard, F., 1998., Astron.Astrophys. 331, L33-L36. +
+
+ +next + +up + +previous +
+ Next: SLA_FK54Z - FK5 to FK4, no P.M. or Parallax +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK524 - FK5 to FK4 +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node108.html b/src/slalib/sun67.htx/node108.html new file mode 100644 index 0000000..504a1a6 --- /dev/null +++ b/src/slalib/sun67.htx/node108.html @@ -0,0 +1,156 @@ + + + + +SLA_FK54Z - FK5 to FK4, no P.M. or Parallax + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FK5HZ - FK5 to Hipparcos, no P.M. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK52H - FK5 to Hipparcos +

+

+

SLA_FK54Z - FK5 to FK4, no P.M. or Parallax +   +

+
+
ACTION: +
Convert a J2000.0 FK5 star position to B1950.0 FK4 assuming +FK5 zero proper motion and parallax. + This routine converts star positions from the new, IAU 1976, + FK5, Fricke system to the old, Bessel-Newcomb, FK4 system. +

CALL: +
CALL sla_FK54Z (R2000,D2000,BEPOCH,R1950,D1950,DR1950,DD1950) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
R2000DJ2000.0 FK5 $\alpha$ (radians)
D2000DJ2000.0 FK5 $\delta$ (radians)
BEPOCHDBesselian epoch (e.g. 1950D0)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
R1950DB1950.0 FK4 $\alpha$ at epoch BEPOCH (radians)
D1950DB1950.0 FK4 $\delta$ at epoch BEPOCH (radians)
DR1950DB1950.0 FK4 proper motion in $\alpha$(radians per tropical year)
DD1950DB1950.0 FK4 proper motion in $\delta$(radians per tropical year)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
Conversion from Julian epoch 2000.0 to Besselian epoch 1950.0 + only is provided for. Conversions involving other epochs will + require use of the appropriate precession routines before and + after this routine is called. +
3. +
Unlike in the sla_FK524 routine, the FK5 proper motions, the + parallax and the radial velocity are presumed zero. +
4. +
It was the intention that FK5 should be a close approximation + to an inertial frame, so that distant objects have zero proper + motion; such objects have (in general) non-zero proper motion + in FK4, and this routine returns those fictitious proper + motions. +
5. +
The position returned by this routine is in the B1950 + reference frame but at Besselian epoch BEPOCH. For + comparison with catalogues the BEPOCH argument will + frequently be 1950D0. +
6. +
See also sla_FK425, sla_FK45Z, sla_FK524. +
+
+ +next + +up + +previous +
+ Next: SLA_FK5HZ - FK5 to Hipparcos, no P.M. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK52H - FK5 to Hipparcos +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node109.html b/src/slalib/sun67.htx/node109.html new file mode 100644 index 0000000..ddda44d --- /dev/null +++ b/src/slalib/sun67.htx/node109.html @@ -0,0 +1,168 @@ + + + + +SLA_FK5HZ - FK5 to Hipparcos, no P.M. + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_FLOTIN - Decode a Real Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK54Z - FK5 to FK4, no P.M. or Parallax +

+

+

SLA_FK5HZ - FK5 to Hipparcos, no P.M. +   +

+
+
ACTION: +
Transform an FK5 (J2000) star position into the frame of the +Hipparcos catalogue, assuming zero Hipparcos proper motion. +

CALL: +
CALL sla_FK52H (R5,D5,EPOCH,RH,DH) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
R5DJ2000.0 FK5 $\alpha$ (radians)
D5DJ2000.0 FK5 $\delta$ (radians)
EPOCHDJulian epoch (TDB)
+

+
RETURNED: +
+
+ + + + + + + + + +
RHDHipparcos $\alpha$ (radians)
DHDHipparcos $\delta$ (radians)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
The FK5 to Hipparcos + transformation consists of a pure rotation and spin; + zonal errors in the FK5 catalogue are not taken into account. +
3. +
The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin + values are as follows (see reference): +


+
+
+

             + + + + + + + + + + + + + + + + + + + + + +
 orientation   spin   
x-19.9     -0.30  
y-9.1     +0.60  
z+22.9     +0.70  
 mas      mas/y 
+


+
+
+
+

+These orientation and spin components are interpreted as + axial vectors. An axial vector points at the pole of + the rotation and its length is the amount of rotation in radians. +

4. +
See also sla_FK52H, sla_H2FK5, sla_HFK5Z. +
+

+
REFERENCE: +
Feissel, M. & Mignard, F., 1998., Astron.Astrophys. 331, L33-L36. +
+
+ +next + +up + +previous +
+ Next: SLA_FLOTIN - Decode a Real Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK54Z - FK5 to FK4, no P.M. or Parallax +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node11.html b/src/slalib/sun67.htx/node11.html new file mode 100644 index 0000000..a950b04 --- /dev/null +++ b/src/slalib/sun67.htx/node11.html @@ -0,0 +1,102 @@ + + + + +Acknowledgements + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: LINKING +
+Up: INTRODUCTION +
+ Previous: New Functions +

+

+

+Acknowledgements +

+SLALIB is descended from a package of routines written +for the AAO 16-bit minicomputers +in the mid-1970s. The coming of the VAX +allowed a much more comprehensive and thorough package +to be designed for Starlink, especially important +at a time when the adoption +of the IAU 1976 resolutions meant that astronomers +would have to cope with a mixture of reference frames, +timescales and nomenclature. +

+Much of the preparatory work on SLALIB was done by +Althea Wilkinson of Manchester University. +During its development, +Andrew Murray, +Catherine Hohenkerk, +Andrew Sinclair, +Bernard Yallop +and +Brian Emerson of Her Majesty's Nautical Almanac Office were consulted +on many occasions; their advice was indispensable. +I am especially grateful to +Catherine Hohenkerk +for supplying preprints of papers, and test data. A number of +enhancements to SLALIB were at the suggestion of +Russell Owen, University of Washington, +the late Phil Hill, St Andrews University, +Bill Vacca, JILA, Boulder and +Ron Maddalena, NRAO. +Mark Calabretta, CSIRO Radiophysics, Sydney supplied changes to suit Convex. +I am indebted to Derek Jones (RGO) for introducing me to the +``universal variables'' method of calculating orbits. +

+The first C version of SLALIB was a hand-coded transcription +of the Starlink Fortran version carried out by +Steve Eaton (University of Leeds) in the course of +MSc work. This was later +enhanced by John Straede (AAO) and Martin Shepherd (Caltech). +The current C SLALIB is a complete rewrite by the present author and +includes a comprehensive validation suite. +Additional comments on the C version came from Bob Payne (NRAO) and +Jeremy Bailey (AAO). +

+

+ +next + +up + +previous +
+ Next: LINKING +
+Up: INTRODUCTION +
+ Previous: New Functions +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node110.html b/src/slalib/sun67.htx/node110.html new file mode 100644 index 0000000..c13c949 --- /dev/null +++ b/src/slalib/sun67.htx/node110.html @@ -0,0 +1,200 @@ + + + + +SLA_FLOTIN - Decode a Real Number + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GALEQ - Galactic to J2000 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK5HZ - FK5 to Hipparcos, no P.M. +

+

+

SLA_FLOTIN - Decode a Real Number +   +

+
+
ACTION: +
Convert free-format input into single precision floating point. +
CALL: +
CALL sla_FLOTIN (STRING, NSTRT, RESLT, JFLAG) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
STRINGCstring containing number to be decoded
NSTRTIpointer to where decoding is to commence
RESLTRcurrent value of result
+

+
RETURNED: +
+
+ + + + + + + + + + + + + +
NSTRTIadvanced to next number
RESLTRresult
JFLAGIstatus: -1 = -OK, 0 = +OK, 1 = null result, 2 = error
+

+
NOTES: +
+
1. +
The reason sla_FLOTIN has separate `OK' status values +for + and - is to enable minus zero to be detected. +This is of crucial importance + when decoding mixed-radix numbers. For example, an angle + expressed as degrees, arcminutes and arcseconds may have a + leading minus sign but a zero degrees field. +
2. +
A TAB is interpreted as a space, and lowercase characters are + interpreted as uppercase. n.b. The test for TAB is + ASCII-specific. +
3. +
The basic format is the sequence of fields $\pm n.n x \pm n$, where $\pm$ is a sign + character `+' or `-', n means a string of decimal digits, + `.' is a decimal point, and x, which indicates an exponent, + means `D' or `E'. Various combinations of these fields can be + omitted, and embedded blanks are permissible in certain places. +
4. +
Spaces: +
    +
  • Leading spaces are ignored. +
  • Embedded spaces are allowed only after +, -, D or E, + and after the decimal point if the first sequence of + digits is absent. +
  • Trailing spaces are ignored; the first signifies + end of decoding and subsequent ones are skipped. +
+
5. +
Delimiters: +
    +
  • Any character other than +,-,0-9,.,D,E or space may be + used to signal the end of the number and terminate decoding. +
  • Comma is recognized by sla_FLOTIN as a special case; it + is skipped, leaving the pointer on the next character. See + 13, below. +
  • Decoding will in all cases terminate if end of string + is reached. +
+
6. +
Both signs are optional. The default is +. +
7. +
The mantissa n.n defaults to unity. +
8. +
The exponent $x\!\pm\!n$ defaults to `E0'. +
9. +
The strings of decimal digits may be of any length. +
10. +
The decimal point is optional for whole numbers. +
11. +
A null result occurs when the string of characters + being decoded does not begin with +,-,0-9,.,D or E, or + consists entirely of spaces. When this condition is + detected, JFLAG is set to 1 and RESLT is left untouched. +
12. +
NSTRT = 1 for the first character in the string. +
13. +
On return from sla_FLOTIN, NSTRT is set ready for the next + decode - following trailing blanks and any comma. If a + delimiter other than comma is being used, NSTRT must be + incremented before the next call to sla_FLOTIN, otherwise + all subsequent calls will return a null result. +
14. +
Errors (JFLAG=2) occur when: +
    +
  • a +, -, D or E is left unsatisfied; or +
  • the decimal point is present without at least + one decimal digit before or after it; or +
  • an exponent more than 100 has been presented. +
+
15. +
When an error has been detected, NSTRT is left + pointing to the character following the last + one used before the error came to light. This + may be after the point at which a more sophisticated + program could have detected the error. For example, + sla_FLOTIN does not detect that `1E999' is unacceptable + (on a computer where this is so) + until the entire number has been decoded. +
16. +
Certain highly unlikely combinations of mantissa and + exponent can cause arithmetic faults during the + decode, in some cases despite the fact that they + together could be construed as a valid number. +
17. +
Decoding is left to right, one pass. +
18. +
See also sla_DFLTIN and sla_INTIN. +
+
+ +next + +up + +previous +
+ Next: SLA_GALEQ - Galactic to J2000 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FK5HZ - FK5 to Hipparcos, no P.M. +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node111.html b/src/slalib/sun67.htx/node111.html new file mode 100644 index 0000000..6e7927c --- /dev/null +++ b/src/slalib/sun67.htx/node111.html @@ -0,0 +1,104 @@ + + + + +SLA_GALEQ - Galactic to J2000 + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GALSUP - Galactic to Supergalactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FLOTIN - Decode a Real Number +

+

+

    +
+SLA_GALEQ - Galactic to J2000 $\alpha,\delta$

+
+
ACTION: +
Transformation from IAU 1958 galactic coordinates +to J2000.0 FK5 equatorial coordinates. +

CALL: +
CALL sla_GALEQ (DL, DB, DR, DD) +

+

+
GIVEN: +
+
+ + + + + +
DL,DBDgalactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$
+

+
RETURNED: +
+
+ + + + + +
DR,DDDJ2000.0 $[\,\alpha,\delta\,]$
+

+
NOTES: +
+
1. +
All arguments are in radians. +
2. +
The equatorial coordinates are J2000.0 FK5. Use the routine +sla_GE50 if conversion to B1950.0 FK4 coordinates is + required. +
+
+ +next + +up + +previous +
+ Next: SLA_GALSUP - Galactic to Supergalactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_FLOTIN - Decode a Real Number +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node112.html b/src/slalib/sun67.htx/node112.html new file mode 100644 index 0000000..cfbdd9b --- /dev/null +++ b/src/slalib/sun67.htx/node112.html @@ -0,0 +1,107 @@ + + + + +SLA_GALSUP - Galactic to Supergalactic + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GE50 - Galactic to B1950 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GALEQ - Galactic to J2000 +

+

+

SLA_GALSUP - Galactic to Supergalactic +   +

+
+
ACTION: +
Transformation from IAU 1958 galactic coordinates to +de Vaucouleurs supergalactic coordinates. +

CALL: +
CALL sla_GALSUP (DL, DB, DSL, DSB) +

+

+
GIVEN: +
+
+ + + + + +
DL,DBDgalactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
DSL,DSBDsupergalactic longitude and latitude (radians)
+

+
REFERENCES: +
+
1. +
de Vaucouleurs, de Vaucouleurs, & Corwin, Second Reference +Catalogue of Bright Galaxies, U.Texas, p8. +
2. +
Systems & Applied Sciences Corp., documentation for the + machine-readable version of the above catalogue, + Contract NAS 5-26490. +
+ (These two references give different values for the galactic + longitude of the supergalactic origin. Both are wrong; the + correct value is $l^{I\!I}=137.37$.) +

+
+ +next + +up + +previous +
+ Next: SLA_GE50 - Galactic to B1950 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GALEQ - Galactic to J2000 +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node113.html b/src/slalib/sun67.htx/node113.html new file mode 100644 index 0000000..e12bf51 --- /dev/null +++ b/src/slalib/sun67.htx/node113.html @@ -0,0 +1,109 @@ + + + + +SLA_GE50 - Galactic to B1950 + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GEOC - Geodetic to Geocentric +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GALSUP - Galactic to Supergalactic +

+

+

    +
+SLA_GE50 - Galactic to B1950 $\alpha,\delta$

+
+
ACTION: +
Transformation from IAU 1958 galactic coordinates to +B1950.0 FK4 equatorial coordinates. +

CALL: +
CALL sla_GE50 (DL, DB, DR, DD) +

+

+
GIVEN: +
+
+ + + + + +
DL,DBDgalactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$
+

+
RETURNED: +
+
+ + + + + +
DR,DDDB1950.0 $[\,\alpha,\delta\,]$
+

+
NOTES: +
+
1. +
All arguments are in radians. +
2. +
The equatorial coordinates are B1950.0 FK4. Use the +routine sla_GALEQ if conversion to J2000.0 FK5 coordinates + is required. +
+

+
REFERENCE: +
Blaauw et al., 1960, Mon.Not.R.astr.Soc., +121, 123. +
+
+ +next + +up + +previous +
+ Next: SLA_GEOC - Geodetic to Geocentric +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GALSUP - Galactic to Supergalactic +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node114.html b/src/slalib/sun67.htx/node114.html new file mode 100644 index 0000000..a2e570a --- /dev/null +++ b/src/slalib/sun67.htx/node114.html @@ -0,0 +1,107 @@ + + + + +SLA_GEOC - Geodetic to Geocentric + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GMST - UT to GMST +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GE50 - Galactic to B1950 +

+

+

SLA_GEOC - Geodetic to Geocentric +   +

+
+
ACTION: +
Convert geodetic position to geocentric. +
CALL: +
CALL sla_GEOC (P, H, R, Z) +

+

+
GIVEN: +
+
+ + + + + + + + + +
PDlatitude (geodetic, radians)
HDheight above reference spheroid (geodetic, metres)
+

+
RETURNED: +
+
+ + + + + + + + + +
RDdistance from Earth axis (AU)
ZDdistance from plane of Earth equator (AU)
+

+
NOTES: +
+
1. +
Geocentric latitude can be obtained by evaluating ATAN2(Z,R). +
2. +
IAU 1976 constants are used. +
+

+
REFERENCE: +
Green, R.M., 1985. Spherical Astronomy, Cambridge U.P., p98. +
+
+ +next + +up + +previous +
+ Next: SLA_GMST - UT to GMST +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GE50 - Galactic to B1950 +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node115.html b/src/slalib/sun67.htx/node115.html new file mode 100644 index 0000000..cee01cc --- /dev/null +++ b/src/slalib/sun67.htx/node115.html @@ -0,0 +1,115 @@ + + + + +SLA_GMST - UT to GMST + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GMSTA - UT to GMST (extra precision) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GEOC - Geodetic to Geocentric +

+

+

SLA_GMST - UT to GMST +   +

+
+
ACTION: +
Conversion from universal time UT1 to Greenwich mean +sidereal time. +

CALL: +
D = sla_GMST (UT1) +

+

+
GIVEN: +
+
+ + + + + +
UT1Duniversal time (strictly UT1) expressed as +modified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
sla_GMSTDGreenwich mean sidereal time (radians)
+

+
NOTES: +
+
1. +
The IAU 1982 expression +(see page S15 of the 1984 Astronomical +Almanac) is used, but rearranged to reduce rounding errors. This + expression is always described as giving the GMST at $0^{\rm h}$UT; + in fact, it gives the difference between the + GMST and the UT, which happens to equal the GMST (modulo + 24 hours) at $0^{\rm h}$UT each day. In sla_GMST, the + entire UT is used directly as the argument for the + canonical formula, and the fractional part of the UT is + added separately; note that the factor $1.0027379\cdots$ does + not appear. +
2. +
See also the routine sla_GMSTA, which + delivers better numerical + precision by accepting the UT date and time as separate arguments. +
+
+ +next + +up + +previous +
+ Next: SLA_GMSTA - UT to GMST (extra precision) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GEOC - Geodetic to Geocentric +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node116.html b/src/slalib/sun67.htx/node116.html new file mode 100644 index 0000000..5055ecb --- /dev/null +++ b/src/slalib/sun67.htx/node116.html @@ -0,0 +1,116 @@ + + + + +SLA_GMSTA - UT to GMST (extra precision) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_GRESID - Gaussian Residual +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GMST - UT to GMST +

+

+

SLA_GMSTA - UT to GMST (extra precision) +   +

+
+
ACTION: +
Conversion from universal time UT1 to Greenwich Mean +sidereal time, with rounding errors minimized. +

CALL: +
D = sla_GMSTA (DATE, UT1) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DATEDUT1 date as Modified Julian Date (integer part +of JD-2400000.5)
UT1DUT1 time (fraction of a day)
+

+
RETURNED: +
+
+ + + + + +
sla_GMSTDGreenwich mean sidereal time (radians)
+

+
NOTES: +
+
1. +
The algorithm is derived from the IAU 1982 expression +(see page S15 of the 1984 Astronomical Almanac). +
2. +
There is no restriction on how the UT is apportioned between the + DATE and UT1 arguments. Either of the two arguments could, for + example, be zero and the entire date+time supplied in the other. + However, the routine is designed to deliver maximum accuracy when + the DATE argument is a whole number and the UT1 argument + lies in the range $[\,0,\,1\,]$, or vice versa. +
3. +
See also the routine sla_GMST, which accepts the UT1 as a single + argument. Compared with sla_GMST, the extra numerical precision + delivered by the present routine is unlikely to be important in + an absolute sense, but may be useful when critically comparing + algorithms and in applications where two sidereal times close + together are differenced. +
+
+ +next + +up + +previous +
+ Next: SLA_GRESID - Gaussian Residual +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GMST - UT to GMST +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node117.html b/src/slalib/sun67.htx/node117.html new file mode 100644 index 0000000..980f93a --- /dev/null +++ b/src/slalib/sun67.htx/node117.html @@ -0,0 +1,92 @@ + + + + +SLA_GRESID - Gaussian Residual + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_H2E - Az,El to +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GMSTA - UT to GMST (extra precision) +

+

+

SLA_GRESID - Gaussian Residual +   +

+
+
ACTION: +
Generate pseudo-random normal deviate or Gaussian residual. +
CALL: +
R = sla_GRESID (S) +

+

+
GIVEN: +
+
+ + + + + +
SRstandard deviation
+

+
NOTES: +
+
1. +
The results of many calls to this routine will be +normally distributed with mean zero and standard deviation S. +
2. +
The Box-Muller algorithm is used. +
3. +
The implementation is machine-dependent. +
+

+
REFERENCE: +
Ahrens & Dieter, 1972. Comm.A.C.M. 15, 873. +
+
+ +next + +up + +previous +
+ Next: SLA_H2E - Az,El to +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GMSTA - UT to GMST (extra precision) +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node118.html b/src/slalib/sun67.htx/node118.html new file mode 100644 index 0000000..83df4b3 --- /dev/null +++ b/src/slalib/sun67.htx/node118.html @@ -0,0 +1,146 @@ + + + + +SLA_H2E - Az,El to + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_H2FK5 - Hipparcos to FK5 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GRESID - Gaussian Residual +

+

+

    +
+SLA_H2E - Az,El to $h,\delta$

+
+
ACTION: +
Horizon to equatorial coordinates +(single precision). +

CALL: +
CALL sla_H2E (AZ, EL, PHI, HA, DEC) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
AZRazimuth (radians)
ELRelevation (radians)
PHIRlatitude (radians)
+

+
RETURNED: +
+
+ + + + + + + + + +
HARhour angle (radians)
DECRdeclination (radians)
+

+
NOTES: +
+
1. +
The sign convention for azimuth is north zero, east $+\pi/2$.
2. +
HA is returned in the range $\pm \pi$. Declination is returned +in the range $\pm \pi$.
3. +
The latitude is (in principle) geodetic. In critical + applications, corrections for polar motion should be applied + (see sla_POLMO). +
4. +
In some applications it will be important to specify the + correct type of elevation in order to produce the required + type of $[\,h,\delta\,]$. In particular, it may be important to + distinguish between the elevation as affected by refraction, + which will yield the observed $[\,h,\delta\,]$, and the elevation + in vacuo, which will yield the topocentric + $[\,h,\delta\,]$. If the + effects of diurnal aberration can be neglected, the + topocentric $[\,h,\delta\,]$ may be used as an approximation to the + apparent $[\,h,\delta\,]$.
5. +
No range checking of arguments is carried out. +
6. +
In applications which involve many such calculations, rather + than calling the present routine it will be more efficient to + use inline code, having previously computed fixed terms such + as sine and cosine of latitude. +
+
+ +next + +up + +previous +
+ Next: SLA_H2FK5 - Hipparcos to FK5 +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_GRESID - Gaussian Residual +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node119.html b/src/slalib/sun67.htx/node119.html new file mode 100644 index 0000000..9133db9 --- /dev/null +++ b/src/slalib/sun67.htx/node119.html @@ -0,0 +1,188 @@ + + + + +SLA_H2FK5 - Hipparcos to FK5 + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_HFK5Z - Hipparcos to FK5, no P.M. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_H2E - Az,El to +

+

+

SLA_H2FK5 - Hipparcos to FK5 +   +

+
+
ACTION: +
Transform a Hipparcos star position and proper motion +into the FK5 (J2000) frame. +

CALL: +
CALL sla_H2FK5 (RH,DH,DRH,DDH,R5,D5,DR5,DD5) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
RHDHipparcos $\alpha$ (radians)
DHDHipparcos $\delta$ (radians)
DRHDHipparcos proper motion in $\alpha$(radians per Julian year)
DDHDHipparcos proper motion in $\delta$(radians per Julian year)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
R5DJ2000.0 FK5 $\alpha$ (radians)
D5DJ2000.0 FK5 $\delta$ (radians)
DR5DJ2000.0 FK5 proper motion in $\alpha$(radians per Julian year)
DD5DFK5 J2000.0 proper motion in $\delta$(radians per Julian year)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
The FK5 to Hipparcos + transformation consists of a pure rotation and spin; + zonal errors in the FK5 catalogue are not taken into account. +
3. +
The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin + values are as follows (see reference): +


+
+
+

             + + + + + + + + + + + + + + + + + + + + + +
 orientation   spin   
x-19.9     -0.30  
y-9.1     +0.60  
z+22.9     +0.70  
 mas      mas/y 
+


+
+
+
+

+These orientation and spin components are interpreted as + axial vectors. An axial vector points at the pole of + the rotation and its length is the amount of rotation in radians. +

4. +
See also sla_FK52H, sla_FK5HZ, sla_HFK5Z. +
+

+
REFERENCE: +
Feissel, M. & Mignard, F., 1998., Astron.Astrophys. 331, L33-L36. +
+
+ +next + +up + +previous +
+ Next: SLA_HFK5Z - Hipparcos to FK5, no P.M. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_H2E - Az,El to +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node12.html b/src/slalib/sun67.htx/node12.html new file mode 100644 index 0000000..d75415d --- /dev/null +++ b/src/slalib/sun67.htx/node12.html @@ -0,0 +1,75 @@ + + + + +LINKING + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SUBPROGRAM SPECIFICATIONS +
+Up: SLALIB Positional Astronomy Library +
+ Previous: Acknowledgements +

+

+

+LINKING +

+

+On Unix systems (Sun, DEC Alpha etc.): +

%  f77 progname.o -L/star/lib `sla_link` -o progname +
+(The above assumes that all Starlink directories have been added to +the LD_LIBRARY_PATH and PATH environment variables +as described in SUN/202.) +

+On VAX/VMS: +

$  LINK progname,SLALIB_DIR:SLALIB/LIB +
+

+
+

+

+ +next + +up + +previous +
+ Next: SUBPROGRAM SPECIFICATIONS +
+Up: SLALIB Positional Astronomy Library +
+ Previous: Acknowledgements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node120.html b/src/slalib/sun67.htx/node120.html new file mode 100644 index 0000000..ffd038a --- /dev/null +++ b/src/slalib/sun67.htx/node120.html @@ -0,0 +1,190 @@ + + + + +SLA_HFK5Z - Hipparcos to FK5, no P.M. + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_IMXV - Apply 3D Reverse Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_H2FK5 - Hipparcos to FK5 +

+

+

SLA_HFK5Z - Hipparcos to FK5, no P.M. +   +

+
+
ACTION: +
Transform a Hipparcos star position +into the FK5 (J2000) frame assuming zero Hipparcos proper motion. +

CALL: +
CALL sla_HFK5Z (RH,DH,EPOCH,R5,D5,DR5,DD5) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
RHDHipparcos $\alpha$ (radians)
DHDHipparcos $\delta$ (radians)
EPOCHDJulian epoch (TDB)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
R5DJ2000.0 FK5 $\alpha$ (radians)
D5DJ2000.0 FK5 $\delta$ (radians)
DR5DJ2000.0 FK5 proper motion in $\alpha$(radians per Julian year)
DD5DFK5 J2000.0 proper motion in $\delta$(radians per Julian year)
+

+
NOTES: +
+
1. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are per year rather than per century. +
2. +
The FK5 to Hipparcos + transformation consists of a pure rotation and spin; + zonal errors in the FK5 catalogue are not taken into account. +
3. +
The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin + values are as follows (see reference): +


+
+
+

             + + + + + + + + + + + + + + + + + + + + + +
 orientation   spin   
x-19.9     -0.30  
y-9.1     +0.60  
z+22.9     +0.70  
 mas      mas/y 
+


+
+
+
+

+These orientation and spin components are interpreted as + axial vectors. An axial vector points at the pole of + the rotation and its length is the amount of rotation in radians. + The order of the rotations, which are very small, +

4. +
It was the intention that Hipparcos should be a close + approximation to an inertial frame, so that distant objects + have zero proper motion; such objects have (in general) + non-zero proper motion in FK5, and this routine returns those + fictitious proper motions. +
5. +
The position returned by this routine is in the FK5 J2000 + reference frame but at Julian epoch EPOCH. +
6. +
See also sla_FK52H, sla_FK5HZ, sla_H2FK5. +
+

+
REFERENCE: +
Feissel, M. & Mignard, F., 1998., Astron.Astrophys. 331, L33-L36. +
+
+ +next + +up + +previous +
+ Next: SLA_IMXV - Apply 3D Reverse Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_H2FK5 - Hipparcos to FK5 +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node121.html b/src/slalib/sun67.htx/node121.html new file mode 100644 index 0000000..68ace5b --- /dev/null +++ b/src/slalib/sun67.htx/node121.html @@ -0,0 +1,118 @@ + + + + +SLA_IMXV - Apply 3D Reverse Rotation + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_INTIN - Decode an Integer Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_HFK5Z - Hipparcos to FK5, no P.M. +

+

+

SLA_IMXV - Apply 3D Reverse Rotation +   +

+
+
ACTION: +
Multiply a 3-vector by the inverse of a rotation +matrix (single precision). +

CALL: +
CALL sla_IMXV (RM, VA, VB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
RMR(3,3)rotation matrix
VAR(3)vector to be rotated
+

+
RETURNED: +
+
+ + + + + +
VBR(3)result vector
+

+
NOTES: +
+
1. +
This routine performs the operation: +
b = M$^{T}\cdot$a +
+ where a and b are the 3-vectors VA and VB + respectively, and M is the $3\times3$ matrix RM. +
2. +
The main function of this routine is apply an inverse + rotation; under these circumstances, ${\bf M}$ is + orthogonal, with its inverse the same as its transpose. +
3. +
To comply with the ANSI Fortran 77 standard, VA and VB must + not be the same array. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
+
+ +next + +up + +previous +
+ Next: SLA_INTIN - Decode an Integer Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_HFK5Z - Hipparcos to FK5, no P.M. +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node122.html b/src/slalib/sun67.htx/node122.html new file mode 100644 index 0000000..b06d5d3 --- /dev/null +++ b/src/slalib/sun67.htx/node122.html @@ -0,0 +1,170 @@ + + + + +SLA_INTIN - Decode an Integer Number + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_INVF - Invert Linear Model +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_IMXV - Apply 3D Reverse Rotation +

+

+

SLA_INTIN - Decode an Integer Number +   +

+
+
ACTION: +
Convert free-format input into an integer. +
CALL: +
CALL sla_INTIN (STRING, NSTRT, IRESLT, JFLAG) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
STRINGCstring containing number to be decoded
NSTRTIpointer to where decoding is to commence
IRESLTIcurrent value of result
+

+
RETURNED: +
+
+ + + + + + + + + + + + + +
NSTRTIadvanced to next number
IRESLTIresult
JFLAGIstatus: -1 = -OK, 0 = +OK, 1 = null result, 2 = error
+

+
NOTES: +
+
1. +
The reason sla_INTIN has separate `OK' status values +for + and - is to enable minus zero to be detected. +This is of crucial importance + when decoding mixed-radix numbers. For example, an angle + expressed as degrees, arcminutes and arcseconds may have a + leading minus sign but a zero degrees field. +
2. +
A TAB is interpreted as a space. n.b. The test for TAB is + ASCII-specific. +
3. +
The basic format is the sequence of fields $\pm n$, where $\pm$ is a sign + character `+' or `-', and n means a string of decimal digits. +
4. +
Spaces: +
    +
  • Leading spaces are ignored. +
  • Spaces between the sign and the number are allowed. +
  • Trailing spaces are ignored; the first signifies + end of decoding and subsequent ones are skipped. +
+
5. +
Delimiters: +
    +
  • Any character other than +,-,0-9 or space may be + used to signal the end of the number and terminate decoding. +
  • Comma is recognized by sla_INTIN as a special case; it + is skipped, leaving the pointer on the next character. See + 9, below. +
  • Decoding will in all cases terminate if end of string + is reached. +
+
6. +
The sign is optional. The default is +. +
7. +
A null result occurs when the string of characters + being decoded does not begin with +,- or 0-9, or + consists entirely of spaces. When this condition is + detected, JFLAG is set to 1 and IRESLT is left untouched. +
8. +
NSTRT = 1 for the first character in the string. +
9. +
On return from sla_INTIN, NSTRT is set ready for the next + decode - following trailing blanks and any comma. If a + delimiter other than comma is being used, NSTRT must be + incremented before the next call to sla_INTIN, otherwise + all subsequent calls will return a null result. +
10. +
Errors (JFLAG=2) occur when: +
    +
  • there is a + or - but no number; or +
  • the number is greater than 231-1. +
+
11. +
When an error has been detected, NSTRT is left + pointing to the character following the last + one used before the error came to light. +
12. +
See also sla_FLOTIN and sla_DFLTIN. +
+
+ +next + +up + +previous +
+ Next: SLA_INVF - Invert Linear Model +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_IMXV - Apply 3D Reverse Rotation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node123.html b/src/slalib/sun67.htx/node123.html new file mode 100644 index 0000000..a3d1a77 --- /dev/null +++ b/src/slalib/sun67.htx/node123.html @@ -0,0 +1,122 @@ + + + + +SLA_INVF - Invert Linear Model + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_KBJ - Select Epoch Prefix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_INTIN - Decode an Integer Number +

+

+

SLA_INVF - Invert Linear Model +   +

+
+
ACTION: +
Invert a linear model of the type produced by the +sla_FITXY routine. +

CALL: +
CALL sla_INVF (FWDS,BKWDS,J) +

+

+
GIVEN: +
+
+ + + + + +
FWDSD(6)model coefficients
+

+
RETURNED: +
+
+ + + + + + + + + +
BKWDSD(6)inverse model
JIstatus: 0 = OK, -1 = no inverse
+

+
NOTES: +
+
1. +
The models relate two sets of $[\,x,y\,]$ coordinates as follows. +Naming the six elements of FWDS a,b,c,d,e & f, +where two sets of coordinates [x1,y1] and + $[x_{2},y_{2}\,]$ are related thus: +
x2 = a + bx1 + cy1
+ y2 = d + ex1 + fy1
+ The present routine generates a new set of coefficients + p,q,r,s,t & u (the array BKWDS) such that: +
x1 = p + qx2 + ry2
+ y1 = s + tx2 + uy2
+
2. +
Two successive calls to this routine will deliver a set + of coefficients equal to the starting values. +
3. +
To comply with the ANSI Fortran 77 standard, FWDS and BKWDS must + not be the same array. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
4. +
See also sla_FITXY, sla_PXY, sla_XY2XY, sla_DCMPF. +
+
+ +next + +up + +previous +
+ Next: SLA_KBJ - Select Epoch Prefix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_INTIN - Decode an Integer Number +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node124.html b/src/slalib/sun67.htx/node124.html new file mode 100644 index 0000000..6337e94 --- /dev/null +++ b/src/slalib/sun67.htx/node124.html @@ -0,0 +1,104 @@ + + + + +SLA_KBJ - Select Epoch Prefix + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_M2AV - Rotation Matrix to Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_INVF - Invert Linear Model +

+

+

SLA_KBJ - Select Epoch Prefix +   +

+
+
ACTION: +
Select epoch prefix `B' or `J'. +
CALL: +
CALL sla_KBJ (JB, E, K, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
JBIsla_DBJIN prefix status: 0=none, 1=`B', 2=`J'
EDepoch - Besselian or Julian
+

+
RETURNED: +
+
+ + + + + + + + + +
KC`B' or `J'
JIstatus: 0=OK
+

+
NOTE: +
The routine is mainly intended for use in conjunction with the +sla_DBJIN routine. If the value of JB indicates that an explicit + B or J prefix was detected by sla_DBJIN, a `B' or `J' + is returned to match. If JB indicates that no explicit B or J + was supplied, the choice is made on the basis of the epoch + itself; B is assumed for E <1984, otherwise J. +
+
+ +next + +up + +previous +
+ Next: SLA_M2AV - Rotation Matrix to Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_INVF - Invert Linear Model +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node125.html b/src/slalib/sun67.htx/node125.html new file mode 100644 index 0000000..2542649 --- /dev/null +++ b/src/slalib/sun67.htx/node125.html @@ -0,0 +1,107 @@ + + + + +SLA_M2AV - Rotation Matrix to Axial Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MAP - Mean to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_KBJ - Select Epoch Prefix +

+

+

SLA_M2AV - Rotation Matrix to Axial Vector +   +

+
+
ACTION: +
From a rotation matrix, determine the corresponding axial vector +(single precision). +

CALL: +
CALL sla_M2AV (RMAT, AXVEC) +

+

+
GIVEN: +
+
+ + + + + +
RMATR(3,3)rotation matrix
+

+
RETURNED: +
+
+ + + + + +
AXVECR(3)axial vector (radians)
+

+
NOTES: +
+
1. +
A rotation matrix describes a rotation about some arbitrary axis. +The axis is called the Euler axis, and the angle through +which the reference frame rotates is called the Euler angle. + The axial vector returned by this routine has the same + direction as the Euler axis, and its magnitude is the Euler angle + in radians. +
2. +
The magnitude and direction of the axial vector can be separated + by means of the routine sla_VN. +
3. +
The reference frame rotates clockwise as seen looking along + the axial vector from the origin. +
4. +
If RMAT is null, so is the result. +
+
+ +next + +up + +previous +
+ Next: SLA_MAP - Mean to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_KBJ - Select Epoch Prefix +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node126.html b/src/slalib/sun67.htx/node126.html new file mode 100644 index 0000000..abe5fb6 --- /dev/null +++ b/src/slalib/sun67.htx/node126.html @@ -0,0 +1,157 @@ + + + + +SLA_MAP - Mean to Apparent + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MAPPA - Mean to Apparent Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_M2AV - Rotation Matrix to Axial Vector +

+

+

SLA_MAP - Mean to Apparent +   +

+
+
ACTION: +
Transform star $[\,\alpha,\delta\,]$ from mean place to geocentric apparent. +The reference frames and timescales used are post IAU 1976. +

CALL: +
CALL sla_MAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
RM,DMDmean $[\,\alpha,\delta\,]$ (radians)
PR,PDDproper motions: $[\,\alpha,\delta\,]$ changes per Julian year
PXDparallax (arcsec)
RVDradial velocity (km s-1, +ve if receding)
EQDepoch and equinox of star data (Julian)
DATEDTDB for apparent place (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
RA,DADapparent $[\,\alpha,\delta\,]$ (radians)
+

+
NOTES: +
+
1. +
EQ is the Julian epoch specifying both the reference +frame and the epoch of the position - usually 2000. +For positions where the epoch and equinox are + different, use the routine sla_PM to apply proper + motion corrections before using this routine. +
2. +
The distinction between the required TDB and TT is + always negligible. Moreover, for all but the most + critical applications UTC is adequate. +
3. +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than + $\dot{\alpha}\cos\delta$, and are per year rather than per century. +
4. +
This routine may be wasteful for some applications + because it recomputes the Earth position/velocity and + the precession/nutation matrix each time, and because + it allows for parallax and proper motion. Where + multiple transformations are to be carried out for one + epoch, a faster method is to call the sla_MAPPA routine + once and then either the sla_MAPQK routine (which includes + parallax and proper motion) or sla_MAPQKZ (which assumes + zero parallax and FK5 proper motion). +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_MAPPA - Mean to Apparent Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_M2AV - Rotation Matrix to Axial Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node127.html b/src/slalib/sun67.htx/node127.html new file mode 100644 index 0000000..6ed5222 --- /dev/null +++ b/src/slalib/sun67.htx/node127.html @@ -0,0 +1,159 @@ + + + + +SLA_MAPPA - Mean to Apparent Parameters + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MAPQK - Quick Mean to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAP - Mean to Apparent +

+

+

SLA_MAPPA - Mean to Apparent Parameters +   +

+
+
ACTION: +
Compute star-independent parameters in preparation for +conversions between mean place and geocentric apparent place. + The parameters produced by this routine are required in the + parallax, light deflection, aberration, and precession/nutation + parts of the mean/apparent transformations. + The reference frames and timescales used are post IAU 1976. +

CALL: +
CALL sla_MAPPA (EQ, DATE, AMPRMS) +

+

+
GIVEN: +
+
+ + + + + + + + + +
EQDepoch of mean equinox to be used (Julian)
DATEDTDB (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
AMPRMSD(21)star-independent mean-to-apparent parameters:
(1)time interval for proper motion (Julian years)
(2-4)barycentric position of the Earth (AU)
(5-7)heliocentric direction of the Earth (unit vector)
(8)(gravitational radius of +Sun)$\times 2 / $(Sun-Earth distance)
(9-11)v: barycentric Earth velocity in units of c
(12)$\sqrt{1-\left\vert\mbox{\bf v}\right\vert^2}$
(13-21)precession/nutation $3\times3$ matrix
+

+
NOTES: +
+
1. +
For DATE, the distinction between the required TDB and TT +is always negligible. Moreover, for all but the most +critical applications UTC is adequate. +
2. +
The accuracy of the routines using the parameters AMPRMS is + limited by the routine sla_EVP, used here to compute the + Earth position and velocity by the methods of Stumpff. + The maximum error in the resulting aberration corrections is + about 0.3 milliarcsecond. +
3. +
The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to + the mean equinox and equator of epoch EQ. +
4. +
The parameters produced by this routine are used by + sla_MAPQK and sla_MAPQKZ. +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_MAPQK - Quick Mean to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAP - Mean to Apparent +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node128.html b/src/slalib/sun67.htx/node128.html new file mode 100644 index 0000000..b705fa9 --- /dev/null +++ b/src/slalib/sun67.htx/node128.html @@ -0,0 +1,187 @@ + + + + +SLA_MAPQK - Quick Mean to Apparent + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MAPQKZ - Quick Mean-Appt, no PM etc. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAPPA - Mean to Apparent Parameters +

+

+

SLA_MAPQK - Quick Mean to Apparent +   +

+
+
ACTION: +
Quick mean to apparent place: transform a star $[\,\alpha,\delta\,]$ from +mean place to geocentric apparent place, given the + star-independent parameters. The reference frames and + timescales used are post IAU 1976. +

CALL: +
CALL sla_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
RM,DMDmean $[\,\alpha,\delta\,]$ (radians)
PR,PDDproper motions: $[\,\alpha,\delta\,]$ changes per Julian year
PXDparallax (arcsec)
RVDradial velocity (km s-1, +ve if receding)
AMPRMSD(21)star-independent mean-to-apparent parameters:
(1)time interval for proper motion (Julian years)
(2-4)barycentric position of the Earth (AU)
(5-7)heliocentric direction of the Earth (unit vector)
(8)(gravitational radius of +Sun)$\times 2 / $(Sun-Earth distance)
(9-11)v: barycentric Earth velocity in units of c
(12)$\sqrt{1-\left\vert\mbox{\bf v}\right\vert^2}$
(13-21)precession/nutation $3\times3$ matrix
+

+
RETURNED: +
+
+ + + + + +
RA,DAD apparent $[\,\alpha,\delta\,]$ (radians)
+

+
NOTES: +
+
1. +
Use of this routine is appropriate when efficiency is important +and where many star positions, all referred to the same equator +and equinox, are to be transformed for one epoch. The + star-independent parameters can be obtained by calling the + sla_MAPPA routine. +
2. +
If the parallax and proper motions are zero the sla_MAPQKZ + routine can be used instead. +
3. +
The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to + the mean equinox and equator of epoch EQ. +
4. +
Strictly speaking, the routine is not valid for solar-system + sources, though the error will usually be extremely small. + However, to prevent gross errors in the case where the + position of the Sun is specified, the gravitational + deflection term is restrained within about $920\hspace{-0.05em}^{'\hspace{-0.1em}'}$ of the + centre of the Sun's disc. The term has a maximum value of + about + $1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.85$ at this radius, and decreases to zero as + the centre of the disc is approached. +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_MAPQKZ - Quick Mean-Appt, no PM etc. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAPPA - Mean to Apparent Parameters +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node129.html b/src/slalib/sun67.htx/node129.html new file mode 100644 index 0000000..6cb5fed --- /dev/null +++ b/src/slalib/sun67.htx/node129.html @@ -0,0 +1,175 @@ + + + + +SLA_MAPQKZ - Quick Mean-Appt, no PM etc. + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MOON - Approx Moon Pos/Vel +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAPQK - Quick Mean to Apparent +

+

+

SLA_MAPQKZ - Quick Mean-Appt, no PM etc. +   +

+
+
ACTION: +
Quick mean to apparent place: transform a star $[\,\alpha,\delta\,]$ from +mean place to geocentric apparent place, given the + star-independent parameters, and assuming zero parallax + and FK5 proper motion. + The reference frames and timescales used are post IAU 1976. +

CALL: +
CALL sla_MAPQKZ (RM, DM, AMPRMS, RA, DA) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
RM,DMDmean $[\,\alpha,\delta\,]$ (radians)
AMPRMSD(21)star-independent mean-to-apparent parameters:
(1)time interval for proper motion (Julian years)
(2-4)barycentric position of the Earth (AU)
(5-7)heliocentric direction of the Earth (unit vector)
(8)(gravitational radius of +Sun)$\times 2 / $(Sun-Earth distance)
(9-11)v: barycentric Earth velocity in units of c
(12)$\sqrt{1-\left\vert\mbox{\bf v}\right\vert^2}$
(13-21)precession/nutation $3\times3$ matrix
+

+
RETURNED: +
+
+ + + + + +
RA,DADapparent $[\,\alpha,\delta\,]$ (radians)
+

+
NOTES: +
+
1. +
Use of this routine is appropriate when efficiency is important +and where many star positions, all with parallax and proper +motion either zero or already allowed for, and all referred to + the same equator and equinox, are to be transformed for one + epoch. The star-independent parameters can be obtained by + calling the sla_MAPPA routine. +
2. +
The corresponding routine for the case of non-zero parallax + and FK5 proper motion is sla_MAPQK. +
3. +
The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to the + mean equinox and equator of epoch EQ. +
4. +
Strictly speaking, the routine is not valid for solar-system + sources, though the error will usually be extremely small. + However, to prevent gross errors in the case where the + position of the Sun is specified, the gravitational + deflection term is restrained within about $920\hspace{-0.05em}^{'\hspace{-0.1em}'}$ of the + centre of the Sun's disc. The term has a maximum value of + about + $1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.85$ at this radius, and decreases to zero as + the centre of the disc is approached. +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_MOON - Approx Moon Pos/Vel +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAPQK - Quick Mean to Apparent +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node13.html b/src/slalib/sun67.htx/node13.html new file mode 100644 index 0000000..c8106bf --- /dev/null +++ b/src/slalib/sun67.htx/node13.html @@ -0,0 +1,489 @@ + + + + +SUBPROGRAM SPECIFICATIONS + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ADDET - Add E-terms of Aberration +
+Up: SLALIB Positional Astronomy Library +
+ Previous: LINKING +

+

+

+SUBPROGRAM SPECIFICATIONS +

+


+ +  + + +
+ +next + +up + +previous +
+ Next: SLA_ADDET - Add E-terms of Aberration +
+Up: SLALIB Positional Astronomy Library +
+ Previous: LINKING +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node130.html b/src/slalib/sun67.htx/node130.html new file mode 100644 index 0000000..99d6086 --- /dev/null +++ b/src/slalib/sun67.htx/node130.html @@ -0,0 +1,140 @@ + + + + +SLA_MOON - Approx Moon Pos/Vel + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MXM - Multiply Matrices +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAPQKZ - Quick Mean-Appt, no PM etc. +

+

+

SLA_MOON - Approx Moon Pos/Vel +   +

+
+
ACTION: +
Approximate geocentric position and velocity of the Moon +(single precision). +

CALL: +
CALL sla_MOON (IY, ID, FD, PV) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IYIyear
IDIday in year (1 = Jan 1st)
FDR fraction of day
+

+
RETURNED: +
+
+ + + + + +
PVR(6)Moon $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, mean equator and equinox of +date (AU, AU s-1)
+

+
NOTES: +
+
1. +
The date and time is TDB (loosely ET) in a Julian calendar +which has been aligned to the ordinary Gregorian +calendar for the interval 1900 March 1 to 2100 February 28. + The year and day can be obtained by calling sla_CALYD or + sla_CLYD. +
2. +
The position is accurate to better than 0.5 arcminute + in direction and 1000 km in distance. The velocity + is accurate to better than + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ per hour in direction + and 4 metres per socond in distance. (RMS figures with respect + to JPL DE200 for the interval 1960-2025 are $14\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ per hour in longitude, $9\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$

+per hour in latitude, 350 km and 2 metres per second in distance.) + Note that the distance accuracy is comparatively poor because this + routine is principally intended for computing topocentric direction. +

3. +
This routine is only a partial implementation of the original + Meeus algorithm (reference below), which offers 4 times the + accuracy in direction and 20 times the accuracy in distance + when fully implemented (as it is in sla_DMOON). +
+

+
REFERENCE: +
Meeus, l'Astronomie, June 1984, p348. +
+
+ +next + +up + +previous +
+ Next: SLA_MXM - Multiply Matrices +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MAPQKZ - Quick Mean-Appt, no PM etc. +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node131.html b/src/slalib/sun67.htx/node131.html new file mode 100644 index 0000000..7ee2c74 --- /dev/null +++ b/src/slalib/sun67.htx/node131.html @@ -0,0 +1,106 @@ + + + + +SLA_MXM - Multiply Matrices + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_MXV - Apply 3D Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MOON - Approx Moon Pos/Vel +

+

+

    +
+SLA_MXM - Multiply $3\times3$ Matrices +

+
+
ACTION: +
Product of two $3\times3$ matrices (single precision). +
CALL: +
CALL sla_MXM (A, B, C) +

+

+
GIVEN: +
+
+ + + + + + + + + +
AR(3,3)matrix A
BR(3,3)matrix B
+

+
RETURNED: +
+
+ + + + + +
CR(3,3)matrix result: A$\times$B
+

+
NOTE: +
To comply with the ANSI Fortran 77 standard, A, B and C must +be different arrays. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
+
+ +next + +up + +previous +
+ Next: SLA_MXV - Apply 3D Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MOON - Approx Moon Pos/Vel +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node132.html b/src/slalib/sun67.htx/node132.html new file mode 100644 index 0000000..5084d3d --- /dev/null +++ b/src/slalib/sun67.htx/node132.html @@ -0,0 +1,117 @@ + + + + +SLA_MXV - Apply 3D Rotation + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_NUT - Nutation Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MXM - Multiply Matrices +

+

+

SLA_MXV - Apply 3D Rotation +   +

+
+
ACTION: +
Multiply a 3-vector by a rotation matrix (single precision). +
CALL: +
CALL sla_MXV (RM, VA, VB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
RMR(3,3)rotation matrix
VAR(3)vector to be rotated
+

+
RETURNED: +
+
+ + + + + +
VBR(3)result vector
+

+
NOTES: +
+
1. +
This routine performs the operation: +
b = M$\cdot$a +
+ where a and b are the 3-vectors VA and VB + respectively, and M is the $3\times3$ matrix RM. +
2. +
The main function of this routine is apply a + rotation; under these circumstances, ${\bf M}$ is a + proper real orthogonal matrix. +
3. +
To comply with the ANSI Fortran 77 standard, VA and VB must + not be the same array. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
+
+ +next + +up + +previous +
+ Next: SLA_NUT - Nutation Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MXM - Multiply Matrices +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node133.html b/src/slalib/sun67.htx/node133.html new file mode 100644 index 0000000..a849a15 --- /dev/null +++ b/src/slalib/sun67.htx/node133.html @@ -0,0 +1,111 @@ + + + + +SLA_NUT - Nutation Matrix + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_NUTC - Nutation Components +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MXV - Apply 3D Rotation +

+

+

SLA_NUT - Nutation Matrix +   +

+
+
ACTION: +
Form the matrix of nutation (IAU 1980 theory) for a given date. +
CALL: +
CALL sla_NUT (DATE, RMATN) +

+

+
GIVEN: +
+
+ + + + + +
DATEDTDB (formerly ET) as Modified Julian Date +(JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
RMATND(3,3)nutation matrix
+

+
NOTE: +
The matrix is in the sense: +
vtrue = M$\cdot$vmean
+ where vtrue is the star vector relative to the + true equator and equinox of date, M is the + $3\times3$ matrix RMATN and + vmean is the star vector relative to the + mean equator and equinox of date. +
+

+
REFERENCES: +
+
1. +
Final report of the IAU Working Group on Nutation, +chairman P.K.Seidelmann, 1980. +
2. +
Kaplan, G.H., 1981. USNO circular No. 163, pA3-6. +
+
+ +next + +up + +previous +
+ Next: SLA_NUTC - Nutation Components +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_MXV - Apply 3D Rotation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node134.html b/src/slalib/sun67.htx/node134.html new file mode 100644 index 0000000..a2b5df6 --- /dev/null +++ b/src/slalib/sun67.htx/node134.html @@ -0,0 +1,102 @@ + + + + +SLA_NUTC - Nutation Components + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_OAP - Observed to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_NUT - Nutation Matrix +

+

+

SLA_NUTC - Nutation Components +   +

+
+
ACTION: +
Nutation (IAU 1980 theory): longitude & obliquity +components, and mean obliquity. +

CALL: +
CALL sla_NUTC (DATE, DPSI, DEPS, EPS0) +

+

+
GIVEN: +
+
+ + + + + +
DATEDTDB (formerly ET) as Modified Julian Date +(JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + + + + + +
DPSI,DEPSDnutation in longitude and obliquity (radians)
EPS0Dmean obliquity (radians)
+

+
REFERENCES: +
+
1. +
Final report of the IAU Working Group on Nutation, +chairman P.K.Seidelmann, 1980. +
2. +
Kaplan, G.H., 1981. USNO circular no. 163, pA3-6. +
+
+ +next + +up + +previous +
+ Next: SLA_OAP - Observed to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_NUT - Nutation Matrix +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node135.html b/src/slalib/sun67.htx/node135.html new file mode 100644 index 0000000..753bc4c --- /dev/null +++ b/src/slalib/sun67.htx/node135.html @@ -0,0 +1,319 @@ + + + + +SLA_OAP - Observed to Apparent + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_OAPQK - Quick Observed to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_NUTC - Nutation Components +

+

+

SLA_OAP - Observed to Apparent +   +

+
+
ACTION: +
Observed to apparent place. +
CALL: +
CALL sla_OAP ( + TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM, + HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
TYPEC*(*)type of coordinates - `R', `H' or `A' (see below)
OB1Dobserved Az, HA or RA (radians; Az is N=0, E=$90^{\circ}$)
OB2Dobserved zenith distance or $\delta$ (radians)
DATED UTC date/time (Modified Julian Date, JD-2400000.5)
DUTD$\Delta$UT: UT1-UTC (UTC seconds)
ELONGMDobserver's mean longitude (radians, east +ve)
PHIMDobserver's mean geodetic latitude (radians)
HMDobserver's height above sea level (metres)
XP,YPDpolar motion $[\,x,y\,]$ coordinates (radians)
TDKDlocal ambient temperature (degrees K; std=273.155D0)
PMBDlocal atmospheric pressure (mB; std=1013.25D0)
RHDlocal relative humidity (in the range 0D0-1D0)
WLDeffective wavelength ($\mu{\rm m}$, e.g. 0.55D0)
TLRDtropospheric lapse rate (degrees K per metre, +e.g. 0.0065D0)
+

+
RETURNED: +
+
+ + + + + +
RAP,DAPDgeocentric apparent $[\,\alpha,\delta\,]$
+

+
NOTES: +
+
1. +
Only the first character of the TYPE argument is significant. +`R' or `r' indicates that OBS1 and OBS2 are the observed Right +Ascension and Declination; `H' or `h' indicates that they are + Hour Angle (west +ve) and Declination; anything else (`A' or + `a' is recommended) indicates that OBS1 and OBS2 are Azimuth + (north zero, east is $90^{\circ}$) and Zenith Distance. (Zenith + distance is used rather than elevation in order to reflect the + fact that no allowance is made for depression of the horizon.) +
2. +
The accuracy of the result is limited by the corrections for + refraction. Providing the meteorological parameters are + known accurately and there are no gross local effects, the + predicted azimuth and elevation should be within about +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ for $\zeta<70^{\circ}$. Even + at a topocentric zenith distance of + $90^{\circ}$, the accuracy in elevation should be better than + 1 arcminute; useful results are available for a further + $3^{\circ}$, beyond which the sla_REFRO routine returns a + fixed value of the refraction. The complementary + routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK) + are self-consistent to better than 1 microarcsecond all over + the celestial sphere. +

3. +
It is advisable to take great care with units, as even + unlikely values of the input parameters are accepted and + processed in accordance with the models used. +
4. +
Observed $[\,Az,El~]$ means the position that would be seen by a + perfect theodolite located at the observer. This is + related to the observed $[\,h,\delta\,]$ via the standard rotation, using + the geodetic latitude (corrected for polar motion), while the + observed HA and RA are related simply through the local + apparent ST. Observed $[\,\alpha,\delta\,]$ or $[\,h,\delta\,]$ thus means the + position that would be seen by a perfect equatorial located + at the observer and with its polar axis aligned to the + Earth's axis of rotation (n.b. not to the refracted pole). + By removing from the observed place the effects of + atmospheric refraction and diurnal aberration, the + geocentric apparent $[\,\alpha,\delta\,]$ is obtained. +
5. +
Frequently, mean rather than apparent + $[\,\alpha,\delta\,]$ will be required, + in which case further transformations will be necessary. The + sla_AMP etc. routines will convert + the apparent $[\,\alpha,\delta\,]$ produced + by the present routine into an FK5 J2000 mean place, by + allowing for the Sun's gravitational lens effect, annual + aberration, nutation and precession. Should FK4 B1950 + coordinates be needed, the routines sla_FK524 etc. will also + need to be applied. +
6. +
To convert to apparent $[\,\alpha,\delta\,]$ the coordinates read from a + real telescope, corrections would have to be applied for + encoder zero points, gear and encoder errors, tube flexure, + the position of the rotator axis and the pointing axis + relative to it, non-perpendicularity between the mounting + axes, and finally for the tilt of the azimuth or polar axis + of the mounting (with appropriate corrections for mount + flexures). Some telescopes would, of course, exhibit other + properties which would need to be accounted for at the + appropriate point in the sequence. +
7. +
The star-independent apparent-to-observed-place parameters + in AOPRMS may be computed by means of the sla_AOPPA routine. + If nothing has changed significantly except the time, the + sla_AOPPAT routine may be used to perform the requisite + partial recomputation of AOPRMS. +
8. +
The DATE argument is UTC expressed as an MJD. This is, + strictly speaking, wrong, because of leap seconds. However, + as long as the $\Delta$UT and the UTC are consistent there + are no difficulties, except during a leap second. In this + case, the start of the 61st second of the final minute should + begin a new MJD day and the old pre-leap $\Delta$UT should + continue to be used. As the 61st second completes, the MJD + should revert to the start of the day as, simultaneously, + the $\Delta$UT changes by one second to its post-leap new value. +
9. +
The $\Delta$UT (UT1-UTC) is tabulated in IERS circulars and + elsewhere. It increases by exactly one second at the end of + each UTC leap second, introduced in order to keep $\Delta$UT + within $\pm$$0^{\rm s}\hspace{-0.3em}.9$.
10. +
IMPORTANT - TAKE CARE WITH THE LONGITUDE SIGN CONVENTION. The + longitude required by the present routine is east-positive, + in accordance with geographical convention (and right-handed). + In particular, note that the longitudes returned by the + sla_OBS routine are west-positive (as in the Astronomical + Almanac before 1984) and must be reversed in sign before use + in the present routine. +
11. +
The polar coordinates XP,YP can be obtained from IERS + circulars and equivalent publications. The + maximum amplitude is about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ . If XP,YP values + are unavailable, use XP=YP=0D0. See page B60 of the 1988 + Astronomical Almanac for a definition of the two angles. +
12. +
The height above sea level of the observing station, HM, + can be obtained from the Astronomical Almanac (Section J + in the 1988 edition), or via the routine sla_OBS. If P, + the pressure in mB, is available, an adequate + estimate of HM can be obtained from the following expression: +
HM=-29.3D0*TSL*LOG(P/1013.25D0) +
+ where TSL is the approximate sea-level air temperature in degrees K + (see Astrophysical Quantities, C.W.Allen, 3rd edition, + §52). Similarly, if the pressure P is not known, + it can be estimated from the height of the observing + station, HM as follows: +
P=1013.25D0*EXP(-HM/(29.3D0*TSL)) +
+ Note, however, that the refraction is proportional to the + pressure and that an accurate P value is important for + precise work. +
13. +
The azimuths etc. used by the present routine are with + respect to the celestial pole. Corrections from the terrestrial pole + can be computed using sla_POLMO. +
+
+ +next + +up + +previous +
+ Next: SLA_OAPQK - Quick Observed to Apparent +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_NUTC - Nutation Components +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node136.html b/src/slalib/sun67.htx/node136.html new file mode 100644 index 0000000..dbf0e88 --- /dev/null +++ b/src/slalib/sun67.htx/node136.html @@ -0,0 +1,258 @@ + + + + +SLA_OAPQK - Quick Observed to Apparent + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_OBS - Observatory Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_OAP - Observed to Apparent +

+

+

SLA_OAPQK - Quick Observed to Apparent +   +

+
+
ACTION: +
Quick observed to apparent place. +
CALL: +
CALL sla_OAPQK (TYPE, OB1, OB2, AOPRMS, RAP, DAP) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
TYPEC*(*)type of coordinates - `R', `H' or `A' (see below)
OB1Dobserved Az, HA or RA (radians; Az is N=0, E=$90^{\circ}$)
OB2Dobserved zenith distance or $\delta$ (radians)
AOPRMSD(14)star-independent apparent-to-observed parameters:
(1)geodetic latitude (radians)
(2,3)sine and cosine of geodetic latitude
(4)magnitude of diurnal aberration vector
(5)height (HM)
(6)ambient temperature (TDK)
(7)pressure (PMB)
(8)relative humidity (RH)
(9)wavelength (WL)
(10)lapse rate (TLR)
(11,12)refraction constants A and B (radians)
(13)longitude + eqn of equinoxes + +``sidereal $\Delta$UT'' (radians)
(14)local apparent sidereal time (radians)
+

+
RETURNED: +
+
+ + + + + +
RAP,DAPDgeocentric apparent $[\,\alpha,\delta\,]$
+

+
NOTES: +
+
1. +
Only the first character of the TYPE argument is significant. +`R' or `r' indicates that OBS1 and OBS2 are the observed Right +Ascension and Declination; `H' or `h' indicates that they are + Hour Angle (west +ve) and Declination; anything else (`A' or + `a' is recommended) indicates that OBS1 and OBS2 are Azimuth + (north zero, east is $90^{\circ}$) and Zenith Distance. (Zenith + distance is used rather than elevation in order to reflect the + fact that no allowance is made for depression of the horizon.) +
2. +
The accuracy of the result is limited by the corrections for + refraction. Providing the meteorological parameters are + known accurately and there are no gross local effects, the + predicted azimuth and elevation should be within about +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ for $\zeta<70^{\circ}$. Even + at a topocentric zenith distance of + $90^{\circ}$, the accuracy in elevation should be better than + 1 arcminute; useful results are available for a further + $3^{\circ}$, beyond which the sla_REFRO routine returns a + fixed value of the refraction. The complementary + routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK) + are self-consistent to better than 1 microarcsecond all over + the celestial sphere. +

3. +
It is advisable to take great care with units, as even + unlikely values of the input parameters are accepted and + processed in accordance with the models used. +
4. +
Observed $[\,Az,El~]$ means the position that would be seen by a + perfect theodolite located at the observer. This is + related to the observed $[\,h,\delta\,]$ via the standard rotation, using + the geodetic latitude (corrected for polar motion), while the + observed HA and RA are related simply through the local + apparent ST. Observed $[\,\alpha,\delta\,]$ or $[\,h,\delta\,]$ thus means the + position that would be seen by a perfect equatorial located + at the observer and with its polar axis aligned to the + Earth's axis of rotation (n.b. not to the refracted pole). + By removing from the observed place the effects of + atmospheric refraction and diurnal aberration, the + geocentric apparent $[\,\alpha,\delta\,]$ is obtained. +
5. +
Frequently, mean rather than apparent + $[\,\alpha,\delta\,]$ will be required, + in which case further transformations will be necessary. The + sla_AMP etc. routines will convert + the apparent $[\,\alpha,\delta\,]$ produced + by the present routine into an FK5 J2000 mean place, by + allowing for the Sun's gravitational lens effect, annual + aberration, nutation and precession. Should FK4 B1950 + coordinates be needed, the routines sla_FK524 etc. will also + need to be applied. +
6. +
To convert to apparent $[\,\alpha,\delta\,]$ the coordinates read from a + real telescope, corrections would have to be applied for + encoder zero points, gear and encoder errors, tube flexure, + the position of the rotator axis and the pointing axis + relative to it, non-perpendicularity between the mounting + axes, and finally for the tilt of the azimuth or polar axis + of the mounting (with appropriate corrections for mount + flexures). Some telescopes would, of course, exhibit other + properties which would need to be accounted for at the + appropriate point in the sequence. +
7. +
The star-independent apparent-to-observed-place parameters + in AOPRMS may be computed by means of the sla_AOPPA routine. + If nothing has changed significantly except the time, the + sla_AOPPAT routine may be used to perform the requisite + partial recomputation of AOPRMS. +
8. +
The azimuths etc. used by the present routine are with + respect to the celestial pole. Corrections from the terrestrial pole + can be computed using sla_POLMO. +
+
+ +next + +up + +previous +
+ Next: SLA_OBS - Observatory Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_OAP - Observed to Apparent +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node137.html b/src/slalib/sun67.htx/node137.html new file mode 100644 index 0000000..eda8158 --- /dev/null +++ b/src/slalib/sun67.htx/node137.html @@ -0,0 +1,247 @@ + + + + +SLA_OBS - Observatory Parameters + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PA - to Parallactic Angle +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_OAPQK - Quick Observed to Apparent +

+

+

SLA_OBS - Observatory Parameters +   +

+
+
ACTION: +
Look up an entry in a standard list of +groundbased observing stations parameters. +

CALL: +
CALL sla_OBS (N, C, NAME, W, P, H) +

+

+
GIVEN: +
+
+ + + + + +
NInumber specifying observing station
+

+
GIVEN or RETURNED: +
+
+ + + + + +
CC*(*)identifier specifying observing station
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
NAMEC*(*)name of specified observing station
WDlongitude (radians, west +ve)
PDgeodetic latitude (radians, north +ve)
HDheight above sea level (metres)
+

+
NOTES: +
+
1. +
Station identifiers C may be up to 10 characters long, +and station names NAME may be up to 40 characters long. +
2. +
C and N are alternative ways of specifying the observing + station. The C option, which is the most generally useful, + may be selected by specifying an N value of zero or less. + If N is 1 or more, the parameters of the Nth station + in the currently supported list are interrogated, and + the station identifier C is returned as well as NAME, W, + P and H. +
3. +
If the station parameters are not available, either because + the station identifier C is not recognized, or because an + N value greater than the number of stations supported is + given, a name of `?' is returned and W, P and H are left in + their current states. +
4. +
Programs can obtain a list of all currently supported + stations by calling the routine repeatedly, with N=1,2,3... + When NAME=`?' is seen, the list of stations has been + exhausted. The stations at the time of writing are listed + below. +
5. +
Station numbers, identifiers, names and other details are + subject to change and should not be hardwired into + application programs. +
6. +
All station identifiers C are uppercase only; lower case + characters must be converted to uppercase by the calling + program. The station names returned may contain both upper- + and lowercase. All characters up to the first space are + checked; thus an abbreviated ID will return the parameters + for the first station in the list which matches the + abbreviation supplied, and no station in the list will ever + contain embedded spaces. C must not have leading spaces. +
7. +
IMPORTANT - BEWARE OF THE LONGITUDE SIGN CONVENTION. The + longitude returned by sla_OBS is + west-positive, following the pre-1984 Astronomical + Almanac. However, this sign convention is left-handed and is + the opposite of the one now used; elsewhere in + SLALIB the preferable east-positive convention is used. In + particular, note that for use in sla_AOP, sla_AOPPA and + sla_OAP the sign of the longitude must be reversed. +
8. +
Users are urged to inform the author of any improvements + they would like to see made. For example: +
    +
  • typographical corrections +
  • more accurate parameters +
  • better station identifiers or names +
  • additional stations +
+Stations supported by sla_OBS at the time of writing: +

+ID 		 NAME 
+ 
+AAT 		 Anglo-Australian 3.9m Telescope 
+ANU2.3 		 Siding Spring 2.3 metre 
+APO3.5 		 Apache Point 3.5m 
+ARECIBO 		 Arecibo 1000 foot 
+ATCA 		 Australia Telescope Compact Array 
+BLOEMF 		 Bloemfontein 1.52 metre 
+BOSQALEGRE 		 Bosque Alegre 1.54 metre 
+CAMB1MILE 		 Cambridge 1 mile 
+CAMB5KM 		 Cambridge 5km 
+CATALINA61 		 Catalina 61 inch 
+CFHT 		 Canada-France-Hawaii 3.6m Telescope 
+CSO 		 Caltech Sub-mm Observatory, Mauna Kea 
+DAO72 		 DAO Victoria BC 1.85 metre 
+DUNLAP74 		 David Dunlap 74 inch 
+DUPONT 		 Du Pont 2.5m Telescope, Las Campanas 
+EFFELSBERG 		 Effelsberg 100 metre 
+ESO3.6 		 ESO 3.6 metre 
+ESONTT 		 ESO 3.5 metre NTT 
+ESOSCHM 		 ESO 1 metre Schmidt, La Silla 
+FCRAO 		 Five College Radio Astronomy Obs 
+FLAGSTF61 		 USNO 61 inch astrograph, Flagstaff 
+GBVA140 		 Greenbank 140 foot 
+GBVA300 		 Greenbank 300 foot 
+GEMININ 		 Gemini North 8-m telescope 
+HARVARD 		 Harvard College Observatory 1.55m 
+HPROV1.52 		 Haute Provence 1.52 metre 
+HPROV1.93 		 Haute Provence 1.93 metre 
+IRTF 		 NASA IR Telescope Facility, Mauna Kea 
+JCMT 		 JCMT 15 metre 
+JODRELL1 		 Jodrell Bank 250 foot 
+KECK1 		 Keck 10m Telescope 1 
+KECK2 		 Keck 10m Telescope 2 
+KISO 		 Kiso 1.05 metre Schmidt, Japan 
+KOTTAMIA 		 Kottamia 74 inch 
+KPNO158 		 Kitt Peak 158 inch 
+KPNO36FT 		 Kitt Peak 36 foot 
+KPNO84 		 Kitt Peak 84 inch 
+KPNO90 		 Kitt Peak 90 inch 
+LICK120 		 Lick 120 inch 
+LOWELL72 		 Perkins 72 inch, Lowell 
+LPO1 		 Jacobus Kapteyn 1m Telescope 
+LPO2.5 		 Isaac Newton 2.5m Telescope 
+LPO4.2 		 William Herschel 4.2m Telescope 
+MAUNAK88 		 Mauna Kea 88 inch 
+MCDONLD2.1 		 McDonald 2.1 metre 
+MCDONLD2.7 		 McDonald 2.7 metre 
+MMT 		 MMT, Mt Hopkins 
+MOPRA 		 ATNF Mopra Observatory 
+MTEKAR 		 Mt Ekar 1.82 metre 
+MTHOP1.5 		 Mt Hopkins 1.5 metre 
+MTLEMMON60 		 Mt Lemmon 60 inch 
+NOBEYAMA 		 Nobeyama 45 metre 
+OKAYAMA 		 Okayama 1.88 metre 
+PALOMAR200 		 Palomar 200 inch 
+PALOMAR48 		 Palomar 48-inch Schmidt 
+PALOMAR60 		 Palomar 60 inch 
+PARKES 		 Parkes 64 metre 
+QUEBEC1.6 		 Quebec 1.6 metre 
+SAAO74 		 Sutherland 74 inch 
+SANPM83 		 San Pedro Martir 83 inch 
+ST.ANDREWS 		 St Andrews University Observatory 
+STEWARD90 		 Steward 90 inch 
+STROMLO74 		 Mount Stromlo 74 inch 
+SUBARU 		 Subaru 8 metre 
+SUGARGROVE 		 Sugar Grove 150 foot 
+TAUTNBG 		 Tautenburg 2 metre 
+TAUTSCHM 		 Tautenberg 1.34 metre Schmidt 
+TIDBINBLA 		 Tidbinbilla 64 metre 
+TOLOLO1.5M 		 Cerro Tololo 1.5 metre 
+TOLOLO4M 		 Cerro Tololo 4 metre 
+UKIRT 		 UK Infra Red Telescope 
+UKST 		 UK 1.2 metre Schmidt, Siding Spring 
+USSR6 		 USSR 6 metre 
+USSR600 		 USSR 600 foot 
+VLA 		 Very Large Array
+
+
+ +next + +up + +previous +
+ Next: SLA_PA - to Parallactic Angle +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_OAPQK - Quick Observed to Apparent +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node138.html b/src/slalib/sun67.htx/node138.html new file mode 100644 index 0000000..d363298 --- /dev/null +++ b/src/slalib/sun67.htx/node138.html @@ -0,0 +1,116 @@ + + + + +SLA_PA - to Parallactic Angle + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PAV - Position-Angle Between Two Directions +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_OBS - Observatory Parameters +

+

+

    +
+SLA_PA - $h,\delta$ to Parallactic Angle +

+
+
ACTION: +
Hour angle and declination to parallactic angle +(double precision). +

CALL: +
D = sla_PA (HA, DEC, PHI) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
HADhour angle in radians (geocentric apparent)
DECDdeclination in radians (geocentric apparent)
PHIDlatitude in radians (geodetic)
+

+
RETURNED: +
+
+ + + + + +
sla_PADparallactic angle (radians, in the range $\pm \pi$)
+

+
NOTES: +
+
1. +
The parallactic angle at a point in the sky is the position +angle of the vertical, i.e. the angle between the direction to +the pole and to the zenith. In precise applications care must + be taken only to use geocentric apparent $[\,h,\delta\,]$ and to consider + separately the effects of atmospheric refraction and telescope + mount errors. +
2. +
At the pole a zero result is returned. +
+
+ +next + +up + +previous +
+ Next: SLA_PAV - Position-Angle Between Two Directions +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_OBS - Observatory Parameters +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node139.html b/src/slalib/sun67.htx/node139.html new file mode 100644 index 0000000..13d3907 --- /dev/null +++ b/src/slalib/sun67.htx/node139.html @@ -0,0 +1,117 @@ + + + + +SLA_PAV - Position-Angle Between Two Directions + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PCD - Apply Radial Distortion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PA - to Parallactic Angle +

+

+

SLA_PAV - Position-Angle Between Two Directions +   +

+
+
ACTION: +
Returns the bearing (position angle) of one celestial +direction with respect to another (single precision). +

CALL: +
R = sla_PAV (V1, V2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
V1R(3)direction cosines of one point
V2R(3)directions cosines of the other point
+

+
RETURNED: +
+
+ + + + + +
sla_PAVRposition-angle of 2nd point with respect to 1st
+

+
NOTES: +
+
1. +
The coordinate frames correspond to $[\,\alpha,\delta\,]$,$[\lambda,\phi]$ etc.. +
2. +
The result is the bearing (position angle), in radians, + of point V2 as seen + from point V1. It is in the range $\pm \pi$. The sense + is such that if V2 + is a small distance due east of V1 the result + is about $+\pi/2$. Zero is returned + if the two points are coincident. +
3. +
The routine sla_BEAR performs an equivalent function except + that the points are specified in the form of spherical coordinates. +
+
+ +next + +up + +previous +
+ Next: SLA_PCD - Apply Radial Distortion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PA - to Parallactic Angle +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node14.html b/src/slalib/sun67.htx/node14.html new file mode 100644 index 0000000..9a2b861 --- /dev/null +++ b/src/slalib/sun67.htx/node14.html @@ -0,0 +1,112 @@ + + + + +SLA_ADDET - Add E-terms of Aberration + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AFIN - Sexagesimal character string to angle +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SUBPROGRAM SPECIFICATIONS +

+

+

SLA_ADDET - Add E-terms of Aberration +   +

+
+
ACTION: +
Add the E-terms (elliptic component of annual aberration) to a +pre IAU 1976 mean place to conform to the old catalogue convention. +

CALL: +
CALL sla_ADDET (RM, DM, EQ, RC, DC) +

+

+
GIVEN: +
+
+ + + + + + + + + +
RM,DMD$[\,\alpha,\delta\,]$ without E-terms (radians)
EQDBesselian epoch of mean equator and equinox
+

+
RETURNED: +
+
+ + + + + +
RC,DCD$[\,\alpha,\delta\,]$ with E-terms included (radians)
+

+
NOTE: +
Most star positions from pre-1984 optical catalogues (or +obtained by astrometry with respect to such stars) have the + E-terms built-in. If it is necessary to convert a formal mean + place (for example a pulsar timing position) to one + consistent with such a star catalogue, then the + $[\,\alpha,\delta\,]$ should be adjusted using this routine. +
+

+
REFERENCE: +
Explanatory Supplement to the Astronomical Ephemeris, +section 2D, page 48. +
+
+ +next + +up + +previous +
+ Next: SLA_AFIN - Sexagesimal character string to angle +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SUBPROGRAM SPECIFICATIONS +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node140.html b/src/slalib/sun67.htx/node140.html new file mode 100644 index 0000000..aaf99dc --- /dev/null +++ b/src/slalib/sun67.htx/node140.html @@ -0,0 +1,148 @@ + + + + +SLA_PCD - Apply Radial Distortion + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PDA2H - H.A. for a Given Azimuth +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PAV - Position-Angle Between Two Directions +

+

+

SLA_PCD - Apply Radial Distortion +   +

+
+
ACTION: +
Apply pincushion/barrel distortion to a tangent-plane $[\,x,y\,]$.
CALL: +
CALL sla_PCD (DISCO,X,Y) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DISCODpincushion/barrel distortion coefficient
X,YDtangent-plane $[\,x,y\,]$
+

+
RETURNED: +
+
+ + + + + +
X,YDdistorted $[\,x,y\,]$
+

+
NOTES: +
+
1. +
The distortion is of the form $\rho = r (1 + c r^{2})$, where r is +the radial distance from the tangent point, c is the DISCO +argument, and $\rho$ is the radial distance in the presence of + the distortion. +
2. +
For pincushion distortion, C is +ve; for + barrel distortion, C is -ve. +
3. +
For X,Y in units of one projection radius (in the case of + a photographic plate, the focal length), the following + DISCO values apply: +


+
+
+

+ + + + + + + + + + + + + + + + + + + + + +
GeometryDISCO
astrograph0.0
Schmidt-0.3333
AAT PF doublet+147.069
AAT PF triplet+178.585
AAT f/8+21.20
JKT f/8+14.6
+


+
+
+

4. +
There is a companion routine, sla_UNPCD, which performs + an approximately inverse operation. +
+
+ +next + +up + +previous +
+ Next: SLA_PDA2H - H.A. for a Given Azimuth +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PAV - Position-Angle Between Two Directions +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node141.html b/src/slalib/sun67.htx/node141.html new file mode 100644 index 0000000..6e011b5 --- /dev/null +++ b/src/slalib/sun67.htx/node141.html @@ -0,0 +1,107 @@ + + + + +SLA_PDA2H - H.A. for a Given Azimuth + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PDQ2H - H.A. for a Given P.A. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PCD - Apply Radial Distortion +

+

+

SLA_PDA2H - H.A. for a Given Azimuth +   +

+
+
ACTION: +
Hour Angle corresponding to a given azimuth (double precision). +
CALL: +
CALL sla_PDA2H (P, D, A, H1, J1, H2, J2) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
PDlatitude
DDdeclination
ADazimuth
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
H1Dhour angle: first solution if any
J1Iflag: 0 = solution 1 is valid
H2Dhour angle: second solution if any
J2Iflag: 0 = solution 2 is valid
+
+ +next + +up + +previous +
+ Next: SLA_PDQ2H - H.A. for a Given P.A. +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PCD - Apply Radial Distortion +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node142.html b/src/slalib/sun67.htx/node142.html new file mode 100644 index 0000000..f105cf4 --- /dev/null +++ b/src/slalib/sun67.htx/node142.html @@ -0,0 +1,108 @@ + + + + +SLA_PDQ2H - H.A. for a Given P.A. + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PERMUT - Next Permutation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PDA2H - H.A. for a Given Azimuth +

+

+

SLA_PDQ2H - H.A. for a Given P.A. +   +

+
+
ACTION: +
Hour Angle corresponding to a given parallactic angle +(double precision). +

CALL: +
CALL sla_PDQ2H (P, D, Q, H1, J1, H2, J2) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
PDlatitude
DDdeclination
QDazimuth
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
H1Dhour angle: first solution if any
J1Iflag: 0 = solution 1 is valid
H2Dhour angle: second solution if any
J2Iflag: 0 = solution 2 is valid
+
+ +next + +up + +previous +
+ Next: SLA_PERMUT - Next Permutation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PDA2H - H.A. for a Given Azimuth +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node143.html b/src/slalib/sun67.htx/node143.html new file mode 100644 index 0000000..46f3e9e --- /dev/null +++ b/src/slalib/sun67.htx/node143.html @@ -0,0 +1,133 @@ + + + + +SLA_PERMUT - Next Permutation + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PERTEL - Perturbed Orbital Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PDQ2H - H.A. for a Given P.A. +

+

+

SLA_PERMUT - Next Permutation +   +

+
+
ACTION: +
Generate the next permutation of a specified number of items. +
CALL: +
CALL sla_PERMUT (N, ISTATE, IORDER, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NInumber of items: there will be N! permutations
ISTATEI(N)state, ISTATE(1)=-1 to initialize
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
ISTATEI(N)state, updated ready for next time
IORDERI(N)next permutation of numbers 1,2,...,N
JIstatus:
-1 = illegal N (zero or less is illegal)
0 = OK
+1 = no more permutations available
+

+
NOTES: +
+
1. +
This routine returns, in the IORDER array, the integers 1 to N +inclusive, in an order that depends on the current contents of +the ISTATE array. Before calling the routine for the first + time, the caller must set the first element of the ISTATE array + to -1 (any negative number will do) to cause the ISTATE array + to be fully initialized. +
2. +
The first permutation to be generated is: +
IORDER(1)=N, IORDER(2)=N-1, ..., IORDER(N)=1 +
+ This is also the permutation returned for the ``finished'' (J=1) case. + The final permutation to be generated is: +
IORDER(1)=1, IORDER(2)=2, ..., IORDER(N)=N +
+
3. +
If the ``finished'' (J=1) status is ignored, the routine continues + to deliver permutations, the pattern repeating every N! calls. +
+
+ +next + +up + +previous +
+ Next: SLA_PERTEL - Perturbed Orbital Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PDQ2H - H.A. for a Given P.A. +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node144.html b/src/slalib/sun67.htx/node144.html new file mode 100644 index 0000000..eb511e6 --- /dev/null +++ b/src/slalib/sun67.htx/node144.html @@ -0,0 +1,310 @@ + + + + +SLA_PERTEL - Perturbed Orbital Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PERTUE - Perturbed Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PERMUT - Next Permutation +

+

+

SLA_PERTEL - Perturbed Orbital Elements +   +

+
+
ACTION: +
Update the osculating elements of an asteroid or comet by +applying planetary perturbations. +

CALL: +
CALL sla_PERTEL ( + JFORM, DATE0, DATE1, + EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0, + EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1, + JSTAT) +

+

+
GIVEN (format and dates): +
+
+ + + + + + + + + + + + + + + + + + + + + +
JFORMIchoice of element set (2 or 3; Note 1)
DATE0Ddate of osculation (TT MJD) for the given
elements
DATE1Ddate of osculation (TT MJD) for the updated
elements
+

+
GIVEN (the unperturbed elements): +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
EPOCH0Depoch of the given element set +(t0 or T, TT MJD;
Note 2)
ORBI0Dinclination (i, radians)
ANODE0Dlongitude of the ascending node ($\Omega$, radians)
PERIH0Dargument of perihelion +($\omega$, radians)
AORQ0Dmean distance or perihelion distance (a or q, AU)
E0Deccentricity (e)
AM0Dmean anomaly (M, radians, JFORM=2 only)
+

+
RETURNED (the updated elements): +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
EPOCH1Depoch of the updated element set +(t0 or T,
TT MJD; Note 2)
ORBI1Dinclination (i, radians)
ANODE1Dlongitude of the ascending node ($\Omega$, radians)
PERIH1Dargument of perihelion +($\omega$, radians)
AORQ1Dmean distance or perihelion distance (a or q, AU)
E1Deccentricity (e)
AM1Dmean anomaly (M, radians, JFORM=2 only)
+

+
RETURNED (status flag): +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
JSTATIstatus:
+102 = warning, distant epoch
+101 = warning, large timespan +(>100 years)
+1 to +8 = coincident with major planet +(Note 6)
0 = OK
-1 = illegal JFORM
-2 = illegal E0
-3 = illegal AORQ0
-4 = internal error
-5 = numerical error
+

+
NOTES: +
+
1. +
Two different element-format options are supported, as follows.
+JFORM=2, suitable for minor planets: +

+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e \leq 10 )$
+
2. +
DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in + the TT timescale (formerly Ephemeris Time, ET), expressed + as Modified Julian Dates (JD-2400000.5). +
    +
  • DATE0 is the instant at which the given + (i.e. unperturbed) osculating elements are correct. +
  • DATE1 is the specified instant at which the updated osculating + elements are correct. +
  • EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1 + (respectively) for the JFORM=2 case, normally used for minor + planets. For the JFORM=3 case, the two epochs will refer to + perihelion passage and so will not, in general, be the same as + DATE0 and/or DATE1 though they may be similar to one another. +
+
3. +
The elements are with respect to the J2000 ecliptic and mean equinox. +
4. +
Unused elements (AM0 and AM1 for JFORM=3) are not accessed. +
5. +
See the sla_PERTUE routine for details of the algorithm used. +
6. +
This routine is not intended to be used for major planets, which + is why JFORM=1 is not available and why there is no opportunity + to specify either the longitude of perihelion or the daily + motion. However, if JFORM=2 elements are somehow obtained for a + major planet and supplied to the routine, sensible results will, + in fact, be produced. This happens because the sla_PERTUE routine + that is called to perform the calculations checks the separation + between the body and each of the planets and interprets a + suspiciously small value (0.001 AU) as an attempt to apply it to + the planet concerned. If this condition is detected, the + contribution from that planet is ignored, and the status is set to + the planet number (Mercury=1,...,Neptune=8) as a warning. +
+

+
REFERENCE: +
Sterne, Theodore E., An Introduction to Celestial Mechanics, +Interscience Publishers, 1960. Section 6.7, p199. +
+
+ +next + +up + +previous +
+ Next: SLA_PERTUE - Perturbed Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PERMUT - Next Permutation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node145.html b/src/slalib/sun67.htx/node145.html new file mode 100644 index 0000000..8fbb853 --- /dev/null +++ b/src/slalib/sun67.htx/node145.html @@ -0,0 +1,279 @@ + + + + +SLA_PERTUE - Perturbed Universal Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PLANEL - Planet Position from Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PERTEL - Perturbed Orbital Elements +

+

+

SLA_PERTUE - Perturbed Universal Elements +   +

+
+
ACTION: +
Update the universal elements of an asteroid or comet by +applying planetary perturbations. +

CALL: +
CALL sla_PERTUE (DATE, U, JSTAT) +

+

+
GIVEN: +
+
+ + + + + +
DATE1Dfinal epoch (TT MJD) for the updated elements
+

+
GIVEN and RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal elements (updated in place)
(1)combined mass (M+m)
(2)total energy of the orbit ($\alpha$)
(3)reference (osculating) epoch (t0)
(4-6)position at reference epoch (${\rm \bf r}_0$)
(7-9)velocity at reference epoch (${\rm \bf v}_0$)
(10)heliocentric distance at reference epoch
(11)${\rm \bf r}_0.{\rm \bf v}_0$
(12)date (t)
(13)universal eccentric anomaly ($\psi$) of date, approx
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
JSTATIstatus:
+102 = warning, distant epoch
+101 = warning, large timespan +(>100 years)
+1 to +8 = coincident with major planet +(Note 5)
0 = OK
-1 = numerical error
+

+
NOTES: +
+
1. +
The ``universal'' elements are those which define the orbit for the +purposes of the method of universal variables (see reference 2). +They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) $\alpha$, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, + (iii) the outwards component of the velocity at the given epoch, + (iv) an estimate of $\psi$, the ``universal eccentric anomaly'' at a + given date and (v) that date. +
2. +
The universal elements are with respect to the J2000 equator and + equinox. +
3. +
The epochs DATE, U(3) and U(12) are all Modified Julian Dates + (JD-2400000.5). +
4. +
The algorithm is a simplified form of Encke's method. It takes as + a basis the unperturbed motion of the body, and numerically + integrates the perturbing accelerations from the major planets. + The expression used is essentially Sterne's 6.7-2 (reference 1). + Everhart and Pitkin (reference 2) suggest rectifying the orbit at + each integration step by propagating the new perturbed position + and velocity as the new universal variables. In the present + routine the orbit is rectified less frequently than this, in order + to gain a slight speed advantage. However, the rectification is + done directly in terms of position and velocity, as suggested by + Everhart and Pitkin, bypassing the use of conventional orbital + elements. +

+The f(q) part of the full Encke method is not used. The purpose + of this part is to avoid subtracting two nearly equal quantities + when calculating the ``indirect member'', which takes account of the + small change in the Sun's attraction due to the slightly displaced + position of the perturbed body. A simpler, direct calculation in + double precision proves to be faster and not significantly less + accurate. +

+Apart from employing a variable timestep, and occasionally + ``rectifying the orbit'' to keep the indirect member small, the + integration is done in a fairly straightforward way. The + acceleration estimated for the middle of the timestep is assumed + to apply throughout that timestep; it is also used in the + extrapolation of the perturbations to the middle of the next + timestep, to predict the new disturbed position. There is no + iteration within a timestep. +

+Measures are taken to reach a compromise between execution time + and accuracy. The starting-point is the goal of achieving + arcsecond accuracy for ordinary minor planets over a ten-year + timespan. This goal dictates how large the timesteps can be, + which in turn dictates how frequently the unperturbed motion has + to be recalculated from the osculating elements. +

+Within predetermined limits, the timestep for the numerical + integration is varied in length in inverse proportion to the + magnitude of the net acceleration on the body from the major + planets. +

+The numerical integration requires estimates of the major-planet + motions. Approximate positions for the major planets (Pluto + alone is omitted) are obtained from the routine sla_PLANET. Two + levels of interpolation are used, to enhance speed without + significantly degrading accuracy. At a low frequency, the routine + sla_PLANET is called to generate updated position+velocity ``state + vectors''. The only task remaining to be carried out at the full + frequency (i.e. at each integration step) is to use the state + vectors to extrapolate the planetary positions. In place of a + strictly linear extrapolation, some allowance is made for the + curvature of the orbit by scaling back the radius vector as the + linear extrapolation goes off at a tangent. +

+Various other approximations are made. For example, perturbations + by Pluto and the minor planets are neglected, relativistic effects + are not taken into account and the Earth-Moon system is treated as + a single body. +

+In the interests of simplicity, the background calculations for + the major planets are carried out en masse. + The mean elements and + state vectors for all the planets are refreshed at the same time, + without regard for orbit curvature, mass or proximity. +

5. +
This routine is not intended to be used for major planets. + However, if major-planet elements are supplied, sensible results + will, in fact, be produced. This happens because the routine + checks the separation between the body and each of the planets and + interprets a suspiciously small value (0.001 AU) as an attempt to + apply the routine to the planet concerned. If this condition + is detected, the + contribution from that planet is ignored, and the status is set to + the planet number (Mercury=1,...,Neptune=8) as a warning. +
+

+
REFERENCES: +
+
1. +
Sterne, Theodore E., An Introduction to Celestial Mechanics, +Interscience Publishers, 1960. Section 6.7, p199. +
2. +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_PLANEL - Planet Position from Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PERTEL - Perturbed Orbital Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node146.html b/src/slalib/sun67.htx/node146.html new file mode 100644 index 0000000..70b9139 --- /dev/null +++ b/src/slalib/sun67.htx/node146.html @@ -0,0 +1,255 @@ + + + + +SLA_PLANEL - Planet Position from Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PLANET - Planetary Ephemerides +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PERTUE - Perturbed Universal Elements +

+

+

SLA_PLANEL - Planet Position from Elements +   +

+
+
ACTION: +
Heliocentric position and velocity of a planet, +asteroid or comet, starting from orbital elements. +

CALL: +
CALL sla_PLANEL ( + DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH, + AORQ, E, AORL, DM, PV, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDModified Julian Date (JD-2400000.5)
JFORMIchoice of element set (1-3, see Note 3, below)
EPOCHDepoch of elements (t0 or T, TT MJD)
ORBINCDinclination (i, radians)
ANODEDlongitude of the ascending node ($\Omega$, radians)
PERIHDlongitude or argument of perihelion +($\varpi$ or $\omega$,
radians)
AORQDmean distance or perihelion distance (a or q, AU)
EDeccentricity (e)
AORLDmean anomaly or longitude +(M or L, radians,
JFORM=1,2 only)
DMDdaily motion (n, radians, JFORM=1 only)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
PVD(6)heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, equatorial, J2000
(AU, AU/s)
JSTATIstatus:
0 = OK
-1 = illegal JFORM
-2 = illegal E
-3 = illegal AORQ
-4 = illegal DM
-5 = numerical error
+

+
NOTES: +
+
1. +
DATE is the instant for which the prediction is +required. It is in the TT timescale (formerly +Ephemeris Time, ET) and is a + Modified Julian Date (JD-2400000.5). +
2. +
The elements are with respect to + the J2000 ecliptic and equinox. +
3. +
Three different element-format options are available, as + follows.
+

+JFORM=1, suitable for the major planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 longitude of perihelion $\varpi$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean longitude L (radians)
+		 DM 		 = 		 daily motion n (radians)        
+
+

+JFORM=2, suitable for minor planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e \leq 10 )$
+
4. +
Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are + not accessed. +
5. +
The reference frame for the result is equatorial and is with + respect to the mean equinox and ecliptic of epoch J2000. +
6. +
The algorithm was originally adapted from the EPHSLA program of + D.H.P.Jones (private communication, 1996). The method + is based on Stumpff's Universal Variables. +
+

+
REFERENCE: +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_PLANET - Planetary Ephemerides +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PERTUE - Perturbed Universal Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node147.html b/src/slalib/sun67.htx/node147.html new file mode 100644 index 0000000..b9d19fb --- /dev/null +++ b/src/slalib/sun67.htx/node147.html @@ -0,0 +1,278 @@ + + + + +SLA_PLANET - Planetary Ephemerides + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PLANTE - of Planet from Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PLANEL - Planet Position from Elements +

+

+

SLA_PLANET - Planetary Ephemerides +   +

+
+
ACTION: +
Approximate heliocentric position and velocity of a planet. +
CALL: +
CALL sla_PLANET (DATE, NP, PV, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDModified Julian Date (JD-2400000.5)
NPIplanet:
1=Mercury
2=Venus
3=Earth-Moon Barycentre
4=Mars
5=Jupiter
6=Saturn
7=Uranus
8=Neptune
9=Pluto
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
PVD(6)heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, equatorial, J2000
(AU, AU/s)
JSTATIstatus:
+1 = warning: date outside of range
0 = OK
-1 = illegal NP (outside 1-9)
-2 = solution didn't converge
+

+
NOTES: +
+
1. +
The epoch, DATE, is in the TDB timescale and is in the form +of a Modified Julian Date (JD-2400000.5). +
2. +
The reference frame is equatorial and is with respect to + the mean equinox and ecliptic of epoch J2000. +
3. +
If a planet number, NP, outside the range 1-9 is supplied, an error + status is returned (JSTAT = -1) and the PV vector + is set to zeroes. +
4. +
The algorithm for obtaining the mean elements of the + planets from Mercury to Neptune is due to + J.L.Simon, P.Bretagnon, J.Chapront, + M.Chapront-Touze, G.Francou and J.Laskar (Bureau des + Longitudes, Paris, France). The (completely different) + algorithm for calculating the ecliptic coordinates of + Pluto is by Meeus. +
5. +
Comparisons of the present routine with the JPL DE200 ephemeris + give the following RMS errors over the interval 1960-2025: + 

+ 		 		 position (km) 		 speed (metre/sec) 
+ 
+		 Mercury 		  334 		  0.437
+		 Venus 		  1060 		  0.855
+		 EMB 		  2010 		  0.815
+		 Mars 		  7690 		  1.98
+		 Jupiter 		  71700 		  7.70
+		 Saturn 		  199000 		  19.4
+		 Uranus 		  564000 		  16.4
+		 Neptune 		  158000 		  14.4
+		 Pluto 		  36400 		  0.137        
+
+ From comparisons with DE102, Simon et al. quote the following + longitude accuracies over the interval 1800-2200: + 

+ 		 Mercury 		  $4\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 Venus 		  $5\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 EMB 		  $6\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 Mars 		 $17\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 Jupiter 		 $71\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 Saturn 		 $81\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 Uranus 		 $86\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
+		 Neptune 		 $11\hspace{-0.05em}^{'\hspace{-0.1em}'}$
+ In the case of Pluto, Meeus quotes an accuracy of + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$

+in longitude and + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ in latitude for the period + 1885-2099. +

+For all except Pluto, over the period 1000-3000, + the accuracy is better than 1.5 + times that over 1800-2200. Outside the interval 1000-3000 the + accuracy declines. For Pluto the accuracy declines rapidly + outside the period 1885-2099. Outside these ranges + (1885-2099 for Pluto, 1000-3000 for the rest) a ``date out + of range'' warning status (JSTAT=+1) is returned. +

6. +
The algorithms for (i) Mercury through Neptune and + (ii) Pluto are completely independent. In the Mercury + through Neptune case, the present SLALIB + implementation differs from the original + Simon et al. Fortran code in the following respects: +
    +
  • The date is supplied as a Modified Julian Date rather + a Julian Date (${\rm MJD} = ({\rm JD} - 2400000.5$). +
  • The result is returned only in equatorial + Cartesian form; the ecliptic + longitude, latitude and radius vector are not returned. +
  • The velocity is in AU per second, not AU per day. +
  • Different error/warning status values are used. +
  • Kepler's Equation is not solved inline. +
  • Polynomials in T are nested to minimize rounding errors. +
  • Explicit double-precision constants are used to avoid + mixed-mode expressions. +
  • There are other, cosmetic, changes to comply with + Starlink/SLALIB style guidelines. +
+ None of the above changes affects the result significantly. +
7. +
NP=3 the result is for the Earth-Moon Barycentre. To + obtain the heliocentric position and velocity of the Earth, + either use the SLALIB routine sla_EVP or call sla_DMOON and + subtract 0.012150581 times the geocentric Moon vector from + the EMB vector produced by the present routine. (The Moon + vector should be precessed to J2000 first, but this can + be omitted for modern epochs without introducing significant + inaccuracy.) +
+

+
REFERENCES: +
+
1. +
Simon et al., +Astron. Astrophys. 282, 663 (1994). +
2. +
Meeus, J., + Astronomical Algorithms, Willmann-Bell (1991). +
+
+ +next + +up + +previous +
+ Next: SLA_PLANTE - of Planet from Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PLANEL - Planet Position from Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node148.html b/src/slalib/sun67.htx/node148.html new file mode 100644 index 0000000..70ca411 --- /dev/null +++ b/src/slalib/sun67.htx/node148.html @@ -0,0 +1,256 @@ + + + + +SLA_PLANTE - of Planet from Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PM - Proper Motion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PLANET - Planetary Ephemerides +

+

+

    +
+SLA_PLANTE - $[\,\alpha,\delta\,]$ of Planet from Elements +

+
+
ACTION: +
Topocentric apparent $[\,\alpha,\delta\,]$ of a Solar-System object whose +heliocentric orbital elements are known. +

CALL: +
CALL sla_PLANTE ( + DATE, ELONG, PHI, JFORM, EPOCH, ORBINC, ANODE, PERIH, + AORQ, E, AORL, DM, RA, DEC, R, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDMJD of observation (JD-2400000.5)
ELONG,PHIDobserver's longitude (east +ve) and latitude
radians)
JFORMIchoice of element set (1-3, see Note 4, below)
EPOCHDepoch of elements (t0 or T, TT MJD)
ORBINCDinclination (i, radians)
ANODEDlongitude of the ascending node ($\Omega$, radians)
PERIHDlongitude or argument of perihelion +($\varpi$ or $\omega$,
radians)
AORQDmean distance or perihelion distance (a or q, AU)
EDeccentricity (e)
AORLDmean anomaly or longitude (M or L,
radians, JFORM=1,2 only)
DMDdaily motion (n, radians, JFORM=1 only)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
RA,DECDtopocentric apparent $[\,\alpha,\delta\,]$ (radians)
RDdistance from observer (AU)
JSTATIstatus:
0 = OK
-1 = illegal JFORM
-2 = illegal E
-3 = illegal AORQ
-4 = illegal DM
-5 = numerical error
+

+
NOTES: +
+
1. +
DATE is the instant for which the prediction is +required. It is in the TT timescale (formerly +Ephemeris Time, ET) and is a + Modified Julian Date (JD-2400000.5). +
2. +
The longitude and latitude allow correction for geocentric + parallax. This is usually a small effect, but can become + important for Earth-crossing asteroids. Geocentric positions + can be generated by appropriate use of the routines + sla_EVP and sla_PLANEL. +
3. +
The elements are with respect to the J2000 ecliptic and equinox. +
4. +
Three different element-format options are available, as + follows.
+

+JFORM=1, suitable for the major planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 longitude of perihelion $\varpi$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e 
+		 AORL 		 = 		 mean longitude L (radians)
+		 DM 		 = 		 daily motion n (radians)        
+
+

+JFORM=2, suitable for minor planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e
+
+
5. +
Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are + not accessed. +
+
+ +next + +up + +previous +
+ Next: SLA_PM - Proper Motion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PLANET - Planetary Ephemerides +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node149.html b/src/slalib/sun67.htx/node149.html new file mode 100644 index 0000000..999078a --- /dev/null +++ b/src/slalib/sun67.htx/node149.html @@ -0,0 +1,135 @@ + + + + +SLA_PM - Proper Motion + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_POLMO - Polar Motion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PLANTE - of Planet from Elements +

+

+

SLA_PM - Proper Motion +   +

+
+
ACTION: +
Apply corrections for proper motion to a star $[\,\alpha,\delta\,]$.
CALL: +
CALL sla_PM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
R0,D0D$[\,\alpha,\delta\,]$ at epoch EP0 (radians)
PR,PDDproper motions: rate of change of +$[\,\alpha,\delta\,]$ (radians per year)
PXDparallax (arcsec)
RVDradial velocity (km s-1, +ve if receding)
EP0Dstart epoch in years (e.g. Julian epoch)
EP1Dend epoch in years (same system as EP0)
+

+
RETURNED: +
+
+ + + + + +
R1,D1D$[\,\alpha,\delta\,]$ at epoch EP1 (radians)
+

+
NOTE: +
The $\alpha$ proper motions are $\dot{\alpha}$ rather than +$\dot{\alpha}\cos\delta$, and are in the same coordinate + system as R0,D0. +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr. Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_POLMO - Polar Motion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PLANTE - of Planet from Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node15.html b/src/slalib/sun67.htx/node15.html new file mode 100644 index 0000000..45c1aeb --- /dev/null +++ b/src/slalib/sun67.htx/node15.html @@ -0,0 +1,230 @@ + + + + +SLA_AFIN - Sexagesimal character string to angle + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AIRMAS - Air Mass +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ADDET - Add E-terms of Aberration +

+

+

SLA_AFIN - Sexagesimal character string to angle +   +

+
+
ACTION: +
Decode a free-format sexagesimal string (degrees, arcminutes, +arcseconds) into a single precision floating point + number (radians). +

CALL: +
CALL sla_AFIN (STRING, NSTRT, RESLT, JF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
STRINGC*(*)string containing deg, arcmin, arcsec fields
NSTRTIpointer to start of decode (beginning of STRING = 1)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NSTRTIadvanced past the decoded angle
RESLTRangle in radians
JFIstatus:
0 = OK
+1 = default, RESLT unchanged (note 2)
-1 = bad degrees (note 3)
-2 = bad arcminutes (note 3)
-3 = bad arcseconds (note 3)
+

+
EXAMPLE: +
+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
argumentbeforeafter
   
STRING'-57 17 44.806 12 34 56.7'unchanged
NSTRT116 (i.e. pointing to 12...)
RESLT--1.00000
JF- 
+
A further call to sla_AFIN, without adjustment of NSTRT, will + decode the second angle, $12^{\circ}\,34^{'}\,56^{''}.7$.
+

+
NOTES: +
+
1. +
The first three ``fields'' in STRING are degrees, arcminutes, +arcseconds, separated by spaces or commas. The degrees field +may be signed, but not the others. The decoding is carried + out by the sla_DFLTIN routine and is free-format. +
2. +
Successive fields may be absent, defaulting to zero. For + zero status, the only combinations allowed are degrees alone, + degrees and arcminutes, and all three fields present. If all + three fields are omitted, a status of +1 is returned and RESLT is + unchanged. In all other cases RESLT is changed. +
3. +
Range checking: +
    +
  • The degrees field is not range checked. However, it is + expected to be integral unless the other two fields are absent. +
  • The arcminutes field is expected to be 0-59, and integral if + the arcseconds field is present. If the arcseconds field + is absent, the arcminutes is expected to be 0-59.9999... +
  • The arcseconds field is expected to be 0-59.9999... +
  • Decoding continues even when a check has failed. Under these + circumstances the field takes the supplied value, defaulting to + zero, and the result RESLT is computed and returned. +
+
4. +
Further fields after the three expected ones are not treated as + an error. The pointer NSTRT is left in the correct state for + further decoding with the present routine or with sla_DFLTIN + etc. See the example, above. +
5. +
If STRING contains hours, minutes, seconds instead of + degrees etc, + or if the required units are turns (or days) instead of radians, + the result RESLT should be multiplied as follows:
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
for STRINGto obtainmultiply RESLT by
   
${\circ}$  '  ''radians1.0
${\circ}$  '  ''turns$1/{2 \pi} = 0.1591549430918953358$
h m sradians15.0
h m sdays$15/{2\pi} = 2.3873241463784300365$
+
+ +next + +up + +previous +
+ Next: SLA_AIRMAS - Air Mass +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ADDET - Add E-terms of Aberration +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node150.html b/src/slalib/sun67.htx/node150.html new file mode 100644 index 0000000..4750c08 --- /dev/null +++ b/src/slalib/sun67.htx/node150.html @@ -0,0 +1,202 @@ + + + + +SLA_POLMO - Polar Motion + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PREBN - Precession Matrix (FK4) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PM - Proper Motion +

+

+

SLA_POLMO - Polar Motion +   +

+
+
ACTION: +
Polar motion: correct site longitude and latitude for polar +motion and calculate azimuth difference between celestial and + terrestrial poles. +

CALL: +
CALL sla_POLMO (ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
ELONGMDmean longitude of the site (radians, east +ve)
PHIMDmean geodetic latitude of the site (radians)
XPDpolar motion x-coordinate (radians)
YPDpolar motion y-coordinate (radians)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + +
ELONGDtrue longitude of the site (radians, east +ve)
PHIDtrue geodetic latitude of the site (radians)
DAZDazimuth correction (terrestrial-celestial, radians)
+

+
NOTES: +
+
1. +
``Mean'' longitude and latitude are the (fixed) values for the +site's location with respect to the IERS terrestrial reference +frame; the latitude is geodetic. TAKE CARE WITH THE LONGITUDE + SIGN CONVENTION. The longitudes used by the present routine + are east-positive, in accordance with geographical convention + (and right-handed). In particular, note that the longitudes + returned by the sla_OBS routine are west-positive, following + astronomical usage, and must be reversed in sign before use in + the present routine. +
2. +
XP and YP are the (changing) coordinates of the Celestial + Ephemeris Pole with respect to the IERS Reference Pole. + XP is positive along the meridian at longitude $0^{\circ}$, and YP is positive along the meridian at longitude + $270^\circ$ (i.e. $90^{\circ}$ west). Values for XP,YP can + be obtained from IERS circulars and equivalent publications; + the maximum amplitude observed so far is about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ . +
3. +
``True'' longitude and latitude are the (moving) values for + the site's location with respect to the celestial ephemeris + pole and the meridian which corresponds to the Greenwich + apparent sidereal time. The true longitude and latitude + link the terrestrial coordinates with the standard celestial + models (for precession, nutation, sidereal time etc). +
4. +
The azimuths produced by sla_AOP and sla_AOPQK are with + respect to due north as defined by the Celestial Ephemeris + Pole, and can therefore be called ``celestial azimuths''. + However, a telescope fixed to the Earth measures azimuth + essentially with respect to due north as defined by the + IERS Reference Pole, and can therefore be called ``terrestrial + azimuth''. Uncorrected, this would manifest itself as a + changing ``azimuth zero-point error''. The value DAZ is the + correction to be added to a celestial azimuth to produce + a terrestrial azimuth. +
5. +
The present routine is rigorous. For most practical + purposes, the following simplified formulae provide an + adequate approximation:
+
+
+ + + + + + + + + + + + + +
ELONG=ELONGM+XP*COS(ELONGM)-YP*SIN(ELONGM)
PHI =PHIM+(XP*SIN(ELONGM)+YP*COS(ELONGM))*TAN(PHIM)
DAZ =-SQRT(XP*XP+YP*YP)*COS(ELONGM-ATAN2(XP,YP))/COS(PHIM)

+
+
+An alternative formulation for DAZ is: +
+
+
+ + + + + + + + + + + + + +
X =COS(ELONGM)*COS(PHIM)
Y =SIN(ELONGM)*COS(PHIM)
DAZ=ATAN2(-X*YP-Y*XP,X*X+Y*Y)
+

+
REFERENCE: +
Seidelmann, P.K. (ed), 1992. Explanatory +Supplement to the Astronomical Almanac, ISBN 0-935702-68-7, + sections 3.27, 4.25, 4.52. +
+
+ +next + +up + +previous +
+ Next: SLA_PREBN - Precession Matrix (FK4) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PM - Proper Motion +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node151.html b/src/slalib/sun67.htx/node151.html new file mode 100644 index 0000000..f7c9a66 --- /dev/null +++ b/src/slalib/sun67.htx/node151.html @@ -0,0 +1,111 @@ + + + + +SLA_PREBN - Precession Matrix (FK4) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PREC - Precession Matrix (FK5) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_POLMO - Polar Motion +

+

+

SLA_PREBN - Precession Matrix (FK4) +   +

+
+
ACTION: +
Generate the matrix of precession between two epochs, +using the old, pre IAU 1976, Bessel-Newcomb model, in + Andoyer's formulation. +

CALL: +
CALL sla_PREBN (BEP0, BEP1, RMATP) +

+

+
GIVEN: +
+
+ + + + + + + + + +
BEP0Dbeginning Besselian epoch
BEP1Dending Besselian epoch
+

+
RETURNED: +
+
+ + + + + +
RMATPD(3,3)precession matrix
+

+
NOTE: +
The matrix is in the sense: +
v1 = M$\cdot$v0
+ where v1 is the star vector relative to the + mean equator and equinox of epoch BEP1, M is the + $3\times3$ matrix RMATP and + v0 is the star vector relative to the + mean equator and equinox of epoch BEP0. +
+

+
REFERENCE: +
Smith et al., 1989. Astr.J. 97, 269. +
+
+ +next + +up + +previous +
+ Next: SLA_PREC - Precession Matrix (FK5) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_POLMO - Polar Motion +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node152.html b/src/slalib/sun67.htx/node152.html new file mode 100644 index 0000000..9e5ea39 --- /dev/null +++ b/src/slalib/sun67.htx/node152.html @@ -0,0 +1,145 @@ + + + + +SLA_PREC - Precession Matrix (FK5) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PRECES - Precession +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PREBN - Precession Matrix (FK4) +

+

+

SLA_PREC - Precession Matrix (FK5) +   +

+
+
ACTION: +
Form the matrix of precession between two epochs (IAU 1976, FK5). +
CALL: +
CALL sla_PREC (EP0, EP1, RMATP) +

+

+
GIVEN: +
+
+ + + + + + + + + +
EP0Dbeginning epoch
EP1Dending epoch
+

+
RETURNED: +
+
+ + + + + +
RMATPD(3,3)precession matrix
+

+
NOTES: +
+
1. +
The epochs are TDB Julian epochs. +
2. +
The matrix is in the sense: +
v1 = M$\cdot$v0
+ where v1 is the star vector relative to the + mean equator and equinox of epoch EP1, M is the + $3\times3$ matrix RMATP and + v0 is the star vector relative to the + mean equator and equinox of epoch EP0. +
3. +
Though the matrix method itself is rigorous, the precession + angles are expressed through canonical polynomials which are + valid only for a limited time span. There are also known + errors in the IAU precession rate. The absolute accuracy + of the present formulation is better than + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ from + 1960AD to 2040AD, better than $1\hspace{-0.05em}^{'\hspace{-0.1em}'}$ from 1640AD to 2360AD, + and remains below $3\hspace{-0.05em}^{'\hspace{-0.1em}'}$ for the whole of the period + 500BC to 3000AD. The errors exceed $10\hspace{-0.05em}^{'\hspace{-0.1em}'}$ outside the + range 1200BC to 3900AD, exceed $100\hspace{-0.05em}^{'\hspace{-0.1em}'}$ outside 4200BC to + 5600AD and exceed $1000\hspace{-0.05em}^{'\hspace{-0.1em}'}$ outside 6800BC to 8200AD. + The SLALIB routine sla_PRECL implements a more elaborate + model which is suitable for problems spanning several + thousand years. +
+

+
REFERENCES: +
+
1. +
Lieske, J.H., 1979. Astr.Astrophys. 73, 282; +equations 6 & 7, p283. +
2. +
Kaplan, G.H., 1981. USNO circular no. 163, pA2. +
+
+ +next + +up + +previous +
+ Next: SLA_PRECES - Precession +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PREBN - Precession Matrix (FK4) +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node153.html b/src/slalib/sun67.htx/node153.html new file mode 100644 index 0000000..e63959a --- /dev/null +++ b/src/slalib/sun67.htx/node153.html @@ -0,0 +1,120 @@ + + + + +SLA_PRECES - Precession + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PRECL - Precession Matrix (latest) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PREC - Precession Matrix (FK5) +

+

+

SLA_PRECES - Precession +   +

+
+
ACTION: +
Precession - either the old ``FK4'' (Bessel-Newcomb, pre IAU 1976) +or new ``FK5'' (Fricke, post IAU 1976) as required. +

CALL: +
CALL sla_PRECES (SYSTEM, EP0, EP1, RA, DC) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
SYSTEMCprecession to be applied: `FK4' or `FK5'
EP0,EP1Dstarting and ending epoch
RA,DCD$[\,\alpha,\delta\,]$, mean equator & equinox of epoch EP0
+

+
RETURNED: +
+
+ + + + + +
RA,DCD$[\,\alpha,\delta\,]$, mean equator & equinox of epoch EP1
+

+
NOTES: +
+
1. +
Lowercase characters in SYSTEM are acceptable. +
2. +
The epochs are Besselian if SYSTEM=`FK4' and Julian if `FK5'. +For example, to precess coordinates in the old system from + equinox 1900.0 to 1950.0 the call would be: +
CALL sla_PRECES ('FK4', 1900D0, 1950D0, RA, DC) +
+
3. +
This routine will NOT correctly convert between the old and + the new systems - for example conversion from B1950 to J2000. + For these purposes see sla_FK425, sla_FK524, sla_FK45Z and + sla_FK54Z. +
4. +
If an invalid SYSTEM is supplied, values of -99D0,-99D0 are + returned for both RA and DC. +
+
+ +next + +up + +previous +
+ Next: SLA_PRECL - Precession Matrix (latest) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PREC - Precession Matrix (FK5) +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node154.html b/src/slalib/sun67.htx/node154.html new file mode 100644 index 0000000..a20e26a --- /dev/null +++ b/src/slalib/sun67.htx/node154.html @@ -0,0 +1,131 @@ + + + + +SLA_PRECL - Precession Matrix (latest) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PRENUT - Precession/Nutation Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRECES - Precession +

+

+

SLA_PRECL - Precession Matrix (latest) +   +

+
+
ACTION: +
Form the matrix of precession between two epochs, using the +model of Simon et al. (1994), which is suitable for long + periods of time. +

CALL: +
CALL sla_PRECL (EP0, EP1, RMATP) +

+

+
GIVEN: +
+
+ + + + + + + + + +
EP0Dbeginning epoch
EP1Dending epoch
+

+
RETURNED: +
+
+ + + + + +
RMATPD(3,3)precession matrix
+

+
NOTES: +
+
1. +
The epochs are TDB Julian epochs. +
2. +
The matrix is in the sense: +
v1 = M$\cdot$v0
+ where v1 is the star vector relative to the + mean equator and equinox of epoch EP1, M is the + $3\times3$ matrix RMATP and + v0 is the star vector relative to the + mean equator and equinox of epoch EP0. +
3. +
The absolute accuracy of the model is limited by the + uncertainty in the general precession, about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ per + 1000 years. The remainder of the formulation provides a + precision of 1 milliarcsecond over the interval from 1000AD + to 3000AD, + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ from 1000BC to 5000AD and + $1\hspace{-0.05em}^{'\hspace{-0.1em}'}$ from 4000BC to 8000AD. +
+

+
REFERENCE: +
Simon, J.L. et al., 1994. Astr.Astrophys. 282, +663. +
+
+ +next + +up + +previous +
+ Next: SLA_PRENUT - Precession/Nutation Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRECES - Precession +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node155.html b/src/slalib/sun67.htx/node155.html new file mode 100644 index 0000000..e7dc899 --- /dev/null +++ b/src/slalib/sun67.htx/node155.html @@ -0,0 +1,110 @@ + + + + +SLA_PRENUT - Precession/Nutation Matrix + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PV2EL - Orbital Elements from Position/Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRECL - Precession Matrix (latest) +

+

+

SLA_PRENUT - Precession/Nutation Matrix +   +

+
+
ACTION: +
Form the matrix of precession and nutation (IAU 1976, FK5). +
CALL: +
CALL sla_PRENUT (EPOCH, DATE, RMATPN) +

+

+
GIVEN: +
+
+ + + + + + + + + +
EPOCHDJulian Epoch for mean coordinates
DATEDModified Julian Date (JD-2400000.5) +for true coordinates
+

+
RETURNED: +
+
+ + + + + +
RMATPND(3,3)combined precession/nutation matrix
+

+
NOTES: +
+
1. +
The epoch and date are TDB. +
2. +
The matrix is in the sense: +
vtrue = M$\cdot$vmean
+ where vtrue is the star vector relative to the + true equator and equinox of epoch DATE, M is the + $3\times3$ matrix RMATPN and + vmean is the star vector relative to the + mean equator and equinox of epoch EPOCH. +
+
+ +next + +up + +previous +
+ Next: SLA_PV2EL - Orbital Elements from Position/Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRECL - Precession Matrix (latest) +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node156.html b/src/slalib/sun67.htx/node156.html new file mode 100644 index 0000000..ab897bc --- /dev/null +++ b/src/slalib/sun67.htx/node156.html @@ -0,0 +1,323 @@ + + + + +SLA_PV2EL - Orbital Elements from Position/Velocity + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PV2UE - Position/Velocity to Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRENUT - Precession/Nutation Matrix +

+

+

SLA_PV2EL - Orbital Elements from Position/Velocity +   +

+
+
ACTION: +
Heliocentric osculating elements obtained from instantaneous +position and velocity. +

CALL: +
CALL sla_PV2EL ( + PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC, + ANODE, PERIH, AORQ, E, AORL, DM, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + +
PVD(6)heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, equatorial, J2000
(AU, AU/s; Note 1)
DATEDdate (TT Modified Julian Date = JD-2400000.5)
PMASSDmass of the planet (Sun = 1; Note 2)
JFORMRIrequested element set (1-3; Note 3)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
JFORMIelement set actually returned (1-3; Note 4)
EPOCHDepoch of elements (t0 or T, TT MJD)
ORBINCDinclination (i, radians)
ANODEDlongitude of the ascending node ($\Omega$, radians)
PERIHDlongitude or argument of perihelion +($\varpi$ or $\omega$,
radians)
AORQDmean distance or perihelion distance (a or q, AU)
EDeccentricity (e)
AORLDmean anomaly or longitude +(M or L, radians,
JFORM=1,2 only)
DMDdaily motion (n, radians, JFORM=1 only)
JSTATIstatus:
0 = OK
-1 = illegal PMASS
-2 = illegal JFORMR
-3 = position/velocity out of allowed range
+

+
NOTES: +
+
1. +
The PV 6-vector is with respect to the mean equator and equinox of +epoch J2000. The orbital elements produced are with respect to +the J2000 ecliptic and mean equinox. +
2. +
The mass, PMASS, is important only for the larger planets. For + most purposes (e.g. asteroids) use 0D0. Values less than zero + are illegal. +
3. +
Three different element-format options are supported, as + follows.
+

+JFORM=1, suitable for the major planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 longitude of perihelion $\varpi$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean longitude L (radians)
+		 DM 		 = 		 daily motion n (radians)        
+
+

+JFORM=2, suitable for minor planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e \leq 10 )$
+
4. +
It may not be possible to generate elements in the form + requested through JFORMR. The caller is notified of the form + of elements actually returned by means of the JFORM argument: +


+ 		 JFORMR 		 JFORM 		 meaning 
+ 
+		      1 		      1 		 OK: elements are in the requested format
+		      1 		      2 		 never happens
+		      1 		      3 		 orbit not elliptical
+		      2 		      1 		 never happens
+		      2 		      2 		 OK: elements are in the requested format
+		      2 		      3 		 orbit not elliptical
+		      3 		      1 		 never happens
+		      3 		      2 		 never happens
+		      3 		      3 		 OK: elements are in the requested format        
+
+
5. +
The arguments returned for each value of JFORM (cf Note 5: + JFORM may not be the same as JFORMR) are as follows: +


+ 		 JFORM 		 1 		 2 		 3 
+ 
+		 EPOCH 		 t0 t0 T 
+		 ORBINC 		 i i i 
+		 ANODE 		 $\Omega$ $\Omega$ $\Omega$ 
+		 PERIH 		 $\varpi$ $\omega$ $\omega$ 
+		 AORQ 		 a a q 
+		 E 		 e e e 
+		 AORL 		 L M -
+		 DM 		 n - 		 -        
+
+

+where: + 


+ 		 t0 is the epoch of the elements (MJD, TT)
+		 T is the epoch of perihelion (MJD, TT)
+		 i is the inclination (radians)
+		 $\Omega$ is the longitude of the ascending node (radians)
+		 $\varpi$ is the longitude of perihelion (radians)
+		 $\omega$ is the argument of perihelion (radians)
+		 a is the mean distance (AU)
+		 q is the perihelion distance (AU)
+		 e is the eccentricity
+		 L is the longitude (radians, $0-2\pi$)		 M is the mean anomaly (radians, $0-2\pi$)		 n is the daily motion (radians)
+		 - 		 means no value is set        
+
+
6. +
At very small inclinations, the longitude of the ascending node + ANODE becomes indeterminate and under some circumstances may be + set arbitrarily to zero. Similarly, if the orbit is close to + circular, the true anomaly becomes indeterminate and under some + circumstances may be set arbitrarily to zero. In such cases, + the other elements are automatically adjusted to compensate, + and so the elements remain a valid description of the orbit. +
+

+
REFERENCE: +
Sterne, Theodore E., An Introduction to Celestial Mechanics, +Interscience Publishers, 1960. +
+
+ +next + +up + +previous +
+ Next: SLA_PV2UE - Position/Velocity to Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRENUT - Precession/Nutation Matrix +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node157.html b/src/slalib/sun67.htx/node157.html new file mode 100644 index 0000000..08c25e9 --- /dev/null +++ b/src/slalib/sun67.htx/node157.html @@ -0,0 +1,203 @@ + + + + +SLA_PV2UE - Position/Velocity to Universal Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PVOBS - Observatory Position & Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PV2EL - Orbital Elements from Position/Velocity +

+

+

SLA_PV2UE - Position/Velocity to Universal Elements +   +

+
+
ACTION: +
Construct a universal element set based on an instantaneous +position and velocity. +

CALL: +
CALL sla_PV2UE (PV, DATE, PMASS, U, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
PVD(6)heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, equatorial, J2000
(AU, AU/s; Note 1)
DATEDdate (TT Modified Julian Date = JD-2400000.5)
PMASSDmass of the planet (Sun = 1; Note 2)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal orbital elements (Note 3)
(1)combined mass (M+m)
(2)total energy of the orbit ($\alpha$)
(3)reference (osculating) epoch (t0)
(4-6)position at reference epoch (${\rm \bf r}_0$)
(7-9)velocity at reference epoch (${\rm \bf v}_0$)
(10)heliocentric distance at reference epoch
(11)${\rm \bf r}_0.{\rm \bf v}_0$
(12)date (t)
(13)universal eccentric anomaly ($\psi$) of date, approx
JSTATIstatus:
0 = OK
-1 = illegal PMASS
-2 = too close to Sun
-3 = too slow
+

+
NOTES: +
+
1. +
The PV 6-vector can be with respect to any chosen inertial frame, +and the resulting universal-element set will be with respect to +the same frame. A common choice will be mean equator and ecliptic + of epoch J2000. +
2. +
The mass, PMASS, is important only for the larger planets. For + most purposes (e.g. asteroids) use 0D0. Values less than zero + are illegal. +
3. +
The ``universal'' elements are those which define the orbit for the + purposes of the method of universal variables (see reference). + They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) $\alpha$, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, + (iii) the outwards component of the velocity at the given epoch, + (iv) an estimate of $\psi$, the ``universal eccentric anomaly'' at a + given date and (v) that date. +
+

+
REFERENCE: +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_PVOBS - Observatory Position & Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PV2EL - Orbital Elements from Position/Velocity +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node158.html b/src/slalib/sun67.htx/node158.html new file mode 100644 index 0000000..02b37a3 --- /dev/null +++ b/src/slalib/sun67.htx/node158.html @@ -0,0 +1,102 @@ + + + + +SLA_PVOBS - Observatory Position & Velocity + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PXY - Apply Linear Model +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PV2UE - Position/Velocity to Universal Elements +

+

+

SLA_PVOBS - Observatory Position & Velocity +   +

+
+
ACTION: +
Position and velocity of an observing station. +
CALL: +
CALL sla_PVOBS (P, H, STL, PV) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
PDlatitude (geodetic, radians)
HDheight above reference spheroid (geodetic, metres)
STLDlocal apparent sidereal time (radians)
+

+
RETURNED: +
+
+ + + + + +
PVD(6)$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ (AU, AU s-1, true equator and equinox +of date)
+

+
NOTE: +
IAU 1976 constants are used. +
+
+ +next + +up + +previous +
+ Next: SLA_PXY - Apply Linear Model +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PV2UE - Position/Velocity to Universal Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node159.html b/src/slalib/sun67.htx/node159.html new file mode 100644 index 0000000..6cf76da --- /dev/null +++ b/src/slalib/sun67.htx/node159.html @@ -0,0 +1,145 @@ + + + + +SLA_PXY - Apply Linear Model + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RANDOM - Random Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PVOBS - Observatory Position & Velocity +

+

+

SLA_PXY - Apply Linear Model +   +

+
+
ACTION: +
Given arrays of expected and measured +$[\,x,y\,]$ coordinates, and a + linear model relating them (as produced by sla_FITXY), compute + the array of predicted coordinates and the RMS residuals. +

CALL: +
CALL sla_PXY (NP,XYE,XYM,COEFFS,XYP,XRMS,YRMS,RRMS) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
NPInumber of samples
XYED(2,NP)expected $[\,x,y\,]$ for each sample
XYMD(2,NP)measured $[\,x,y\,]$ for each sample
COEFFSD(6)coefficients of model (see below)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
XYPD(2,NP)predicted $[\,x,y\,]$ for each sample
XRMSDRMS in X
YRMSDRMS in Y
RRMSD total RMS (vector sum of XRMS and YRMS)
+

+
NOTES: +
+
1. +
The model is supplied in the array COEFFS. Naming the +six elements of COEFFS a,b,c,d,e & f, +the model transforms measured coordinates + $[x_{m},y_{m}\,]$ into predicted coordinates + $[x_{p},y_{p}\,]$ as follows: +
xp = a + bxm + cym
+ yp = d + exm + fym
+
2. +
The residuals are (xp-xe) and (yp-ye). +
3. +
If NP is less than or equal to zero, no coordinates are + transformed, and the RMS residuals are all zero. +
4. +
See also sla_FITXY, sla_INVF, sla_XY2XY, sla_DCMPF +
+
+ +next + +up + +previous +
+ Next: SLA_RANDOM - Random Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PVOBS - Observatory Position & Velocity +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node16.html b/src/slalib/sun67.htx/node16.html new file mode 100644 index 0000000..682e1dd --- /dev/null +++ b/src/slalib/sun67.htx/node16.html @@ -0,0 +1,121 @@ + + + + +SLA_AIRMAS - Air Mass + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ALTAZ - Velocities etc. for Altazimuth Mount +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AFIN - Sexagesimal character string to angle +

+

+

SLA_AIRMAS - Air Mass +   +

+
+
ACTION: +
Air mass at given zenith distance (double precision). +
CALL: +
D = sla_AIRMAS (ZD) +

+

+
GIVEN: +
+
+ + + + + +
ZDDobserved zenith distance (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_AIRMASDair mass (1 at zenith)
+

+
NOTES: +
+
1. +
The observed zenith distance referred to above means +``as affected by refraction''. +
2. +
The routine uses Hardie's (1962) polynomial fit to Bemporad's + data for the relative air mass, X, in units of thickness at the + zenith as tabulated by Schoenberg (1929). This is adequate for all + normal needs as it is accurate to better than + 0.1% up to X = 6.8 and better than 1% up to X = 10. + Bemporad's tabulated values are unlikely to be trustworthy + to such accuracy + because of variations in density, pressure and other + conditions in the atmosphere from those assumed in his work. +
3. +
The sign of the ZD is ignored. +
4. +
At zenith distances greater than about $\zeta = 87^{\circ}$ the + air mass is held constant to avoid arithmetic overflows. +
+

+
REFERENCES: +
+
1. +
Hardie, R.H., 1962, in Astronomical Techniques +ed. W.A. Hiltner, University of Chicago Press, p180. +
2. +
Schoenberg, E., 1929, Hdb. d. Ap., + Berlin, Julius Springer, 2, 268. +
+
+ +next + +up + +previous +
+ Next: SLA_ALTAZ - Velocities etc. for Altazimuth Mount +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AFIN - Sexagesimal character string to angle +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node160.html b/src/slalib/sun67.htx/node160.html new file mode 100644 index 0000000..972237c --- /dev/null +++ b/src/slalib/sun67.htx/node160.html @@ -0,0 +1,98 @@ + + + + +SLA_RANDOM - Random Number + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RANGE - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PXY - Apply Linear Model +

+

+

SLA_RANDOM - Random Number +   +

+
+
ACTION: +
Generate pseudo-random real number in the range $0 \leq x < 1$.
CALL: +
R = sla_RANDOM (SEED) +

+

+
GIVEN: +
+
+ + + + + +
SEEDRan arbitrary real number
+

+
RETURNED: +
+
+ + + + + + + + + +
SEEDRa new arbitrary value
sla_RANDOMRPseudo-random real number $0 \leq x < 1$.
+

+
NOTE: +
The implementation is machine-dependent. +
+
+ +next + +up + +previous +
+ Next: SLA_RANGE - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PXY - Apply Linear Model +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node161.html b/src/slalib/sun67.htx/node161.html new file mode 100644 index 0000000..b8c2cb4 --- /dev/null +++ b/src/slalib/sun67.htx/node161.html @@ -0,0 +1,93 @@ + + + + +SLA_RANGE - Put Angle into Range + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RANORM - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RANDOM - Random Number +

+

+

    +
+SLA_RANGE - Put Angle into Range $\pm \pi$

+
+
ACTION: +
Normalize an angle into the range $\pm \pi$ (single precision). +
CALL: +
R = sla_RANGE (ANGLE) +

+

+
GIVEN: +
+
+ + + + + +
ANGLERangle in radians
+

+
RETURNED: +
+
+ + + + + +
sla_RANGERANGLE expressed in the range $\pm \pi$.
+
+ +next + +up + +previous +
+ Next: SLA_RANORM - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RANDOM - Random Number +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node162.html b/src/slalib/sun67.htx/node162.html new file mode 100644 index 0000000..3317041 --- /dev/null +++ b/src/slalib/sun67.htx/node162.html @@ -0,0 +1,93 @@ + + + + +SLA_RANORM - Put Angle into Range + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RCC - Barycentric Coordinate Time +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RANGE - Put Angle into Range +

+

+

    +
+SLA_RANORM - Put Angle into Range $0\!-\!2\pi$

+
+
ACTION: +
Normalize an angle into the range $0\!-\!2\pi$ (single precision). +
CALL: +
R = sla_RANORM (ANGLE) +

+

+
GIVEN: +
+
+ + + + + +
ANGLERangle in radians
+

+
RETURNED: +
+
+ + + + + +
sla_RANORMRANGLE expressed in the range $0\!-\!2\pi$
+
+ +next + +up + +previous +
+ Next: SLA_RCC - Barycentric Coordinate Time +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RANGE - Put Angle into Range +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node163.html b/src/slalib/sun67.htx/node163.html new file mode 100644 index 0000000..4f6cf04 --- /dev/null +++ b/src/slalib/sun67.htx/node163.html @@ -0,0 +1,166 @@ + + + + +SLA_RCC - Barycentric Coordinate Time + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RDPLAN - Apparent of Planet +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RANORM - Put Angle into Range +

+

+

SLA_RCC - Barycentric Coordinate Time +   +

+
+
CALL: +
D = sla_RCC (TDB, UT1, WL, U, V) +
ACTION: +
The relativistic clock correction TDB-TT, the + difference between proper time + on Earth and coordinate time in the solar system barycentric + space-time frame of reference. The proper time is TT; the + coordinate time is an implementation of TDB. +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + +
TDBDcoordinate time (MJD: JD-2400000.5)
UT1Duniversal time (fraction of one day)
WLDclock longitude (radians west)
UDclock distance from Earth spin axis (km)
VDclock distance north of Earth equatorial plane (km)
+

+
RETURNED: +
+
+ + + + + +
sla_RCCDTDB-TT (sec)
+

+
NOTES: +
+
1. +
TDB may be considered to +be the coordinate time in the solar system barycentre frame of +reference, and TT is the proper time given by clocks at mean sea + level on the Earth. +
2. +
The result has a main (annual) sinusoidal term of amplitude + approximately 1.66ms, plus planetary terms up to about + 20$\mu$s, and lunar and diurnal terms up to 2$\mu$s. The + variation arises from the transverse Doppler effect and the + gravitational red-shift as the observer varies in speed and + moves through different gravitational potentials. +
3. +
The argument TDB is, strictly, the barycentric coordinate time; + however, the terrestrial proper time (TT) can in practice be used. +
4. +
The geocentric model is that of Fairhead & Bretagnon (1990), + in its full + form. It was supplied by Fairhead (private communication) + as a Fortran subroutine. A number of coding changes were made to + this subroutine in order + match the calling sequence of previous versions of the present + routine, to comply with Starlink programming standards and to + avoid compilation problems on certain machines. On the supported + computer types, + the numerical results are essentially unaffected by the + changes. The topocentric model is from Moyer (1981) and Murray (1983). + During the interval 1950-2050, the absolute accuracy of the + geocentric model is better than $\pm3$ nanoseconds + relative to direct numerical integrations using the JPL DE200/LE200 + solar system ephemeris. +
5. +
The IAU definition of TDB is that it must differ from TT only by + periodic terms. Though practical, this is an imprecise definition + which ignores the existence of very long-period and secular effects + in the dynamics of the solar system. As a consequence, different + implementations of TDB will, in general, differ in zero-point and + will drift linearly relative to one other. +
+

+
REFERENCES: +
+
1. +
Fairhead, L. & +Bretagnon, P., 1990. Astr.Astrophys. 229, 240-247. +
2. +
Moyer, T.D., 1981. Cel.Mech. 23, 33. +
3. +
Murray, C.A., 1983, Vectorial Astrometry, Adam Hilger. +
+
+ +next + +up + +previous +
+ Next: SLA_RDPLAN - Apparent of Planet +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RANORM - Put Angle into Range +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node164.html b/src/slalib/sun67.htx/node164.html new file mode 100644 index 0000000..d45ee2f --- /dev/null +++ b/src/slalib/sun67.htx/node164.html @@ -0,0 +1,184 @@ + + + + +SLA_RDPLAN - Apparent of Planet + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFCO - Refraction Constants +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RCC - Barycentric Coordinate Time +

+

+

    +
+SLA_RDPLAN - Apparent $[\,\alpha,\delta\,]$ of Planet +

+
+
ACTION: +
Approximate topocentric apparent $[\,\alpha,\delta\,]$ and angular +size of a planet. +

CALL: +
CALL sla_RDPLAN (DATE, NP, ELONG, PHI, RA, DEC, DIAM) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDMJD of observation (JD-2400000.5)
NPIplanet:
1=Mercury
2=Venus
3=Moon
4=Mars
5=Jupiter
6=Saturn
7=Uranus
8=Neptune
9=Pluto
else=Sun
ELONG,PHIDobserver's longitude (east +ve) and latitude +(radians)
+

+
RETURNED: +
+
+ + + + + + + + + +
RA,DECDtopocentric apparent $[\,\alpha,\delta\,]$ (radians)
DIAMDangular diameter (equatorial, radians)
+

+
NOTES: +
+
1. +
The date is in a dynamical timescale (TDB, formerly ET) +and is in the form of a Modified +Julian Date (JD-2400000.5). For all practical purposes, TT can + be used instead of TDB, and for many applications UT will do + (except for the Moon). +
2. +
The longitude and latitude allow correction for geocentric + parallax. This is a major effect for the Moon, but in the + context of the limited accuracy of the present routine its + effect on planetary positions is small (negligible for the + outer planets). Geocentric positions can be generated by + appropriate use of the routines sla_DMOON and sla_PLANET. +
3. +
The direction accuracy (arcsec, 1000-3000AD) is of order: + 

+ 		 Sun 		   5
+		 Mercury 		   2
+		 Venus 		 10
+		 Moon 		 30
+		 Mars 		 50
+		 Jupiter 		 90
+		 Saturn 		 90
+		 Uranus 		 90
+		 Neptune 		 10
+		 Pluto 		  1   (1885-2099AD only)        
+
+ The angular diameter accuracy is about 0.4% for the Moon, + and 0.01% or better for the Sun and planets. + For more information on accuracy, + refer to the routines sla_PLANET and sla_DMOON, + which the present routine uses. +
+
+ +next + +up + +previous +
+ Next: SLA_REFCO - Refraction Constants +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RCC - Barycentric Coordinate Time +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node165.html b/src/slalib/sun67.htx/node165.html new file mode 100644 index 0000000..1fadca0 --- /dev/null +++ b/src/slalib/sun67.htx/node165.html @@ -0,0 +1,176 @@ + + + + +SLA_REFCO - Refraction Constants + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFCOQ - Refraction Constants (fast) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RDPLAN - Apparent of Planet +

+

+

SLA_REFCO - Refraction Constants +   +

+
+
ACTION: +
Determine the constants a and b in the +atmospheric refraction model + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$, where $\zeta$ is the observed zenith distance + (i.e. affected by refraction) and $\Delta \zeta$ is + what to add to $\zeta$ to give the topocentric + (i.e. in vacuo) zenith distance. +

CALL: +
CALL sla_REFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REFA, REFB) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
HMDheight of the observer above sea level (metre)
TDKDambient temperature at the observer (degrees K)
PMBDpressure at the observer (mB)
RHDrelative humidity at the observer (range 0-1)
WLDeffective wavelength of the source ($\mu{\rm m}$)
PHIDlatitude of the observer (radian, astronomical)
TLRDtemperature lapse rate in the troposphere +(degrees K per metre)
EPSDprecision required to terminate iteration (radian)
+

+
RETURNED: +
+
+ + + + + + + + + +
REFAD$\tan \zeta$ coefficient (radians)
REFBD$\tan^{3} \zeta$ coefficient (radians)
+

+
NOTES: +
+
1. +
Suggested values for the TLR and EPS arguments are 0.0065D0 and +1D-8 respectively. +
2. +
The radio refraction is chosen by specifying WL >100 $\mu{\rm m}$.
3. +
The routine is a slower but more accurate alternative to the + sla_REFCOQ routine. The constants it produces give perfect + agreement with sla_REFRO at zenith distances + $\tan^{-1} 1$ ($45^\circ$) and $\tan^{-1} 4$ ($\sim 76^\circ$). + At other zenith distances, the model achieves: +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ accuracy for $\zeta<80^{\circ}$,

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$ accuracy for $\zeta<60^{\circ}$, and +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.001$ accuracy for $\zeta<45^{\circ}$.

+
+ +next + +up + +previous +
+ Next: SLA_REFCOQ - Refraction Constants (fast) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RDPLAN - Apparent of Planet +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node166.html b/src/slalib/sun67.htx/node166.html new file mode 100644 index 0000000..4dd74d2 --- /dev/null +++ b/src/slalib/sun67.htx/node166.html @@ -0,0 +1,428 @@ + + + + +SLA_REFCOQ - Refraction Constants (fast) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFRO - Refraction +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFCO - Refraction Constants +

+

+

SLA_REFCOQ - Refraction Constants (fast) +   +

+
+
ACTION: +
Determine the constants a and b in the +atmospheric refraction model + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$, where $\zeta$ is the observed zenith distance + (i.e. affected by refraction) and $\Delta \zeta$ is + what to add to $\zeta$ to give the topocentric + (i.e. in vacuo) zenith distance. (This is a fast + alternative to the sla_REFCO routine - see notes.) +

CALL: +
CALL sla_REFCOQ (TDK, PMB, RH, WL, REFA, REFB) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
TDKDambient temperature at the observer (degrees K)
PMBDpressure at the observer (mB)
RHDrelative humidity at the observer (range 0-1)
WLDeffective wavelength of the source ($\mu{\rm m}$)
+

+
RETURNED: +
+
+ + + + + + + + + +
REFAD$\tan \zeta$ coefficient (radians)
REFBD$\tan^{3} \zeta$ coefficient (radians)
+

+
NOTES: +
+
1. +
The radio refraction is chosen by specifying WL >100 $\mu{\rm m}$.
2. +
The model is an approximation, for moderate zenith distances, +to the predictions of the sla_REFRO routine. The approximation + is maintained across a range of conditions, and applies to + both optical/IR and radio. +
3. +
The algorithm is a fast alternative to the sla_REFCO routine. + The latter calls the sla_REFRO routine itself: this involves + integrations through a model atmosphere, and is costly in + processor time. However, the model which is produced is precisely + correct for two zenith distances ($45^\circ$ and $\sim\!76^\circ$) and at other zenith distances is limited in accuracy only by the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ formulation + itself. The present routine is not as accurate, though it + satisfies most practical requirements. +
4. +
The model omits the effects of (i) height above sea level (apart + from the reduced pressure itself), (ii) latitude (i.e. the + flattening of the Earth) and (iii) variations in tropospheric + lapse rate. +
5. +
The model has been tested using the following range of conditions: +
+
$\cdot$
lapse rates 0.0055, 0.0065, 0.0075 degrees K per metre +
$\cdot$
latitudes $0^{\circ}$, $25^\circ$, $50^\circ$, $75^\circ$
$\cdot$
heights 0, 2500, 5000 metres above sea level +
$\cdot$
pressures mean for height -10% to +5% in steps of 5% +
$\cdot$
temperatures $-10^\circ$ to $+20^\circ$ with respect to + $280^\circ$K at sea level +
$\cdot$
relative humidity 0, 0.5, 1 +
$\cdot$
wavelength 0.4, 0.6, ... $2\mu{\rm m}$, + radio +
$\cdot$
zenith distances $15^\circ$, $45^\circ$, $75^\circ$
+ For the above conditions, the comparison with sla_REFRO + was as follows: +


+
+
+

           + + + + + + + + + + + + + + + + + +
 worstRMS
optical/IR628
radio31949
 masmas
+


+
+
+
+

+For this particular set of conditions: +

+
$\cdot$
lapse rate $6.5^\circ K km^{-1}$
$\cdot$
latitude $50^\circ$
$\cdot$
sea level +
$\cdot$
pressure 1005mB +
$\cdot$
temperature $7^\circ$C +
$\cdot$
humidity 80% +
$\cdot$
wavelength 5740A +
+ the results were as follows: +


+
+
+

           + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
$\zeta$sla_REFROsla_REFCOQSaastamoinen
1010.2710.2710.27
2021.1921.2021.19
3033.6133.6133.60
4048.8248.8348.81
4558.1658.1858.16
5069.2869.3069.27
5582.9782.9982.95
60100.51100.54100.50
65124.23124.26124.20
70158.63158.68158.61
72177.32177.37177.31
74200.35200.38200.32
76229.45229.43229.42
78267.44267.29267.41
80319.13318.55319.10
degarcsecarcsecarcsec
+


+
+
+
+

+The values for Saastamoinen's formula (which includes terms + up to $\tan^5$) are taken from Hohenkerk and Sinclair (1985). +

+The results from the much slower but more accurate sla_REFCO + routine have not been included in the tabulation as they are + identical to those in the sla_REFRO column to the + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$

+resolution used. +

6. +
Outlandish input parameters are silently limited + to mathematically safe values. Zero pressure is permissible, + and causes zeroes to be returned. +
7. +
The algorithm draws on several sources, as follows: +
    +
  • The formula for the saturation vapour pressure of water as + a function of temperature and temperature is taken from + expressions A4.5-A4.7 of Gill (1982). +
  • The formula for the water vapour pressure, given the + saturation pressure and the relative humidity is from + Crane (1976), expression 2.5.5. +
  • The refractivity of air is a function of temperature, + total pressure, water-vapour pressure and, in the case + of optical/IR but not radio, wavelength. The formulae + for the two cases are developed from the Essen and Froome + expressions adopted in Resolution 1 of the 12th International + Geodesy Association General Assembly (1963). +
+ The above three items are as used in the sla_REFRO routine. +
    +
  • The formula for $\beta~(=H_0/r_0)$ is + an adaption of expression 9 from Stone (1996). The + adaptations, arrived at empirically, consist of (i) a + small adjustment to the coefficient and (ii) a humidity + term for the radio case only. +
  • The formulae for the refraction constants as a function of + n-1 and $\beta$ are from Green (1987), expression 4.31. +
+

+
REFERENCES: +
+
1. +
Crane, R.K., Meeks, M.L. (ed), ``Refraction Effects in +the Neutral Atmosphere'', +Methods of Experimental Physics: Astrophysics 12B, + Academic Press, 1976. +
2. +
Gill, Adrian E., Atmosphere-Ocean Dynamics, + Academic Press, 1982. +
3. +
Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note + No. 63, 1985. +
4. +
International Geodesy Association General Assembly, Bulletin + Géodésique 70 p390, 1963. +
5. +
Stone, Ronald C., P.A.S.P. 108 1051-1058, 1996. +
6. +
Green, R.M., Spherical Astronomy, Cambridge + University Press, 1987. +
+
+ +next + +up + +previous +
+ Next: SLA_REFRO - Refraction +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFCO - Refraction Constants +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node167.html b/src/slalib/sun67.htx/node167.html new file mode 100644 index 0000000..f422ec8 --- /dev/null +++ b/src/slalib/sun67.htx/node167.html @@ -0,0 +1,232 @@ + + + + +SLA_REFRO - Refraction + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFV - Apply Refraction to Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFCOQ - Refraction Constants (fast) +

+

+

SLA_REFRO - Refraction +   +

+
+
ACTION: +
Atmospheric refraction, for radio or optical/IR wavelengths. +
CALL: +
CALL sla_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ZOBSDobserved zenith distance of the source (radians)
HMDheight of the observer above sea level (metre)
TDKDambient temperature at the observer (degrees K)
PMBDpressure at the observer (mB)
RHDrelative humidity at the observer (range 0-1)
WLDeffective wavelength of the source ($\mu{\rm m}$)
PHIDlatitude of the observer (radian, astronomical)
TLRDtemperature lapse rate in the troposphere +(degrees K per metre)
EPSDprecision required to terminate iteration (radian)
+

+
RETURNED: +
+
+ + + + + +
REFDrefraction: in vacuo ZD minus observed ZD (radians)
+

+
NOTES: +
+
1. +
A suggested value for the TLR argument is 0.0065D0. The +refraction is significantly affected by TLR, and if studies +of the local atmosphere have been carried out a better TLR + value may be available. +
2. +
A suggested value for the EPS argument is 1D-8. The result is + usually at least two orders of magnitude more computationally + precise than the supplied EPS value. +
3. +
The routine computes the refraction for zenith distances up + to and a little beyond $90^{\circ}$ using the method of Hohenkerk + & Sinclair (NAO Technical Notes 59 and 63, subsequently adopted + in the Explanatory Supplement to the Astronomical Almanac, + 1992 - see section 3.281). +
4. +
The code is based on the AREF optical/IR refraction subroutine + of C.Hohenkerk (HMNAO, September 1984), with extensions to + support the radio case. The modifications to the original HMNAO + optical/IR refraction code which affect the results are: +
    +
  • Murray's values for the gas constants have been used + (Vectorial Astrometry, Adam Hilger, 1983). +
  • A better model for Ps(T) has been adopted (taken from + Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982). +
  • More accurate expressions for Pwo have been adopted + (again from Gill 1982). +
  • Provision for radio wavelengths has been added using + expressions devised by A.T.Sinclair, RGO (private + communication 1989), based on the Essen & Froome + refractivity formula adopted in Resolution 1 of the + 12th International Geodesy Association General Assembly + (Bulletin Géodésique 70 p390, 1963). +
+ None of the changes significantly affects the optical/IR results + with respect to the algorithm given in the 1992 Explanatory + Supplement. For example, at $70^\circ$ zenith distance the present + routine agrees with the ES algorithm to better than + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.05$

+for any reasonable combination of parameters. However, the + improved water-vapour expressions do make a significant difference + in the radio band, at $70^\circ$ zenith distance reaching almost + $4\hspace{-0.05em}^{'\hspace{-0.1em}'}$ for a hot, humid, low-altitude site during a period of + low pressure. +

5. +
The radio refraction is chosen by specifying WL >100 $\mu{\rm m}$. Because the algorithm takes no account of the ionosphere, the + accuracy deteriorates at low frequencies, below about 30MHz. +
6. +
Before use, the value of ZOBS is expressed in the range $\pm \pi$. If this ranged ZOBS is negative, the result REF is computed from its + absolute value before being made negative to match. In addition, if + it has an absolute value greater than $93^\circ$, a fixed REF value + equal to the result for ZOBS $=93^\circ$ is returned, appropriately + signed. +
7. +
As in the original Hohenkerk and Sinclair algorithm, fixed values + of the water vapour polytrope exponent, the height of the + tropopause, and the height at which refraction is negligible are + used. +
8. +
The radio refraction has been tested against work done by + Iain Coulson, JACH, (private communication 1995) for the + James Clerk Maxwell Telescope, Mauna Kea. For typical conditions, + agreement at the + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ level is achieved for moderate ZD, + worsening to perhaps + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ - + $1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0$ at ZD $80^\circ$. At hot and humid sea-level sites the accuracy will not be as good. +
9. +
It should be noted that the relative humidity RH is formally + defined in terms of ``mixing ratio'' rather than pressures or + densities as is often stated. It is the mass of water per unit + mass of dry air divided by that for saturated air at the same + temperature and pressure (see Gill 1982). The familiar + $\nu=p_w/p_s$ or $\nu=\rho_w/\rho_s$ expressions can differ from + the formal definition by several percent, significant in the + radio case. +
+
+ +next + +up + +previous +
+ Next: SLA_REFV - Apply Refraction to Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFCOQ - Refraction Constants (fast) +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node168.html b/src/slalib/sun67.htx/node168.html new file mode 100644 index 0000000..c695ed9 --- /dev/null +++ b/src/slalib/sun67.htx/node168.html @@ -0,0 +1,276 @@ + + + + +SLA_REFV - Apply Refraction to Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFZ - Apply Refraction to ZD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFRO - Refraction +

+

+

SLA_REFV - Apply Refraction to Vector +   +

+
+
ACTION: +
Adjust an unrefracted Cartesian vector to include the effect of +atmospheric refraction, using the simple + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model. +

CALL: +
CALL sla_REFV (VU, REFA, REFB, VR) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
VUDunrefracted position of the source ($[\,Az,El~]$ 3-vector)
REFAD$\tan \zeta$ coefficient (radians)
REFBD$\tan^{3} \zeta$ coefficient (radians)
+

+
RETURNED: +
+
+ + + + + +
VRDrefracted position of the source ($[\,Az,El~]$ 3-vector)
+

+
NOTES: +
+
1. +
This routine applies the adjustment for refraction in the +opposite sense to the usual one - it takes an unrefracted +(in vacuo) position and produces an observed (refracted) + position, whereas the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model strictly + applies to the case where an observed position is to have the + refraction removed. The unrefracted to refracted case is + harder, and requires an inverted form of the text-book + refraction models; the algorithm used here is equivalent to + one iteration of the Newton-Raphson method applied to the + above formula. +
2. +
Though optimized for speed rather than precision, the present + routine achieves consistency with the refracted-to-unrefracted + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model at better than 1 microarcsecond within + $30^\circ$ of the zenith and remains within 1 milliarcsecond to + $\zeta=70^\circ$. The inherent accuracy of the model is, of + course, far worse than this - see the documentation for sla_REFCO + for more information. +
3. +
At low elevations (below about $3^{\circ}$) the refraction + correction is held back to prevent arithmetic problems and + wildly wrong results. Over a wide range of observer heights + and corresponding temperatures and pressures, the following + levels of accuracy are achieved, relative to numerical + integration through a model atmosphere: +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
$\zeta_{obs}$error 
   
$80^\circ$$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$ 
$81^\circ$$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$ 
$82^\circ$$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$ 
$83^\circ$$3\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$84^\circ$$7\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$85^\circ$$17\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$86^\circ$$45\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$87^\circ$$150\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$88^\circ$$340\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$89^\circ$$620\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$90^{\circ}$$1100\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$91^\circ$$1900\hspace{-0.05em}^{'\hspace{-0.1em}'}$< high-altitude
$92^\circ$$3200\hspace{-0.05em}^{'\hspace{-0.1em}'}$< sites only
+
4. +
See also the routine sla_REFZ, which performs the adjustment to + the zenith distance rather than in $[\,x,y,z\,]$. The present routine is faster than sla_REFZ and, + except very low down, + is equally accurate for all practical purposes. However, beyond + about $\zeta=84^\circ$ sla_REFZ should be used, and for the utmost + accuracy iterative use of sla_REFRO should be considered. +
+
+ +next + +up + +previous +
+ Next: SLA_REFZ - Apply Refraction to ZD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFRO - Refraction +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node169.html b/src/slalib/sun67.htx/node169.html new file mode 100644 index 0000000..6180ab0 --- /dev/null +++ b/src/slalib/sun67.htx/node169.html @@ -0,0 +1,275 @@ + + + + +SLA_REFZ - Apply Refraction to ZD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RVEROT - RV Corrn to Earth Centre +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFV - Apply Refraction to Vector +

+

+

SLA_REFZ - Apply Refraction to ZD +   +

+
+
ACTION: +
Adjust an unrefracted zenith distance to include the effect of +atmospheric refraction, using the simple + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model. +

CALL: +
CALL sla_REFZ (ZU, REFA, REFB, ZR) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
ZUDunrefracted zenith distance of the source (radians)
REFAD$\tan \zeta$ coefficient (radians)
REFBD$\tan^{3} \zeta$ coefficient (radians)
+

+
RETURNED: +
+
+ + + + + +
ZRDrefracted zenith distance (radians)
+

+
NOTES: +
+
1. +
This routine applies the adjustment for refraction in the +opposite sense to the usual one - it takes an unrefracted +(in vacuo) position and produces an observed (refracted) + position, whereas the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model strictly + applies to the case where an observed position is to have the + refraction removed. The unrefracted to refracted case is + harder, and requires an inverted form of the text-book + refraction models; the formula used here is based on the + Newton-Raphson method. For the utmost numerical consistency + with the refracted to unrefracted model, two iterations are + carried out, achieving agreement at the 10-11 arcsecond level + for $\zeta=80^\circ$. The inherent accuracy of the model + is, of course, far worse than this - see the documentation for + sla_REFCO for more information. +
2. +
At $\zeta=83^\circ$, the rapidly-worsening + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model is abandoned and an empirical formula takes over: +

+

\begin{displaymath} +\Delta \zeta = F \left( + \frac{0^\circ\hspace{-0.37em}.\hspa... + ...hspace{0.02em}00202 E^2} + {1 + 0.28385 E +0.02390 E^2} \right) \end{displaymath}

+where $E=90^\circ-\zeta_{true}$ and F is a factor chosen to meet the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ formula at $\zeta=83^\circ$. Over a + wide range of observer heights and corresponding temperatures and + pressures, the following levels of accuracy are achieved, + relative to numerical integration through a model atmosphere: +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
$\zeta_{obs}$error 
   
$80^\circ$$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$ 
$81^\circ$$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$ 
$82^\circ$$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ 
$83^\circ$$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ 
$84^\circ$$4\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.9$ 
$85^\circ$$5\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$ 
$86^\circ$$6\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ 
$87^\circ$$7\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ 
$88^\circ$$11\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$89^\circ$$21\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$90^{\circ}$$43\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$91^\circ$$92\hspace{-0.05em}^{'\hspace{-0.1em}'}$< high-altitude
$92^\circ$$220\hspace{-0.05em}^{'\hspace{-0.1em}'}$< sites only
+
3. +
See also the routine sla_REFV, which performs the adjustment in + $[\,x,y,z\,]$, and with the emphasis on speed rather than numerical accuracy. +
+
+ +next + +up + +previous +
+ Next: SLA_RVEROT - RV Corrn to Earth Centre +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFV - Apply Refraction to Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node17.html b/src/slalib/sun67.htx/node17.html new file mode 100644 index 0000000..c44bc9c --- /dev/null +++ b/src/slalib/sun67.htx/node17.html @@ -0,0 +1,205 @@ + + + + +SLA_ALTAZ - Velocities etc. for Altazimuth Mount + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AMP - Apparent to Mean +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AIRMAS - Air Mass +

+

+

SLA_ALTAZ - Velocities etc. for Altazimuth Mount +   +

+
+
ACTION: +
Positions, velocities and accelerations for an altazimuth +telescope mount tracking a star (double precision). +

CALL: +
CALL sla_ALTAZ ( + HA, DEC, PHI, + AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
HADhour angle
DECDdeclination
PHIDobservatory latitude
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
AZDazimuth
AZDDazimuth velocity
AZDDDazimuth acceleration
ELDelevation
ELDDelevation velocity
ELDDDelevation acceleration
PADparallactic angle
PADDparallactic angle velocity
PADDDparallactic angle acceleration
+

+
NOTES: +
+
1. +
Natural units are used throughout. HA, DEC, PHI, AZ, EL +and ZD are in radians. The velocities and accelerations +assume constant declination and constant rate of change of + hour angle (as for tracking a star); the units of AZD, ELD + and PAD are radians per radian of HA, while the units of AZDD, + ELDD and PADD are radians per radian of HA squared. To + convert into practical degree- and second-based units: +

+ + + + + + + + + + + + + + + + +
angles$\times 360/2\pi$$\rightarrow$degrees
velocities$\times (2\pi/86400) \times (360/2\pi)$$\rightarrow$degree/sec
accelerations$\times (2\pi/86400)^2 \times (360/2\pi)$$\rightarrow$degree/sec/sec
+

+Note that the seconds here are sidereal rather than SI. One + sidereal second is about 0.99727 SI seconds. +

+The velocity and acceleration factors assume the sidereal + tracking case. Their respective numerical values are (exactly) + 1/240 and (approximately) 1/3300236.9. +

2. +
Azimuth is returned in the range $[\,0,2\pi\,]$; north is zero, + and east is $+\pi/2$. Elevation and parallactic angle are + returned in the range $\pm\pi/2$. Position angle is +ve + for a star west of the meridian and is the angle NP-star-zenith. +
3. +
The latitude is geodetic as opposed to geocentric. The + hour angle and declination are topocentric. Refraction and + deficiencies in the telescope mounting are ignored. The + purpose of the routine is to give the general form of the + quantities. The details of a real telescope could profoundly + change the results, especially close to the zenith. +
4. +
No range checking of arguments is carried out. +
5. +
In applications which involve many such calculations, rather + than calling the present routine it will be more efficient to + use inline code, having previously computed fixed terms such + as sine and cosine of latitude, and (for tracking a star) + sine and cosine of declination. +
+
+ +next + +up + +previous +
+ Next: SLA_AMP - Apparent to Mean +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AIRMAS - Air Mass +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node170.html b/src/slalib/sun67.htx/node170.html new file mode 100644 index 0000000..3f0f1a1 --- /dev/null +++ b/src/slalib/sun67.htx/node170.html @@ -0,0 +1,111 @@ + + + + +SLA_RVEROT - RV Corrn to Earth Centre + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RVGALC - RV Corrn to Galactic Centre +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFZ - Apply Refraction to ZD +

+

+

SLA_RVEROT - RV Corrn to Earth Centre +   +

+
+
ACTION: +
Velocity component in a given direction due to Earth rotation. +
CALL: +
R = sla_RVEROT (PHI, RA, DA, ST) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
PHIRgeodetic latitude of observing station (radians)
RA,DARapparent $[\,\alpha,\delta\,]$ (radians)
STRlocal apparent sidereal time (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_RVEROTRComponent of Earth rotation in +direction RA,DA (km s-1)
+

+
NOTES: +
+
1. +
Sign convention: the result is positive when the observatory +is receding from the given point on the sky. +
2. +
Accuracy: the simple algorithm used assumes a spherical Earth and + an observing station at sea level; for actual observing + sites, the error is unlikely to be greater than 0.0005 km s-1. + For applications requiring greater precision, use the routine + sla_PVOBS. +
+
+ +next + +up + +previous +
+ Next: SLA_RVGALC - RV Corrn to Galactic Centre +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFZ - Apply Refraction to ZD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node171.html b/src/slalib/sun67.htx/node171.html new file mode 100644 index 0000000..307d861 --- /dev/null +++ b/src/slalib/sun67.htx/node171.html @@ -0,0 +1,115 @@ + + + + +SLA_RVGALC - RV Corrn to Galactic Centre + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RVLG - RV Corrn to Local Group +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVEROT - RV Corrn to Earth Centre +

+

+

SLA_RVGALC - RV Corrn to Galactic Centre +   +

+
+
ACTION: +
Velocity component in a given direction due to the rotation +of the Galaxy. +

CALL: +
R = sla_RVGALC (R2000, D2000) +

+

+
GIVEN: +
+
+ + + + + +
R2000,D2000RJ2000.0 mean $[\,\alpha,\delta\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_RVGALCRComponent of dynamical LSR motion in direction +R2000,D2000 (km s-1)
+

+
NOTES: +
+
1. +
Sign convention: the result is positive when the LSR +is receding from the given point on the sky. +
2. +
The Local Standard of Rest used here is a point in the + vicinity of the Sun which is in a circular orbit around + the Galactic centre. Sometimes called the dynamical LSR, + it is not to be confused with a kinematical LSR, which + is the mean standard of rest of star catalogues or stellar + populations. +
3. +
The dynamical LSR velocity due to Galactic rotation is assumed to + be 220 km s-1 towards $l^{I\!I}=90^{\circ}$, $b^{I\!I}=0$.
+

+
REFERENCE: +
Kerr & Lynden-Bell (1986), MNRAS, 221, p1023. +
+
+ +next + +up + +previous +
+ Next: SLA_RVLG - RV Corrn to Local Group +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVEROT - RV Corrn to Earth Centre +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node172.html b/src/slalib/sun67.htx/node172.html new file mode 100644 index 0000000..561680e --- /dev/null +++ b/src/slalib/sun67.htx/node172.html @@ -0,0 +1,101 @@ + + + + +SLA_RVLG - RV Corrn to Local Group + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RVLSRD - RV Corrn to Dynamical LSR +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVGALC - RV Corrn to Galactic Centre +

+

+

SLA_RVLG - RV Corrn to Local Group +   +

+
+
ACTION: +
Velocity component in a given direction due to the combination +of the rotation of the Galaxy and the motion of the Galaxy + relative to the mean motion of the local group. +

CALL: +
R = sla_RVLG (R2000, D2000) +

+

+
GIVEN: +
+
+ + + + + +
R2000,D2000RJ2000.0 mean $[\,\alpha,\delta\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_RVLGRComponent of solar (n.b.) +motion in direction R2000,D2000 (km s-1)
+

+
NOTE: +
Sign convention: the result is positive when +the Sun is receding from the given point on the sky. +
+

+
REFERENCE: +
IAU Trans. 1976. 16B, p201. +
+
+ +next + +up + +previous +
+ Next: SLA_RVLSRD - RV Corrn to Dynamical LSR +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVGALC - RV Corrn to Galactic Centre +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node173.html b/src/slalib/sun67.htx/node173.html new file mode 100644 index 0000000..2ae01da --- /dev/null +++ b/src/slalib/sun67.htx/node173.html @@ -0,0 +1,121 @@ + + + + +SLA_RVLSRD - RV Corrn to Dynamical LSR + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_RVLSRK - RV Corrn to Kinematical LSR +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVLG - RV Corrn to Local Group +

+

+

SLA_RVLSRD - RV Corrn to Dynamical LSR +   +

+
+
ACTION: +
Velocity component in a given direction due to the Sun's +motion with respect to the ``dynamical'' Local Standard of Rest. +

CALL: +
R = sla_RVLSRD (R2000, D2000) +

+

+
GIVEN: +
+
+ + + + + +
R2000,D2000RJ2000.0 mean $[\,\alpha,\delta\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_RVLSRDRComponent of peculiar solar motion +in direction R2000,D2000 (km s-1)
+

+
NOTES: +
+
1. +
Sign convention: the result is positive when +the Sun is receding from the given point on the sky. +
2. +
The Local Standard of Rest used here is the dynamical LSR, + a point in the vicinity of the Sun which is in a circular + orbit around the Galactic centre. The Sun's motion with + respect to the dynamical LSR is called the peculiar solar + motion. +
3. +
There is another type of LSR, called a kinematical LSR. A + kinematical LSR is the mean standard of rest of specified star + catalogues or stellar populations, and several slightly + different kinematical LSRs are in use. The Sun's motion with + respect to an agreed kinematical LSR is known as the + standard solar motion. + The dynamical LSR is seldom used by observational astronomers, + who conventionally use a kinematical LSR such as the one implemented + in the routine sla_RVLSRK. +
4. +
The peculiar solar motion is from Delhaye (1965), in Stars + and Stellar Systems, vol 5, p73: in Galactic Cartesian + coordinates (+9,+12,+7) km s-1. + This corresponds to about 16.6 km s-1 + towards Galactic coordinates $l^{I\!I}=53^{\circ},b^{I\!I}=+25^{\circ}$.
+
+ +next + +up + +previous +
+ Next: SLA_RVLSRK - RV Corrn to Kinematical LSR +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVLG - RV Corrn to Local Group +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node174.html b/src/slalib/sun67.htx/node174.html new file mode 100644 index 0000000..f243766 --- /dev/null +++ b/src/slalib/sun67.htx/node174.html @@ -0,0 +1,126 @@ + + + + +SLA_RVLSRK - RV Corrn to Kinematical LSR + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_S2TP - Spherical to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVLSRD - RV Corrn to Dynamical LSR +

+

+

SLA_RVLSRK - RV Corrn to Kinematical LSR +   +

+
+
ACTION: +
Velocity component in a given direction due to the Sun's +motion with respect to a kinematical Local Standard of Rest. +

CALL: +
R = sla_RVLSRK (R2000, D2000) +

+

+
GIVEN: +
+
+ + + + + +
R2000,D2000RJ2000.0 mean $[\,\alpha,\delta\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_RVLSRKRComponent of standard solar motion +in direction R2000,D2000 (km s-1)
+

+
NOTES: +
+
1. +
Sign convention: the result is positive when +the Sun is receding from the given point on the sky. +
2. +
The Local Standard of Rest used here is one of several + kinematical LSRs in common use. A kinematical LSR is the + mean standard of rest of specified star catalogues or stellar + populations. The Sun's motion with respect to a kinematical + LSR is known as the standard solar motion. +
3. +
There is another sort of LSR, seldom used by observational + astronomers, called the dynamical LSR. This is a + point in the vicinity of the Sun which is in a circular orbit + around the Galactic centre. The Sun's motion with respect to + the dynamical LSR is called the peculiar solar motion. To + obtain a radial velocity correction with respect to the + dynamical LSR use the routine sla_RVLSRD. +
4. +
The adopted standard solar motion is 20 km s-1 + towards $\alpha=18^{\rm h},\delta=+30^{\circ}$ (1900). +
+

+
REFERENCES: +
+
1. +
Delhaye (1965), in Stars and Stellar Systems, vol 5, p73. +
2. +
Methods of Experimental Physics (ed Meeks), vol 12, +part C, sec 6.1.5.2, p281. +
+
+ +next + +up + +previous +
+ Next: SLA_S2TP - Spherical to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVLSRD - RV Corrn to Dynamical LSR +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node175.html b/src/slalib/sun67.htx/node175.html new file mode 100644 index 0000000..5c3e6c7 --- /dev/null +++ b/src/slalib/sun67.htx/node175.html @@ -0,0 +1,129 @@ + + + + +SLA_S2TP - Spherical to Tangent Plane + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SEP - Angle Between 2 Points on Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVLSRK - RV Corrn to Kinematical LSR +

+

+

SLA_S2TP - Spherical to Tangent Plane +   +

+
+
ACTION: +
Projection of spherical coordinates onto the tangent plane +(single precision). +

CALL: +
CALL sla_S2TP (RA, DEC, RAZ, DECZ, XI, ETA, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
RA,DECRspherical coordinates of star (radians)
RAZ,DECZRspherical coordinates of tangent point (radians)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
XI,ETARtangent plane coordinates (radians)
JIstatus:
0 = OK, star on tangent plane
1 = error, star too far from axis
2 = error, antistar on tangent plane
3 = error, antistar too far from axis
+

+
NOTES: +
+
1. +
The projection is called the gnomonic projection; the +Cartesian coordinates $[\,\xi,\eta\,]$ are called +standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
2. +
When working in $[\,x,y,z\,]$ rather than spherical coordinates, the + equivalent Cartesian routine sla_V2TP is available. +
+
+ +next + +up + +previous +
+ Next: SLA_SEP - Angle Between 2 Points on Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_RVLSRK - RV Corrn to Kinematical LSR +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node176.html b/src/slalib/sun67.htx/node176.html new file mode 100644 index 0000000..a12d2ab --- /dev/null +++ b/src/slalib/sun67.htx/node176.html @@ -0,0 +1,100 @@ + + + + +SLA_SEP - Angle Between 2 Points on Sphere + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SMAT - Solve Simultaneous Equations +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_S2TP - Spherical to Tangent Plane +

+

+

SLA_SEP - Angle Between 2 Points on Sphere +   +

+
+
ACTION: +
Angle between two points on a sphere (single precision). +
CALL: +
R = sla_SEP (A1, B1, A2, B2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
A1,B1Rspherical coordinates of one point (radians)
A2,B2Rspherical coordinates of the other point (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_SEPRangle between [A1,B1] and [A2,B2] in radians
+

+
NOTES: +
+
1. +
The spherical coordinates are right ascension and declination, +longitude and latitude, etc. in radians. +
2. +
The result is always positive. +
+
+ +next + +up + +previous +
+ Next: SLA_SMAT - Solve Simultaneous Equations +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_S2TP - Spherical to Tangent Plane +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node177.html b/src/slalib/sun67.htx/node177.html new file mode 100644 index 0000000..733a9c6 --- /dev/null +++ b/src/slalib/sun67.htx/node177.html @@ -0,0 +1,152 @@ + + + + +SLA_SMAT - Solve Simultaneous Equations + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SUBET - Remove E-terms +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SEP - Angle Between 2 Points on Sphere +

+

+

SLA_SMAT - Solve Simultaneous Equations +   +

+
+
ACTION: +
Matrix inversion and solution of simultaneous equations +(single precision). +

CALL: +
CALL sla_SMAT (N, A, Y, D, JF, IW) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
NInumber of unknowns
AR(N,N)matrix
YR(N)vector
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
AR(N,N)matrix inverse
YR(N)solution
DRdeterminant
JFIsingularity flag: 0=OK
IWI(N)workspace
+

+
NOTES: +
+
1. +
For the set of n simultaneous linear equations in n unknowns: +
A$\cdot$y = x +
+ where: +
    +
  • A is a non-singular $n \times n$ matrix, +
  • y is the vector of n unknowns, and +
  • x is the known vector, +
+ sla_SMAT computes: +
    +
  • the inverse of matrix A, +
  • the determinant of matrix A, and +
  • the vector of n unknowns y. +
+ Argument N is the order n, A (given) is the matrix A, + Y (given) is the vector x and Y (returned) + is the vector y. + The argument A (returned) is the inverse matrix A-1, + and D is det(A). +
2. +
JF is the singularity flag. If the matrix is non-singular, + JF=0 is returned. If the matrix is singular, JF=-1 + and D=0.0 are returned. In the latter case, the contents + of array A on return are undefined. +
3. +
The algorithm is Gaussian elimination with partial pivoting. + This method is very fast; some much slower algorithms can give + better accuracy, but only by a small factor. +
4. +
This routine replaces the obsolete sla_SMATRX. +
+
+ +next + +up + +previous +
+ Next: SLA_SUBET - Remove E-terms +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SEP - Angle Between 2 Points on Sphere +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node178.html b/src/slalib/sun67.htx/node178.html new file mode 100644 index 0000000..3d7a547 --- /dev/null +++ b/src/slalib/sun67.htx/node178.html @@ -0,0 +1,111 @@ + + + + +SLA_SUBET - Remove E-terms + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SUPGAL - Supergalactic to Galactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SMAT - Solve Simultaneous Equations +

+

+

SLA_SUBET - Remove E-terms +   +

+
+
ACTION: +
Remove the E-terms (elliptic component of annual aberration) +from a pre IAU 1976 catalogue $[\,\alpha,\delta\,]$ to give a mean place. +

CALL: +
CALL sla_SUBET (RC, DC, EQ, RM, DM) +

+

+
GIVEN: +
+
+ + + + + + + + + +
RC,DCD$[\,\alpha,\delta\,]$ with E-terms included (radians)
EQDBesselian epoch of mean equator and equinox
+

+
RETURNED: +
+
+ + + + + +
RM,DMD$[\,\alpha,\delta\,]$ without E-terms (radians)
+

+
NOTE: +
Most star positions from pre-1984 optical catalogues (or +obtained by astrometry with respect to such stars) have the + E-terms built-in. This routine converts such a position to a + formal mean place (allowing, for example, comparison with a + pulsar timing position). +
+

+
REFERENCE: +
Explanatory Supplement to the Astronomical Ephemeris, +section 2D, page 48. +
+
+ +next + +up + +previous +
+ Next: SLA_SUPGAL - Supergalactic to Galactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SMAT - Solve Simultaneous Equations +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node179.html b/src/slalib/sun67.htx/node179.html new file mode 100644 index 0000000..1b5da60 --- /dev/null +++ b/src/slalib/sun67.htx/node179.html @@ -0,0 +1,107 @@ + + + + +SLA_SUPGAL - Supergalactic to Galactic + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SVD - Singular Value Decomposition +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SUBET - Remove E-terms +

+

+

SLA_SUPGAL - Supergalactic to Galactic +   +

+
+
ACTION: +
Transformation from de Vaucouleurs supergalactic coordinates +to IAU 1958 galactic coordinates. +

CALL: +
CALL sla_GALSUP (DL, DB, DSL, DSB) +

+

+
GIVEN: +
+
+ + + + + +
DSL,DSBDsupergalactic longitude and latitude (radians)
+

+
RETURNED: +
+
+ + + + + +
DL,DBDgalactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$ (radians)
+

+
REFERENCES: +
+
1. +
de Vaucouleurs, de Vaucouleurs, & Corwin, Second Reference +Catalogue of Bright Galaxies, U.Texas, p8. +
2. +
Systems & Applied Sciences Corp., documentation for the + machine-readable version of the above catalogue, + Contract NAS 5-26490. +
+ (These two references give different values for the galactic + longitude of the supergalactic origin. Both are wrong; the + correct value is $l^{I\!I}=137.37$.) +

+
+ +next + +up + +previous +
+ Next: SLA_SVD - Singular Value Decomposition +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SUBET - Remove E-terms +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node18.html b/src/slalib/sun67.htx/node18.html new file mode 100644 index 0000000..e3aee75 --- /dev/null +++ b/src/slalib/sun67.htx/node18.html @@ -0,0 +1,135 @@ + + + + +SLA_AMP - Apparent to Mean + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AMPQK - Quick Apparent to Mean +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ALTAZ - Velocities etc. for Altazimuth Mount +

+

+

SLA_AMP - Apparent to Mean +   +

+
+
ACTION: +
Convert star $[\,\alpha,\delta\,]$ from geocentric apparent to +mean place (post IAU 1976). +

CALL: +
CALL sla_AMP (RA, DA, DATE, EQ, RM, DM) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
RA,DADapparent $[\,\alpha,\delta\,]$ (radians)
DATEDTDB for apparent place (JD-2400000.5)
EQDequinox: Julian epoch of mean place
+

+
RETURNED: +
+
+ + + + + +
RM,DMDmean $[\,\alpha,\delta\,]$ (radians)
+

+
NOTES: +
+
1. +
The distinction between the required TDB and TT is +always negligible. Moreover, for all but the most +critical applications UTC is adequate. +
2. +
The accuracy is limited by the routine sla_EVP, called + by sla_MAPPA, which computes the Earth position and + velocity using the methods of Stumpff. The maximum + error is about 0.3 milliarcsecond. +
3. +
Iterative techniques are used for the aberration and + light deflection corrections so that the routines + sla_AMP (or sla_AMPQK) and sla_MAP (or sla_MAPQK) are + accurate inverses; even at the edge of the Sun's disc + the discrepancy is only about 1 nanoarcsecond. +
4. +
Where multiple apparent places are to be converted to + mean places, for a fixed date and equinox, it is more + efficient to use the sla_MAPPA routine to compute the + required parameters once, followed by one call to + sla_AMPQK per star. +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_AMPQK - Quick Apparent to Mean +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ALTAZ - Velocities etc. for Altazimuth Mount +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node180.html b/src/slalib/sun67.htx/node180.html new file mode 100644 index 0000000..2372b60 --- /dev/null +++ b/src/slalib/sun67.htx/node180.html @@ -0,0 +1,184 @@ + + + + +SLA_SVD - Singular Value Decomposition + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SVDCOV - Covariance Matrix from SVD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SUPGAL - Supergalactic to Galactic +

+

+

SLA_SVD - Singular Value Decomposition +   +

+
+
ACTION: +
Singular value decomposition. +This routine expresses a given matrix A as the product of + three matrices U, W, VT: + 

+ 		 A = U $\cdot$ W $\cdot$ VT
+
+ where: + 

+ 		 A 		 is any m (rows) $\times n$ (columns) matrix,                       where $m \geq n$ 
+		 U 		 is an $m \times n$ column-orthogonal matrix
+		 W 		 is an $n \times n$ diagonal matrix with                       $w_{ii} \geq 0$ 
+		 VT is the transpose of an $n \times n$                             orthogonal matrix
+
+

CALL: +
CALL sla_SVD (M, N, MP, NP, A, W, V, WORK, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
M,NIm, n, the numbers of rows and columns in matrix A
MP,NPIphysical dimensions of array containing matrix A
AD(MP,NP)array containing $m \times n$ matrix A
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
AD(MP,NP)array containing $m \times n$ column-orthogonal +matrix U
WD(N)$n \times n$ diagonal matrix W +(diagonal elements only)
VD(NP,NP)array containing $n \times n$ orthogonal +matrix V (n.b. not VT)
WORKD(N)workspace
JSTATI0 = OK, -1 = array A wrong shape, >0 = index of W +for which convergence failed (see note 3, below)
+

+
NOTES: +
+
1. +
M and N are the logical dimensions of the +matrices and vectors concerned, which can be located in +arrays of larger physical dimensions, given by MP and NP. +
2. +
V contains matrix V, not the transpose of matrix V. +
3. +
If the status JSTAT is greater than zero, this need not + necessarily be treated as a failure. It means that, due to + chance properties of the matrix A, the QR transformation + phase of the routine did not fully converge in a predefined + number of iterations, something that very seldom occurs. + When this condition does arise, it is possible that the + elements of the diagonal matrix W have not been correctly + found. However, in practice the results are likely to + be trustworthy. Applications should report the condition + as a warning, but then proceed normally. +
+

+
REFERENCES: +
The algorithm is an adaptation of the routine SVD in the EISPACK +library (Garbow et al. 1977, EISPACK Guide Extension, + Springer Verlag), which is a FORTRAN 66 implementation of the Algol + routine SVD of Wilkinson & Reinsch 1971 (Handbook for Automatic + Computation, vol 2, ed Bauer et al., Springer Verlag). These + references give full details of the algorithm used here. + A good account of the use of SVD in least squares problems is given + in Numerical Recipes (Press et al. 1987, Cambridge + University Press), which includes another variant of the EISPACK code. +
+
+ +next + +up + +previous +
+ Next: SLA_SVDCOV - Covariance Matrix from SVD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SUPGAL - Supergalactic to Galactic +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node181.html b/src/slalib/sun67.htx/node181.html new file mode 100644 index 0000000..76e49b9 --- /dev/null +++ b/src/slalib/sun67.htx/node181.html @@ -0,0 +1,122 @@ + + + + +SLA_SVDCOV - Covariance Matrix from SVD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_SVDSOL - Solution Vector from SVD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SVD - Singular Value Decomposition +

+

+

SLA_SVDCOV - Covariance Matrix from SVD +   +

+
+
ACTION: +
From the W and V matrices from the SVD +factorization of a matrix + (as obtained from the sla_SVD routine), obtain + the covariance matrix. +

CALL: +
CALL sla_SVDCOV (N, NP, NC, W, V, WORK, CVM) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + +
NIn, the number of rows and columns in +matrices W and V
NPIfirst dimension of array containing $n \times n$matrix V
NCIfirst dimension of array CVM
WD(N)$n \times n$ diagonal matrix W +(diagonal elements only)
VD(NP,NP)array containing $n \times n$ orthogonal matrix V
+

+
RETURNED: +
+
+ + + + + + + + + +
WORKD(N)workspace
CVMD(NC,NC)array to receive covariance matrix
+

+
REFERENCE: +
Numerical Recipes, section 14.3. +
+
+ +next + +up + +previous +
+ Next: SLA_SVDSOL - Solution Vector from SVD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SVD - Singular Value Decomposition +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node182.html b/src/slalib/sun67.htx/node182.html new file mode 100644 index 0000000..f99ea3f --- /dev/null +++ b/src/slalib/sun67.htx/node182.html @@ -0,0 +1,201 @@ + + + + +SLA_SVDSOL - Solution Vector from SVD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_TP2S - Tangent Plane to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SVDCOV - Covariance Matrix from SVD +

+

+

SLA_SVDSOL - Solution Vector from SVD +   +

+
+
ACTION: +
From a given vector and the SVD of a matrix (as obtained from +the sla_SVD routine), obtain the solution vector. + This routine solves the equation: + 

+ 		 A $\cdot$ x = b         
+
+ where: + 

+ 		 A 		 is a given m (rows) $\times n$ (columns)                       matrix, where $m \geq n$ 
+		 x 		 is the n-vector we wish to find, and
+		 b 		 is a given m-vector         
+
+ by means of the Singular Value Decomposition method (SVD). +

CALL: +
CALL sla_SVDSOL (M, N, MP, NP, B, U, W, V, WORK, X) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
M,NIm, n, the numbers of rows and columns in matrix A
MP,NPIphysical dimensions of array containing matrix A
BD(M)known vector b
UD(MP,NP)array containing $m \times n$ matrix U
WD(N)$n \times n$ diagonal matrix W +(diagonal elements only)
VD(NP,NP)array containing $n \times n$ orthogonal matrix V
+

+
RETURNED: +
+
+ + + + + + + + + +
WORKD(N)workspace
XD(N)unknown vector x
+

+
NOTES: +
+
1. +
In the Singular Value Decomposition method (SVD), +the matrix A is first factorized (for example by +the routine sla_SVD) into the following components: + 

+ 		 A = U $\cdot$ W $\cdot$ VT
+
+ where: + 

+ 		 A 		 is any m (rows) $\times n$ (columns) matrix,                      where m > n 
+		 U 		 is an $m \times n$ column-orthogonal matrix
+		 W 		 is an $n \times n$ diagonal matrix with                      $w_{ii} \geq 0$ 
+		 VT is the transpose of an $n \times n$                            orthogonal matrix        
+
+ Note that m and n are the logical dimensions of the + matrices and vectors concerned, which can be located in + arrays of larger physical dimensions MP and NP. + The solution is then found from the expression: + 

+ 		 x = V $\cdot~[diag(1/$W$_{j})]
+ \cdot ($U$^{T}\cdot$b)        
+
+
2. +
If matrix A is square, and if the diagonal matrix W is not + altered, the method is equivalent to conventional solution + of simultaneous equations. +
3. +
If m > n, the result is a least-squares fit. +
4. +
If the solution is poorly determined, this shows up in the + SVD factorization as very small or zero Wj values. Where + a Wj value is small but non-zero it can be set to zero to + avoid ill effects. The present routine detects such zero + Wj values and produces a sensible solution, with highly + correlated terms kept under control rather than being allowed + to elope to infinity, and with meaningful values for the + other terms. +
+

+
REFERENCE: +
Numerical Recipes, section 2.9. +
+
+ +next + +up + +previous +
+ Next: SLA_TP2S - Tangent Plane to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SVDCOV - Covariance Matrix from SVD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node183.html b/src/slalib/sun67.htx/node183.html new file mode 100644 index 0000000..ae3acd0 --- /dev/null +++ b/src/slalib/sun67.htx/node183.html @@ -0,0 +1,109 @@ + + + + +SLA_TP2S - Tangent Plane to Spherical + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_TP2V - Tangent Plane to Direction Cosines +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SVDSOL - Solution Vector from SVD +

+

+

SLA_TP2S - Tangent Plane to Spherical +   +

+
+
ACTION: +
Transform tangent plane coordinates into spherical +coordinates (single precision) +

CALL: +
CALL sla_TP2S (XI, ETA, RAZ, DECZ, RA, DEC) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETARtangent plane rectangular coordinates (radians)
RAZ,DECZRspherical coordinates of tangent point (radians)
+

+
RETURNED: +
+
+ + + + + +
RA,DECRspherical coordinates (radians)
+

+
NOTES: +
+
1. +
The projection is called the gnomonic projection; the +Cartesian coordinates $[\,\xi,\eta\,]$ are called +standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
2. +
When working in $[\,x,y,z\,]$ rather than spherical coordinates, the + equivalent Cartesian routine sla_TP2V is available. +
+
+ +next + +up + +previous +
+ Next: SLA_TP2V - Tangent Plane to Direction Cosines +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_SVDSOL - Solution Vector from SVD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node184.html b/src/slalib/sun67.htx/node184.html new file mode 100644 index 0000000..f069a46 --- /dev/null +++ b/src/slalib/sun67.htx/node184.html @@ -0,0 +1,117 @@ + + + + +SLA_TP2V - Tangent Plane to Direction Cosines + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_TPS2C - Plate centre from and +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TP2S - Tangent Plane to Spherical +

+

+

SLA_TP2V - Tangent Plane to Direction Cosines +   +

+
+
ACTION: +
Given the tangent-plane coordinates of a star and the direction +cosines of the tangent point, determine the direction cosines + of the star + (single precision). +

CALL: +
CALL sla_TP2V (XI, ETA, V0, V) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETARtangent plane coordinates of star (radians)
V0R(3)direction cosines of tangent point
+

+
RETURNED: +
+
+ + + + + +
VR(3)direction cosines of star
+

+
NOTES: +
+
1. +
If vector V0 is not of unit length, the returned vector V will +be wrong. +
2. +
If vector V0 points at a pole, the returned vector V will be + based on the arbitrary assumption that $\alpha=0$ at + the tangent point. +
3. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
4. +
This routine is the Cartesian equivalent of the routine sla_TP2S. +
+
+ +next + +up + +previous +
+ Next: SLA_TPS2C - Plate centre from and +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TP2S - Tangent Plane to Spherical +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node185.html b/src/slalib/sun67.htx/node185.html new file mode 100644 index 0000000..0313e77 --- /dev/null +++ b/src/slalib/sun67.htx/node185.html @@ -0,0 +1,168 @@ + + + + +SLA_TPS2C - Plate centre from and + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_TPV2C - Plate centre from and x,y,z +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TP2V - Tangent Plane to Direction Cosines +

+

+

    +
+SLA_TPS2C - Plate centre from $\xi,\eta$ and $\alpha,\delta$

+
+
ACTION: +
From the tangent plane coordinates of a star of known $[\,\alpha,\delta\,]$,determine the $[\,\alpha,\delta\,]$ of the tangent point (single precision) +

CALL: +
CALL sla_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETARtangent plane rectangular coordinates (radians)
RA,DECRspherical coordinates (radians)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
RAZ1,DECZ1Rspherical coordinates of tangent point, +solution 1
RAZ2,DECZ2Rspherical coordinates of tangent point, +solution 2
NInumber of solutions:
0 = no solutions returned (note 2)
1 = only the first solution is useful (note 3)
2 = there are two useful solutions (note 3)
+

+
NOTES: +
+
1. +
The RAZ1 and RAZ2 values returned are in the range $0\!-\!2\pi$.
2. +
Cases where there is no solution can only arise near the poles. +For example, it is clearly impossible for a star at the pole + itself to have a non-zero $\xi$ value, and hence it is + meaningless to ask where the tangent point would have to be + to bring about this combination of $\xi$ and $\delta$.
3. +
Also near the poles, cases can arise where there are two useful + solutions. The argument N indicates whether the second of the + two solutions returned is useful. N=1 + indicates only one useful solution, the usual case; under + these circumstances, the second solution corresponds to the + ``over-the-pole'' case, and this is reflected in the values + of RAZ2 and DECZ2 which are returned. +
4. +
The DECZ1 and DECZ2 values returned are in the range $\pm \pi$, but in the ordinary, non-pole-crossing, case, the range is + $\pm\pi/2$.
5. +
RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians. +
6. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
7. +
When working in $[\,x,y,z\,]$ rather than spherical coordinates, the + equivalent Cartesian routine sla_TPV2C is available. +
+
+ +next + +up + +previous +
+ Next: SLA_TPV2C - Plate centre from and x,y,z +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TP2V - Tangent Plane to Direction Cosines +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node186.html b/src/slalib/sun67.htx/node186.html new file mode 100644 index 0000000..32d0e60 --- /dev/null +++ b/src/slalib/sun67.htx/node186.html @@ -0,0 +1,144 @@ + + + + +SLA_TPV2C - Plate centre from and x,y,z + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_UE2EL - Universal to Conventional Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TPS2C - Plate centre from and +

+

+

    +
+SLA_TPV2C - Plate centre from $\xi,\eta$ and x,y,z +

+
+
ACTION: +
From the tangent plane coordinates of a star of known +direction cosines, determine the direction cosines + of the tangent point (single precision) +

CALL: +
CALL sla_TPV2C (XI, ETA, V, V01, V02, N) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETARtangent plane coordinates of star (radians)
VR(3)direction cosines of star
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
V01R(3)direction cosines of tangent point, solution 1
V01R(3)direction cosines of tangent point, solution 2
NInumber of solutions:
0 = no solutions returned (note 2)
1 = only the first solution is useful (note 3)
2 = there are two useful solutions (note 3)
+

+
NOTES: +
+
1. +
The vector V must be of unit length or the result will be wrong. +
2. +
Cases where there is no solution can only arise near the poles. +For example, it is clearly impossible for a star at the pole + itself to have a non-zero XI value. +
3. +
Also near the poles, cases can arise where there are two useful + solutions. The argument N indicates whether the second of the + two solutions returned is useful. + N=1 + indicates only one useful solution, the usual case; under these + circumstances, the second solution can be regarded as valid if + the vector V02 is interpreted as the ``over-the-pole'' case. +
4. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
5. +
This routine is the Cartesian equivalent of the routine sla_TPS2C. +
+
+ +next + +up + +previous +
+ Next: SLA_UE2EL - Universal to Conventional Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TPS2C - Plate centre from and +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node187.html b/src/slalib/sun67.htx/node187.html new file mode 100644 index 0000000..9b71eb3 --- /dev/null +++ b/src/slalib/sun67.htx/node187.html @@ -0,0 +1,378 @@ + + + + +SLA_UE2EL - Universal to Conventional Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_UE2PV - Pos/Vel from Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TPV2C - Plate centre from and x,y,z +

+

+

SLA_UE2EL - Universal to Conventional Elements +   +

+
+
ACTION: +
Transform universal elements into conventional heliocentric +osculating elements. +

CALL: +
CALL sla_UE2EL ( + U, JFORMR, + JFORM, EPOCH, ORBINC, ANODE, PERIH, + AORQ, E, AORL, DM, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal orbital elements (updated; Note 1)
(1)combined mass (M+m)
(2)total energy of the orbit ($\alpha$)
(3)reference (osculating) epoch (t0)
(4-6)position at reference epoch (${\rm \bf r}_0$)
(7-9)velocity at reference epoch (${\rm \bf v}_0$)
(10)heliocentric distance at reference epoch
(11)${\rm \bf r}_0.{\rm \bf v}_0$
(12)date (t)
(13)universal eccentric anomaly ($\psi$) of date, approx
   
JFORMRIrequested element set (1-3; Note 3)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
JFORMIelement set actually returned (1-3; Note 4)
EPOCHDepoch of elements (t0 or T, TT MJD)
ORBINCDinclination (i, radians)
ANODEDlongitude of the ascending node ($\Omega$, radians)
PERIHDlongitude or argument of perihelion +($\varpi$ or $\omega$,
radians)
AORQDmean distance or perihelion distance (a or q, AU)
EDeccentricity (e)
AORLDmean anomaly or longitude +(M or L, radians,
JFORM=1,2 only)
DMDdaily motion (n, radians, JFORM=1 only)
JSTATIstatus:
0 = OK
-1 = illegal PMASS
-2 = illegal JFORMR
-3 = position/velocity out of allowed range
+

+
NOTES: +
+
1. +
The ``universal'' elements are those which define the orbit for the +purposes of the method of universal variables (see reference 2). +They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) $\alpha$, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, + (iii) the outwards component of the velocity at the given epoch, + (iv) an estimate of $\psi$, the ``universal eccentric anomaly'' at a + given date and (v) that date. +
2. +
The universal elements are with respect to the mean equator and + equinox of epoch J2000. The orbital elements produced are with + respect to the J2000 ecliptic and mean equinox. +
3. +
Three different element-format options are supported, as + follows.
+

+JFORM=1, suitable for the major planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 longitude of perihelion $\varpi$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean longitude L (radians)
+		 DM 		 = 		 daily motion n (radians)        
+
+

+JFORM=2, suitable for minor planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e \leq 10 )$
+
4. +
It may not be possible to generate elements in the form + requested through JFORMR. The caller is notified of the form + of elements actually returned by means of the JFORM argument: +


+ 		 JFORMR 		 JFORM 		 meaning 
+ 
+		      1 		      1 		 OK: elements are in the requested format
+		      1 		      2 		 never happens
+		      1 		      3 		 orbit not elliptical
+		      2 		      1 		 never happens
+		      2 		      2 		 OK: elements are in the requested format
+		      2 		      3 		 orbit not elliptical
+		      3 		      1 		 never happens
+		      3 		      2 		 never happens
+		      3 		      3 		 OK: elements are in the requested format        
+
+
5. +
The arguments returned for each value of JFORM (cf Note 5: + JFORM may not be the same as JFORMR) are as follows: +


+ 		 JFORM 		 1 		 2 		 3 
+ 
+		 EPOCH 		 t0 t0 T 
+		 ORBINC 		 i i i 
+		 ANODE 		 $\Omega$ $\Omega$ $\Omega$ 
+		 PERIH 		 $\varpi$ $\omega$ $\omega$ 
+		 AORQ 		 a a q 
+		 E 		 e e e 
+		 AORL 		 L M -
+		 DM 		 n - 		 -        
+
+

+where: + 


+ 		 t0 is the epoch of the elements (MJD, TT)
+		 T is the epoch of perihelion (MJD, TT)
+		 i is the inclination (radians)
+		 $\Omega$ is the longitude of the ascending node (radians)
+		 $\varpi$ is the longitude of perihelion (radians)
+		 $\omega$ is the argument of perihelion (radians)
+		 a is the mean distance (AU)
+		 q is the perihelion distance (AU)
+		 e is the eccentricity
+		 L is the longitude (radians, $0-2\pi$)		 M is the mean anomaly (radians, $0-2\pi$)		 n is the daily motion (radians)
+		 - 		 means no value is set        
+
+
6. +
At very small inclinations, the longitude of the ascending node + ANODE becomes indeterminate and under some circumstances may be + set arbitrarily to zero. Similarly, if the orbit is close to + circular, the true anomaly becomes indeterminate and under some + circumstances may be set arbitrarily to zero. In such cases, + the other elements are automatically adjusted to compensate, + and so the elements remain a valid description of the orbit. +
+

+
REFERENCES: +
+
1. +
Sterne, Theodore E., An Introduction to Celestial Mechanics, +Interscience Publishers, 1960. Section 6.7, p199. +
2. +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_UE2PV - Pos/Vel from Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TPV2C - Plate centre from and x,y,z +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node188.html b/src/slalib/sun67.htx/node188.html new file mode 100644 index 0000000..bc0c8bd --- /dev/null +++ b/src/slalib/sun67.htx/node188.html @@ -0,0 +1,220 @@ + + + + +SLA_UE2PV - Pos/Vel from Universal Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_UNPCD - Remove Radial Distortion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_UE2EL - Universal to Conventional Elements +

+

+

SLA_UE2PV - Pos/Vel from Universal Elements +   +

+
+
ACTION: +
Heliocentric position and velocity of a planet, asteroid or comet, +starting from orbital elements in the ``universal variables'' form. +

CALL: +
CALL sla_UE2PV (DATE, U, PV, JSTAT) +

+

+
GIVEN: +
+
+ + + + + +
DATEDdate (TT Modified Julian Date = JD-2400000.5)
+

+
GIVEN and RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal orbital elements (updated; Note 1)
(1)combined mass (M+m)
(2)total energy of the orbit ($\alpha$)
(3)reference (osculating) epoch (t0)
(4-6)position at reference epoch (${\rm \bf r}_0$)
(7-9)velocity at reference epoch (${\rm \bf v}_0$)
(10)heliocentric distance at reference epoch
(11)${\rm \bf r}_0.{\rm \bf v}_0$
(12)date (t)
(13)universal eccentric anomaly ($\psi$) of date, approx
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
PVD(6)heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, equatorial, J2000
(AU, AU/s; Note 1)
JSTATIstatus:
0 = OK
-1 = radius vector zero
-2 = failed to converge
+

+
NOTES: +
+
1. +
The ``universal'' elements are those which define the orbit for the +purposes of the method of universal variables (see reference). +They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) $\alpha$, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, + (iii) the outwards component of the velocity at the given epoch, + (iv) an estimate of $\psi$, the ``universal eccentric anomaly'' at a + given date and (v) that date. +
2. +
The companion routine is sla_EL2UE. This takes the conventional + orbital elements and transforms them into the set of numbers + needed by the present routine. A single prediction requires one + one call to sla_EL2UE followed by one call to the present routine; + for convenience, the two calls are packaged as the routine + sla_PLANEL. Multiple predictions may be made by again + calling sla_EL2UE once, but then calling the present routine + multiple times, which is faster than multiple calls to sla_PLANEL. +

+It is not obligatory to use sla_EL2UE to obtain the parameters. + However, it should be noted that because sla_EL2UE performs its + own validation, no checks on the contents of the array U are made + by the present routine. +

3. +
DATE is the instant for which the prediction is required. It is + in the TT timescale (formerly Ephemeris Time, ET) and is a + Modified Julian Date (JD-2400000.5). +
4. +
The universal elements supplied in the array U are in canonical + units (solar masses, AU and canonical days). The position and + velocity are not sensitive to the choice of reference frame. The + sla_EL2UE routine in fact produces coordinates with respect to the + J2000 equator and equinox. +
5. +
The algorithm was originally adapted from the EPHSLA program of + D.H.P.Jones (private communication, 1996). The method + is based on Stumpff's Universal Variables. +
+

+
REFERENCE: +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_UNPCD - Remove Radial Distortion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_UE2EL - Universal to Conventional Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node189.html b/src/slalib/sun67.htx/node189.html new file mode 100644 index 0000000..a19516f --- /dev/null +++ b/src/slalib/sun67.htx/node189.html @@ -0,0 +1,160 @@ + + + + +SLA_UNPCD - Remove Radial Distortion + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_V2TP - Direction Cosines to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_UE2PV - Pos/Vel from Universal Elements +

+

+

SLA_UNPCD - Remove Radial Distortion +   +

+
+
ACTION: +
Remove pincushion/barrel distortion from a distorted +$[\,x,y\,]$ to give tangent-plane $[\,x,y\,]$.

CALL: +
CALL sla_UNPCD (DISCO,X,Y) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DISCODpincushion/barrel distortion coefficient
X,YDdistorted $[\,x,y\,]$
+

+
RETURNED: +
+
+ + + + + +
X,YDtangent-plane $[\,x,y\,]$
+

+
NOTES: +
+
1. +
The distortion is of the form $\rho = r (1 + c r^{2})$, where r is +the radial distance from the tangent point, c is the DISCO +argument, and $\rho$ is the radial distance in the presence of + the distortion. +
2. +
For pincushion distortion, C is +ve; for + barrel distortion, C is -ve. +
3. +
For X,Y in units of one projection radius (in the case of + a photographic plate, the focal length), the following + DISCO values apply: +


+
+
+

+ + + + + + + + + + + + + + + + + + + + + +
GeometryDISCO
astrograph0.0
Schmidt-0.3333
AAT PF doublet+147.069
AAT PF triplet+178.585
AAT f/8+21.20
JKT f/8+14.6
+


+
+
+

4. +
The present routine is an approximate inverse to the + companion routine sla_PCD, obtained from two iterations + of Newton's method. The mismatch between the sla_PCD + and sla_UNPCD is negligible for astrometric applications; + to reach 1 milliarcsec at the edge of the AAT triplet or + Schmidt field would require field diameters of $2^{\circ} + \hspace{-0.37em}.\hspace{0.02em}4$ and $42^{\circ}$ respectively. +
+
+ +next + +up + +previous +
+ Next: SLA_V2TP - Direction Cosines to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_UE2PV - Pos/Vel from Universal Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node19.html b/src/slalib/sun67.htx/node19.html new file mode 100644 index 0000000..3a52cd9 --- /dev/null +++ b/src/slalib/sun67.htx/node19.html @@ -0,0 +1,160 @@ + + + + +SLA_AMPQK - Quick Apparent to Mean + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AOP - Apparent to Observed +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AMP - Apparent to Mean +

+

+

SLA_AMPQK - Quick Apparent to Mean +   +

+
+
ACTION: +
Convert star $[\,\alpha,\delta\,]$ from geocentric apparent to mean place +(post IAU 1976). Use of this routine is appropriate when + efficiency is important and where many star positions are + all to be transformed for one epoch and equinox. The + star-independent parameters can be obtained by calling + the sla_MAPPA routine. +

CALL: +
CALL sla_AMPQK (RA, DA, AMPRMS, RM, DM) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
RA,DADapparent $[\,\alpha,\delta\,]$ (radians)
AMPRMSD(21)star-independent mean-to-apparent parameters:
(1)time interval for proper motion (Julian years)
(2-4)barycentric position of the Earth (AU)
(5-7)heliocentric direction of the Earth (unit vector)
(8)(gravitational radius of +Sun)$\times 2 / $(Sun-Earth distance)
(9-11)v: barycentric Earth velocity in units of c
(12)$\sqrt{1-\left\vert\mbox{\bf v}\right\vert^2}$
(13-21)precession/nutation $3\times3$ matrix
+

+
RETURNED: +
+
+ + + + + +
RM,DMDmean $[\,\alpha,\delta\,]$ (radians)
+

+
NOTES: +
+
1. +
The accuracy is limited by the routine sla_EVP, called +by sla_MAPPA, which computes the Earth position and +velocity using the methods of Stumpff. The maximum + error is about 0.3 milliarcsecond. +
2. +
Iterative techniques are used for the aberration and + light deflection corrections so that the routines + sla_AMP (or sla_AMPQK) and sla_MAP (or sla_MAPQK) are + accurate inverses; even at the edge of the Sun's disc + the discrepancy is only about 1 nanoarcsecond. +
+

+
REFERENCES: +
+
1. +
1984 Astronomical Almanac, pp B39-B41. +
2. +
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6. +
+
+ +next + +up + +previous +
+ Next: SLA_AOP - Apparent to Observed +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AMP - Apparent to Mean +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node190.html b/src/slalib/sun67.htx/node190.html new file mode 100644 index 0000000..09def53 --- /dev/null +++ b/src/slalib/sun67.htx/node190.html @@ -0,0 +1,137 @@ + + + + +SLA_V2TP - Direction Cosines to Tangent Plane + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_VDV - Scalar Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_UNPCD - Remove Radial Distortion +

+

+

SLA_V2TP - Direction Cosines to Tangent Plane +   +

+
+
ACTION: +
Given the direction cosines of a star and of the tangent point, +determine the star's tangent-plane coordinates + (single precision). +

CALL: +
CALL sla_V2TP (V, V0, XI, ETA, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
VR(3)direction cosines of star
V0R(3)direction cosines of tangent point
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
XI,ETARtangent plane coordinates (radians)
JIstatus:
0 = OK, star on tangent plane
1 = error, star too far from axis
2 = error, antistar on tangent plane
3 = error, antistar too far from axis
+

+
NOTES: +
+
1. +
If vector V0 is not of unit length, or if vector V is of zero +length, the results will be wrong. +
2. +
If V0 points at a pole, the returned $\xi,\eta$ will be based on the + arbitrary assumption that $\alpha=0$ at the tangent point. +
3. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
4. +
This routine is the Cartesian equivalent of the routine sla_S2TP. +
+
+ +next + +up + +previous +
+ Next: SLA_VDV - Scalar Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_UNPCD - Remove Radial Distortion +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node191.html b/src/slalib/sun67.htx/node191.html new file mode 100644 index 0000000..427bf46 --- /dev/null +++ b/src/slalib/sun67.htx/node191.html @@ -0,0 +1,91 @@ + + + + +SLA_VDV - Scalar Product + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_VN - Normalize Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_V2TP - Direction Cosines to Tangent Plane +

+

+

SLA_VDV - Scalar Product +   +

+
+
ACTION: +
Scalar product of two 3-vectors (single precision). +
CALL: +
R = sla_VDV (VA, VB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
VAR(3)first vector
VBR(3)second vector
+

+
RETURNED: +
+
+ + + + + +
sla_VDVRscalar product VA.VB
+
+ +next + +up + +previous +
+ Next: SLA_VN - Normalize Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_V2TP - Direction Cosines to Tangent Plane +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node192.html b/src/slalib/sun67.htx/node192.html new file mode 100644 index 0000000..dd4d9b6 --- /dev/null +++ b/src/slalib/sun67.htx/node192.html @@ -0,0 +1,95 @@ + + + + +SLA_VN - Normalize Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_VXV - Vector Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_VDV - Scalar Product +

+

+

SLA_VN - Normalize Vector +   +

+
+
ACTION: +
Normalize a 3-vector, also giving the modulus (single precision). +
CALL: +
CALL sla_VN (V, UV, VM) +

+

+
GIVEN: +
+
+ + + + + +
VR(3)vector
+

+
RETURNED: +
+
+ + + + + + + + + +
UVR(3)unit vector in direction of V
VMRmodulus of V
+

+
NOTE: +
If the modulus of V is zero, UV is set to zero as well. +
+
+ +next + +up + +previous +
+ Next: SLA_VXV - Vector Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_VDV - Scalar Product +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node193.html b/src/slalib/sun67.htx/node193.html new file mode 100644 index 0000000..8f27978 --- /dev/null +++ b/src/slalib/sun67.htx/node193.html @@ -0,0 +1,93 @@ + + + + +SLA_VXV - Vector Product + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_WAIT - Time Delay +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_VN - Normalize Vector +

+

+

SLA_VXV - Vector Product +   +

+
+
ACTION: +
Vector product of two 3-vectors (single precision). +
CALL: +
CALL sla_VXV (VA, VB, VC) +

+

+
GIVEN: +
+
+ + + + + + + + + +
VAR(3)first vector
VBR(3)second vector
+

+
RETURNED: +
+
+ + + + + +
VCR(3)vector product VA$\times$VB
+
+ +next + +up + +previous +
+ Next: SLA_WAIT - Time Delay +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_VN - Normalize Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node194.html b/src/slalib/sun67.htx/node194.html new file mode 100644 index 0000000..55a0ed7 --- /dev/null +++ b/src/slalib/sun67.htx/node194.html @@ -0,0 +1,91 @@ + + + + +SLA_WAIT - Time Delay + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_XY2XY - Apply Linear Model to an +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_VXV - Vector Product +

+

+

SLA_WAIT - Time Delay +   +

+
+
ACTION: +
Wait for a specified interval. +
CALL: +
CALL sla_WAIT (DELAY) +

+

+
GIVEN: +
+
+ + + + + +
DELAYRdelay in seconds
+

+
NOTES: +
+
1. +
The implementation is machine-specific. +
2. +
The delay actually requested is restricted to the range +100ns-200s in the present implementation. +
3. +
There is no guarantee of accuracy, though on almost all + types of computer the program will certainly not + resume execution before the stated interval has + elapsed. +
+
+ +next + +up + +previous +
+ Next: SLA_XY2XY - Apply Linear Model to an +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_VXV - Vector Product +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node195.html b/src/slalib/sun67.htx/node195.html new file mode 100644 index 0000000..2b33ece --- /dev/null +++ b/src/slalib/sun67.htx/node195.html @@ -0,0 +1,114 @@ + + + + +SLA_XY2XY - Apply Linear Model to an + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ZD - to Zenith Distance +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_WAIT - Time Delay +

+

+

    +
+SLA_XY2XY - Apply Linear Model to an $[\,x,y\,]$

+
+
ACTION: +
Transform one $[\,x,y\,]$ into another using a linear model of the type +produced by the sla_FITXY routine. +

CALL: +
CALL sla_XY2XY (X1,Y1,COEFFS,X2,Y2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
X1,Y1D$[\,x,y\,]$ before transformation
COEFFSD(6)transformation coefficients (see note)
+

+
RETURNED: +
+
+ + + + + +
X2,Y2D$[\,x,y\,]$ after transformation
+

+
NOTES: +
+
1. +
The model relates two sets of $[\,x,y\,]$ coordinates as follows. +Naming the six elements of COEFFS a,b,c,d,e & f, +the present routine performs the transformation: +
x2 = a + bx1 + cy1
+ y2 = d + ex1 + fy1
+
2. +
See also sla_FITXY, sla_PXY, sla_INVF, sla_DCMPF. +
+
+ +next + +up + +previous +
+ Next: SLA_ZD - to Zenith Distance +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_WAIT - Time Delay +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node196.html b/src/slalib/sun67.htx/node196.html new file mode 100644 index 0000000..0dc168b --- /dev/null +++ b/src/slalib/sun67.htx/node196.html @@ -0,0 +1,137 @@ + + + + +SLA_ZD - to Zenith Distance + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: EXPLANATION AND EXAMPLES +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_XY2XY - Apply Linear Model to an +

+

+

    +
+SLA_ZD - $h,\delta$ to Zenith Distance +

+
+
ACTION: +
Hour angle and declination to zenith distance +(double precision). +

CALL: +
D = sla_ZD (HA, DEC, PHI) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
HADhour angle in radians
DECDdeclination in radians
PHIDlatitude in radians
+

+
RETURNED: +
+
+ + + + + +
sla_ZDDzenith distance (radians, $0\!-\!\pi$)
+

+
NOTES: +
+
1. +
The latitude must be geodetic. In critical applications, +corrections for polar motion should be applied (see sla_POLMO). +
2. +
In some applications it will be important to specify the + correct type of hour angle and declination in order to + produce the required type + of zenith distance. In particular, it may be + important to distinguish between the zenith distance + as affected by refraction, which would require the + observed $[\,h,\delta\,]$, and the zenith distance in vacuo, + which would require the topocentric $[\,h,\delta\,]$. If + the effects of diurnal aberration can be neglected, the + apparent $[\,h,\delta\,]$ may be used instead of the + topocentric $[\,h,\delta\,]$.
3. +
No range checking of arguments is done. +
4. +
In applications which involve many zenith distance calculations, + rather than calling the present routine it will be more + efficient to use inline code, having previously computed fixed + terms such as sine and cosine of latitude, and perhaps sine and + cosine of declination. +
+

+
+

+

+ +next + +up + +previous +
+ Next: EXPLANATION AND EXAMPLES +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_XY2XY - Apply Linear Model to an +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node197.html b/src/slalib/sun67.htx/node197.html new file mode 100644 index 0000000..ae8cd55 --- /dev/null +++ b/src/slalib/sun67.htx/node197.html @@ -0,0 +1,171 @@ + + + + +EXPLANATION AND EXAMPLES + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Spherical Trigonometry +
+Up: SLALIB Positional Astronomy Library +
+ Previous: SLA_ZD - to Zenith Distance +

+

+

+EXPLANATION AND EXAMPLES +

+To guide the writer of positional-astronomy applications software, +this final chapter puts the SLALIB routines into the context of +astronomical phenomena and techniques, and presents a few +``cookbook'' examples +of the SLALIB calls in action. The astronomical content of the chapter +is not, of course, intended to be a substitute for specialist text-books on +positional astronomy, but may help bridge the gap between +such books and the SLALIB routines. For further reading, the following +cover a wide range of material and styles: + +Also of considerable value, though out of date in places, are: + +Only brief details of individual SLALIB routines are given here, and +readers will find it useful to refer to the subprogram specifications +elsewhere in this document. The source code for the SLALIB routines +(available in both Fortran and C) is also intended to be used as +documentation. +

+

+ +  + + +
+ +next + +up + +previous +
+ Next: Spherical Trigonometry +
+Up: SLALIB Positional Astronomy Library +
+ Previous: SLA_ZD - to Zenith Distance +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node198.html b/src/slalib/sun67.htx/node198.html new file mode 100644 index 0000000..30aa3e8 --- /dev/null +++ b/src/slalib/sun67.htx/node198.html @@ -0,0 +1,167 @@ + + + + +Spherical Trigonometry + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Formatting angles +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: EXPLANATION AND EXAMPLES +

+

+

+Spherical Trigonometry +

+Celestial phenomena occur at such vast distances from the +observer that for most practical purposes there is no need to +work in 3D; only the direction +of a source matters, not how far away it is. Things can +therefore be viewed as if they were happening +on the inside of sphere with the observer at the centre - +the celestial sphere. Problems involving +positions and orientations in the sky can then be solved by +using the formulae of spherical trigonometry, which +apply to spherical triangles, the sides of which are +great circles. +

+Positions on the celestial sphere may be specified by using +a spherical polar coordinate system, defined in terms of +some fundamental plane and a line in that plane chosen to +represent zero longitude. Mathematicians usually work with the +co-latitude, with zero at the principal pole, whereas most +astronomical coordinate systems use latitude, reckoned plus and +minus from the equator. +Astronomical coordinate systems may be either right-handed +(e.g. right ascension and declination $[\,\alpha,\delta\,]$,Galactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$)or left-handed (e.g. hour angle and +declination $[\,h,\delta\,]$). In some cases +different conventions have been used in the past, a fruitful source of +mistakes. Azimuth and geographical longitude are examples; azimuth +is now generally reckoned north through east +(making a left-handed system); geographical longitude is now usually +taken to increase eastwards (a right-handed system) but astronomers +used to employ a west-positive convention. In reports +and program comments it is wise to spell out what convention +is being used, if there is any possibility of confusion. +

+When applying spherical trigonometry formulae, attention must be +paid to +rounding errors (for example it is a bad idea to find a +small angle through its cosine) and to the possibility of +problems close to poles. +Also, if a formulation relies on inspection to establish +the quadrant of the result, it is an indication that a vector-related +method might be preferable. +

+As well as providing many routines which work in terms of specific +spherical coordinates such as $[\,\alpha,\delta\,]$, SLALIB provides +two routines which operate directly on generic spherical +coordinates: +sla_SEP +computes the separation between +two points (the distance along a great circle) and +sla_BEAR +computes the bearing (or position angle) +of one point seen from the other. The routines +sla_DSEP +and +sla_DBEAR +are double precision equivalents. As a simple demonstration +of SLALIB, we will use these facilities to estimate the distance from +London to Sydney and the initial compass heading: +

+            IMPLICIT NONE
+
+      *  Degrees to radians
+            REAL D2R
+            PARAMETER (D2R=0.01745329252)
+
+      *  Longitudes and latitudes (radians) for London and Sydney
+            REAL AL,BL,AS,BS
+            PARAMETER (AL=-0.2*D2R,BL=51.5*D2R,AS=151.2*D2R,BS=-33.9*D2R)
+
+      *  Earth radius in km (spherical approximation)
+            REAL RKM
+            PARAMETER (RKM=6375.0)
+
+            REAL sla_SEP,sla_BEAR
+
+
+      *  Distance and initial heading (N=0, E=90)
+            WRITE (*,'(1X,I5,'' km,'',I4,'' deg'')')
+           :    NINT(sla_SEP(AL,BL,AS,BS)*RKM),NINT(sla_BEAR(AL,BL,AS,BS)/D2R)
+
+            END
+
+

(The result is 17011 km, $61^\circ$.) +

+The routines +sla_PAV and +sla_DPAV +are equivalents of sla_BEAR and sla_DBEAR but starting from +direction-cosines instead of spherical coordinates. +

+

+ +  + + +
+ +next + +up + +previous +
+ Next: Formatting angles +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: EXPLANATION AND EXAMPLES +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node199.html b/src/slalib/sun67.htx/node199.html new file mode 100644 index 0000000..93a4839 --- /dev/null +++ b/src/slalib/sun67.htx/node199.html @@ -0,0 +1,174 @@ + + + + +Formatting angles + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Vectors and Matrices +
+Up: Spherical Trigonometry +
+ Previous: Spherical Trigonometry +

+

+

+Formatting angles +

+SLALIB has routines for decoding decimal numbers +from character form and for converting angles to and from +sexagesimal form (hours, minutes, seconds or degrees, +arcminutes, arcseconds). These apparently straightforward +operations contain hidden traps which the SLALIB routines +avoid. +

+There are five routines for decoding numbers from a character +string, such as might be entered using a keyboard. +They all work in the same style, and successive calls +can work their way along a single string decoding +a sequence of numbers of assorted types. Number +fields can be separated by spaces or commas, and can be defaulted +to previous values or to preset defaults. +

+Three of the routines decode single numbers: +sla_INTIN +(integer), +sla_FLOTIN +(single precision floating point) and +sla_DFLTIN +(double precision). A minus sign can be +detected even when the number is zero; this avoids +the frequently-encountered ``minus zero'' bug, where +declinations etc. in +the range $0^{\circ}$ to $-1^{\circ}$ mysteriously migrate to +the range $0^{\circ}$ to $+1^{\circ}$.Here is an example (in Fortran) where we wish to +read two numbers, and integer IX and a real, Y, +with X defaulting to zero and Y defaulting to +X: +

+            DOUBLE PRECISION Y
+            CHARACTER*80 A
+            INTEGER IX,I,J
+
+      *  Input the string to be decoded
+            READ (*,'(A)') A
+
+      *  Preset IX to its default value
+            IX = 0
+
+      *  Point to the start of the string
+            I = 1
+
+      *  Decode an integer
+            CALL sla_INTIN(A,I,IX,J)
+            IF (J.GT.1) GO TO ... (bad IX)
+
+      *  Preset Y to its default value
+            Y = DBLE(IX)
+
+      *  Decode a double precision number
+            CALL sla_DFLTIN(A,I,Y,J)
+            IF (J.GT.1) GO TO ... (bad Y)
+
+

+Two additional routines decode a 3-field sexagesimal number: +sla_AFIN +(degrees, arcminutes, arcseconds to single +precision radians) and +sla_DAFIN +(the same but double precision). They also +work using other units such as hours etc. if +you multiply the result by the appropriate factor. An example +Fortran program which uses +sla_DAFIN +was given earlier, in section 1.2. +

+SLALIB provides four routines for expressing an angle in radians +in a preferred range. The function +sla_RANGE +expresses an angle +in the range $\pm \pi$;sla_RANORM +expresses an angle in the range +$0-2\pi$. The functions +sla_DRANGE +and +sla_DRANRM +are double precision versions. +

+Several routines +(sla_CTF2D, +sla_CR2AF +etc.) are provided to convert +angles to and from +sexagesimal form (hours, minute, seconds or degrees, +arcminutes and arcseconds). +They avoid the common +``converting from integer to real at the wrong time'' +bug, which produces angles like $24^{h}\,59^{m}\,59^{s}.999$.Here is a program which displays an hour angle +stored in radians: +

+            DOUBLE PRECISION HA
+            CHARACTER SIGN
+            INTEGER IHMSF(4)
+            :
+            CALL sla_DR2TF(3,HA,SIGN,IHMSF)
+            WRITE (*,'(1X,A,3I3.2,''.'',I3.3)') SIGN,IHMSF
+
+

+

+ +next + +up + +previous +
+ Next: Vectors and Matrices +
+Up: Spherical Trigonometry +
+ Previous: Spherical Trigonometry +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node2.html b/src/slalib/sun67.htx/node2.html new file mode 100644 index 0000000..2e1859d --- /dev/null +++ b/src/slalib/sun67.htx/node2.html @@ -0,0 +1,85 @@ + + + + +INTRODUCTION + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Purpose +
+Up: SLALIB Positional Astronomy Library +
+ Previous: Abstract +

+

+

+INTRODUCTION +

+
+ +  + + +
+ +next + +up + +previous +
+ Next: Purpose +
+Up: SLALIB Positional Astronomy Library +
+ Previous: Abstract +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node20.html b/src/slalib/sun67.htx/node20.html new file mode 100644 index 0000000..e544154 --- /dev/null +++ b/src/slalib/sun67.htx/node20.html @@ -0,0 +1,320 @@ + + + + +SLA_AOP - Apparent to Observed + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AOPPA - Appt-to-Obs Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AMPQK - Quick Apparent to Mean +

+

+

SLA_AOP - Apparent to Observed +   +

+
+
ACTION: +
Apparent to observed place, for optical sources distant from +the solar system. +

CALL: +
CALL sla_AOP ( + RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP, + TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
RAP,DAPDgeocentric apparent $[\,\alpha,\delta\,]$ (radians)
DATEDUTC date/time (Modified Julian Date, JD-2400000.5)
DUTD$\Delta$UT: UT1-UTC (UTC seconds)
ELONGMDobserver's mean longitude (radians, east +ve)
PHIMDobserver's mean geodetic latitude (radians)
HMDobserver's height above sea level (metres)
XP,YPDpolar motion $[\,x,y\,]$ coordinates (radians)
TDKDlocal ambient temperature (degrees K; std=273.155D0)
PMBDlocal atmospheric pressure (mB; std=1013.25D0)
RHDlocal relative humidity (in the range 0D0-1D0)
WLDeffective wavelength ($\mu{\rm m}$, e.g. 0.55D0)
TLRDtropospheric lapse rate (degrees K per metre, +e.g. 0.0065D0)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
AOBDobserved azimuth (radians: N=0, E=$90^{\circ}$)
ZOBDobserved zenith distance (radians)
HOBDobserved Hour Angle (radians)
DOBDobserved $\delta$ (radians)
ROBDobserved $\alpha$ (radians)
+

+
NOTES: +
+
1. +
This routine returns zenith distance rather than elevation +in order to reflect the fact that no allowance is made for +depression of the horizon. +
2. +
The accuracy of the result is limited by the corrections for + refraction. Providing the meteorological parameters are + known accurately and there are no gross local effects, the + predicted azimuth and elevation should be within about +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ for $\zeta<70^{\circ}$. Even + at a topocentric zenith distance of + $90^{\circ}$, the accuracy in elevation should be better than + 1 arcminute; useful results are available for a further + $3^{\circ}$, beyond which the sla_REFRO routine returns a + fixed value of the refraction. The complementary + routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK) + are self-consistent to better than 1 microarcsecond all over + the celestial sphere. +

3. +
It is advisable to take great care with units, as even + unlikely values of the input parameters are accepted and + processed in accordance with the models used. +
4. +
Apparent $[\,\alpha,\delta\,]$ means the geocentric apparent right ascension + and declination, which is obtained from a catalogue mean place + by allowing for space motion, parallax, precession, nutation, + annual aberration, and the Sun's gravitational lens effect. For + star positions in the FK5 system (i.e. J2000), these effects can + be applied by means of the sla_MAP etc. routines. Starting from + other mean place systems, additional transformations will be + needed; for example, FK4 (i.e. B1950) mean places would first + have to be converted to FK5, which can be done with the + sla_FK425 etc. routines. +
5. +
Observed $[\,Az,El~]$ means the position that would be seen by a + perfect theodolite located at the observer. This is obtained + from the geocentric apparent $[\,\alpha,\delta\,]$ by allowing for Earth + orientation and diurnal aberration, rotating from equator + to horizon coordinates, and then adjusting for refraction. + The $[\,h,\delta\,]$ is obtained by rotating back into equatorial + coordinates, using the geodetic latitude corrected for polar + motion, and is the position that would be seen by a perfect + equatorial located at the observer and with its polar axis + aligned to the Earth's axis of rotation (n.b. not to the + refracted pole). Finally, the $\alpha$ is obtained by subtracting + the h from the local apparent ST. +
6. +
To predict the required setting of a real telescope, the + observed place produced by this routine would have to be + adjusted for the tilt of the azimuth or polar axis of the + mounting (with appropriate corrections for mount flexures), + for non-perpendicularity between the mounting axes, for the + position of the rotator axis and the pointing axis relative + to it, for tube flexure, for gear and encoder errors, and + finally for encoder zero points. Some telescopes would, of + course, exhibit other properties which would need to be + accounted for at the appropriate point in the sequence. +
7. +
This routine takes time to execute, due mainly to the + rigorous integration used to evaluate the refraction. + For processing multiple stars for one location and time, + call sla_AOPPA once followed by one call per star to sla_AOPQK. + Where a range of times within a limited period of a few hours + is involved, and the highest precision is not required, call + sla_AOPPA once, followed by a call to sla_AOPPAT each time the + time changes, followed by one call per star to sla_AOPQK. +
8. +
The DATE argument is UTC expressed as an MJD. This is, + strictly speaking, wrong, because of leap seconds. However, + as long as the $\Delta$UT and the UTC are consistent there + are no difficulties, except during a leap second. In this + case, the start of the 61st second of the final minute should + begin a new MJD day and the old pre-leap $\Delta$UT should + continue to be used. As the 61st second completes, the MJD + should revert to the start of the day as, simultaneously, + the $\Delta$UT changes by one second to its post-leap new value. +
9. +
The $\Delta$UT (UT1-UTC) is tabulated in IERS circulars and + elsewhere. It increases by exactly one second at the end of + each UTC leap second, introduced in order to keep $\Delta$UT + within $\pm$$0^{\rm s}\hspace{-0.3em}.9$.
10. +
IMPORTANT - TAKE CARE WITH THE LONGITUDE SIGN CONVENTION. The + longitude required by the present routine is east-positive, + in accordance with geographical convention (and right-handed). + In particular, note that the longitudes returned by the + sla_OBS routine are west-positive (as in the Astronomical + Almanac before 1984) and must be reversed in sign before use + in the present routine. +
11. +
The polar coordinates XP,YP can be obtained from IERS + circulars and equivalent publications. The + maximum amplitude is about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ . If XP,YP values + are unavailable, use XP=YP=0D0. See page B60 of the 1988 + Astronomical Almanac for a definition of the two angles. +
12. +
The height above sea level of the observing station, HM, + can be obtained from the Astronomical Almanac (Section J + in the 1988 edition), or via the routine sla_OBS. If P, + the pressure in mB, is available, an adequate + estimate of HM can be obtained from the following expression: +
HM=-29.3D0*TSL*LOG(P/1013.25D0) +
+ where TSL is the approximate sea-level air temperature in degrees K + (see Astrophysical Quantities, C.W.Allen, 3rd edition, + §52). Similarly, if the pressure P is not known, + it can be estimated from the height of the observing + station, HM as follows: +
P=1013.25D0*EXP(-HM/(29.3D0*TSL)) +
+ Note, however, that the refraction is proportional to the + pressure and that an accurate P value is important for + precise work. +
13. +
The azimuths etc. used by the present routine are with + respect to the celestial pole. Corrections to the terrestrial pole + can be computed using sla_POLMO. +
+
+ +next + +up + +previous +
+ Next: SLA_AOPPA - Appt-to-Obs Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AMPQK - Quick Apparent to Mean +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node200.html b/src/slalib/sun67.htx/node200.html new file mode 100644 index 0000000..cbbad9d --- /dev/null +++ b/src/slalib/sun67.htx/node200.html @@ -0,0 +1,168 @@ + + + + +Vectors and Matrices + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Using vectors +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Formatting angles +

+

+

+Vectors and Matrices +

+As an alternative to employing a spherical polar coordinate system, +the direction of an object can be defined in terms of the sum of any +three vectors as long as they are different and +not coplanar. In practice, three vectors at right angles are +usually chosen, forming a system +of Cartesian coordinates. The x- and y-axes +lie in the fundamental plane (e.g. the equator in the +case of $[\,\alpha,\delta\,]$), with the x-axis pointing to zero longitude. +The z-axis is normal to the fundamental plane and points +towards positive latitudes. The y-axis can lie in either +of the two possible directions, depending on whether the +coordinate system is right-handed or left-handed. +The three axes are sometimes called +a triad. For most applications involving arbitrarily +distant objects such as stars, the vector which defines +the direction concerned is constrained to have unit length. +The x-, y- and z-components +can be regarded as the scalar (dot) product of this vector +onto the three axes of the triad in turn. Because the vector +is a unit vector, +each of the three dot-products is simply the cosine of the angle +between the unit vector and the axis concerned, and the +x-, y- and z-components are sometimes +called direction cosines. +

+For some applications involving objects +with the Solar System, unit vectors are inappropriate, and +it is necessary to use vectors scaled in length-units such as +AU, km etc. +In these cases the origin of the coordinate system may not be +the observer, but instead might be the Sun, the Solar-System +barycentre, the centre of the Earth etc. But whatever the application, +the final direction in which the observer sees the object can be +expressed as direction cosines. +

+But where has this got us? Instead of two numbers - a longitude and +a latitude - we now have three numbers to look after +- the x-, y- and +z-components - whose quadratic sum we have somehow to contrive to +be unity. And, in addition to this apparent redundancy, +most people find it harder to visualize +problems in terms of $[\,x,y,z\,]$ than in $[\,\theta,\phi~]$.Despite these objections, the vector approach turns out to have +significant advantages over the spherical trigonometry approach: +

+A number of important transformations in positional +astronomy turn out to be nothing more than changes of coordinate +system, something which is especially convenient if +the vector approach is used. A direction with respect +to one triad can be expressed relative to another triad simply +by multiplying the $[\,x,y,z\,]$ column vector by the appropriate +$3\times3$ orthogonal matrix +(a tensor of Rank 2, or dyadic). The three rows of this +rotation matrix +are the vectors in the old coordinate system of the three +new axes, and the transformation amounts to obtaining the +dot-product of the direction-vector with each of the three +new axes. Precession, nutation, $[\,h,\delta\,]$ to $[\,Az,El~]$,$[\,\alpha,\delta\,]$ to $[\,l^{I\!I},b^{I\!I}\,]$ and so on are typical examples of the +technique. A useful property of the rotation matrices +is that they can be inverted simply by taking the transpose. +

+The elements of these vectors and matrices are assorted combinations of +the sines and cosines of the various angles involved (hour angle, +declination and so on, depending on which transformation is +being applied). If you write out the matrix multiplications +in full you get expressions which are essentially the same as the +equivalent spherical trigonometry formulae. Indeed, many of the +standard formulae of spherical trigonometry are most easily +derived by expressing the problem initially in +terms of vectors. +

+

+ +  + + +
+ +next + +up + +previous +
+ Next: Using vectors +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Formatting angles +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node201.html b/src/slalib/sun67.htx/node201.html new file mode 100644 index 0000000..4613125 --- /dev/null +++ b/src/slalib/sun67.htx/node201.html @@ -0,0 +1,215 @@ + + + + +Using vectors + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Celestial Coordinate Systems +
+Up: Vectors and Matrices +
+ Previous: Vectors and Matrices +

+

+

+Using vectors +

+SLALIB provides conversions between spherical and vector +form +(sla_CS2C, +sla_CC2S +etc.), plus an assortment +of standard vector and matrix operations +(sla_VDV, +sla_MXV +etc.). +There are also routines +(sla_EULER +etc.) for creating a rotation matrix +from three Euler angles (successive rotations about +specified Cartesian axes). Instead of Euler angles, a rotation +matrix can be expressed as an axial vector (the pole of the rotation, +and the amount of rotation), and routines are provided for this +(sla_AV2M, +sla_M2AV +etc.). +

+Here is an example where spherical coordinates P1 and Q1 +undergo a coordinate transformation and become P2 and Q2; +the transformation consists of a rotation of the coordinate system +through angles A, B and C about the +z, new y and new z axes respectively: +

+            REAL A,B,C,R(3,3),P1,Q1,V1(3),V2(3),P2,Q2
+             :
+      *  Create rotation matrix
+            CALL sla_EULER('ZYZ',A,B,C,R)
+
+      *  Transform position (P,Q) from spherical to Cartesian
+            CALL sla_CS2C(P1,Q1,V1)
+
+      *  Multiply by rotation matrix
+            CALL sla_MXV(R,V1,V2)
+
+      *  Back to spherical
+            CALL sla_CC2S(V2,P2,Q2)
+
+

+Small adjustments to the direction of a position +vector are often most conveniently described in terms of +$[\,\Delta x,\Delta y, \Delta z\,]$. Adding the correction +vector needs careful handling if the position +vector is to remain of length unity, an advisable precaution which +ensures that +the $[\,x,y,z\,]$ components are always available to mean the cosines of +the angles between the vector and the axis concerned. Two types +of shifts are commonly used, +the first where a small vector of arbitrary direction is +added to the unit vector, and the second where there is a displacement +in the latitude coordinate (declination, elevation etc.) alone. +

+For a shift produced by adding a small $[\,x,y,z\,]$ vector ${\bf D}$ to a +unit vector ${\bf V1}$, the resulting vector ${\bf V2}$ has direction +$<{\bf V1}+{\bf D}\gt$ but is no longer of unit length. A better approximation +is available if the result is multiplied by a scaling factor of +$(1-{\bf D}\cdot{\bf V1})$, where the dot +means scalar product. In Fortran: +

+            F = (1D0-(DX*V1X+DY*V1Y+DZ*V1Z))
+            V2X = F*(V1X+DX)
+            V2Y = F*(V1Y+DY)
+            V2Z = F*(V1Z+DZ)
+
+

+The correction for diurnal aberration (discussed later) is +an example of this form of shift. +

+As an example of the second kind of displacement +we will apply a small change in elevation $\delta E$ to an +$[\,Az,El~]$ direction vector. The direction of the +result can be obtained by making the allowable approximation +${\tan \delta E\approx\delta E}$ and adding a adjustment +vector of length $\delta E$ normal +to the direction vector in the vertical plane containing the direction +vector. The z-component of the adjustment vector is +$\delta E \cos E$,and the horizontal component is +$\delta E \sin E$ which has then to be +resolved into x and y in proportion to their current sizes. To +approximate a unit vector more closely, a correction factor of +$\cos \delta E$ can then be applied, which is nearly +$(1-\delta E^2 /2)$ for +small $\delta E$. Expressed in Fortran, for initial vector +V1X,V1Y,V1Z, change in elevation DEL +(+ve $\equiv$ upwards), and result +vector V2X,V2Y,V2Z: +

+            COSDEL = 1D0-DEL*DEL/2D0
+            R1 = SQRT(V1X*V1X+V1Y*V1Y)
+            F = COSDEL*(R1-DEL*V1Z)/R1
+            V2X = F*V1X
+            V2Y = F*V1Y
+            V2Z = COSDEL*(V1Z+DEL*R1)
+
+

+An example of this type of shift is the correction for atmospheric +refraction (see later). +Depending on the relationship between $\delta E$ and E, special +handling at the pole (the zenith for our example) may be required. +

+SLALIB includes routines for the case where both a position +and a velocity are involved. The routines +sla_CS2C6 +and +sla_CC62S +convert from $[\theta,\phi,\dot{\theta},\dot{\phi}]$to $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ and back; +sla_DCS26 +and +sla_DC62S +are double precision equivalents. +

+

+ +next + +up + +previous +
+ Next: Celestial Coordinate Systems +
+Up: Vectors and Matrices +
+ Previous: Vectors and Matrices +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node202.html b/src/slalib/sun67.htx/node202.html new file mode 100644 index 0000000..a161c65 --- /dev/null +++ b/src/slalib/sun67.htx/node202.html @@ -0,0 +1,254 @@ + + + + +Celestial Coordinate Systems + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Precession and Nutation +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Using vectors +

+

+

+Celestial Coordinate Systems +

+SLALIB has routines to perform transformations +of celestial positions between different spherical +coordinate systems, including those shown in the following table: +

+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
systemsymbolslongitudelatitudex-y planelong. zeroRH/LH
horizon-azimuthelevationhorizontalnorthL
equatorial$\alpha,\delta$R.A.Dec.equatorequinoxR
local equ.$h,\delta$H.A.Dec.equatormeridianL
ecliptic$\lambda,\beta$ecl. long.ecl. lat.eclipticequinoxR
galactic$l^{I\!I},b^{I\!I}$gal. long.gal. lat.gal. equatorgal. centreR
supergalacticSGL,SGBSG long.SG lat.SG equatornode w. gal. equ.R
+Transformations between $[\,h,\delta\,]$ and $[\,Az,El~]$ can be performed by +calling +sla_E2H +and +sla_H2E, +or, in double precision, +sla_DE2H +and +sla_DH2E. +There is also a routine for obtaining +zenith distance alone for a given $[\,h,\delta\,]$,sla_ZD, +and one for determining the parallactic angle, +sla_PA. +Three routines are included which relate to altazimuth telescope +mountings. For a given $[\,h,\delta\,]$ and latitude, +sla_ALTAZ +returns the azimuth, elevation and parallactic angle, plus +velocities and accelerations for sidereal tracking. +The routines +sla_PDA2H +and +sla_PDQ2H +predict at what hour angle a given azimuth or +parallactic angle will be reached. +

+The routines +sla_EQECL +and +sla_ECLEQ +transform between ecliptic +coordinates and $[\,\alpha,\delta\,]$; there is also a routine for generating the +equatorial to ecliptic rotation matrix for a given date: +sla_ECMAT. +

+For conversion between Galactic coordinates and $[\,\alpha,\delta\,]$ there are +two sets of routines, depending on whether the $[\,\alpha,\delta\,]$ is +old-style, B1950, or new-style, J2000; +sla_EG50 +and +sla_GE50 +are $[\,\alpha,\delta\,]$ to $[\,l^{I\!I},b^{I\!I}\,]$ and vice versa for the B1950 case, while +sla_EQGAL +and +sla_GALEQ +are the J2000 equivalents. +

+Finally, the routines +sla_GALSUP +and +sla_SUPGAL +transform $[\,l^{I\!I},b^{I\!I}\,]$ to de Vaucouleurs supergalactic longitude and latitude +and vice versa. +

+It should be appreciated that the table, above, constitutes +a gross oversimplification. Apparently +simple concepts such as equator, equinox etc. are apt to be very hard to +pin down precisely (polar motion, orbital perturbations ...) and +some have several interpretations, all subtly different. The various +frames move in complicated ways with respect to one another or to +the stars (themselves in motion). And in some instances the +coordinate system is slightly distorted, so that the +ordinary rules of spherical trigonometry no longer strictly apply. +

+These caveats +apply particularly to the bewildering variety of different +$[\,\alpha,\delta\,]$ systems that are in use. Figure 1 shows how +some of these systems are related, to one another and +to the direction in which a celestial source actually +appears in the sky. At the top of the diagram are +the various sorts of mean place +found in star catalogues and papers;[*] at the bottom is the +observed $[\,Az,El~]$, where a perfect theodolite would +be pointed to see the source; and in the body of +the diagram are +the intermediate processing steps and coordinate +systems. To help +understand this diagram, and the SLALIB routines that can +be used to carry out the various calculations, we will look at the coordinate +systems involved, and the astronomical phenomena that +affect them. +

+
+

  + + + +
Figure 1: +Relationship Between Celestial Coordinates
\begin{figure} +\begin{center} +\begin{tabular} +{\vert cccccc\vert} \hline +& & & &... + ...2000, all of the precession and E-terms corrections +are superfluous.\end{figure}
+
+
+
+ +next + +up + +previous +
+ Next: Precession and Nutation +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Using vectors +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node203.html b/src/slalib/sun67.htx/node203.html new file mode 100644 index 0000000..fd18b48 --- /dev/null +++ b/src/slalib/sun67.htx/node203.html @@ -0,0 +1,187 @@ + + + + +Precession and Nutation + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLALIB support for precession and nutation +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Celestial Coordinate Systems +

+

+

+Precession and Nutation +

+Right ascension and declination, ($[\,\alpha,\delta\,]$), are the names +of the longitude and latitude in a spherical +polar coordinate system based on the Earth's axis of rotation. +The zero point of $\alpha$ is the point of intersection of +the celestial +equator and the ecliptic (the apparent path of the Sun +through the year) where the Sun moves into the northern +hemisphere. This point is called the +first point of Aries, +the vernal equinox (with apologies to +southern-hemisphere readers) or simply the equinox.[*] +

+This simple picture is unfortunately +complicated by the difficulty of defining +a suitable equator and equinox. One problem is that the +Sun's apparent motion is not completely regular, due to the +ellipticity of the Earth's orbit and its continuous disturbance +by the Moon and planets. This is dealt with by +separating the motion into (i) a smooth and steady mean Sun +and (ii) a set of periodic corrections and perturbations; only the former +is involved in establishing reference frames and timescales. +A second, far larger problem, is that +the celestial equator and the ecliptic +are both moving with respect to the stars. +These motions arise because of the gravitational +interactions between the Earth and the other solar-system bodies. +

+By far the largest effect is the +so-called ``precession of the equinoxes'', where the Earth's +rotation axis sweeps out a cone centred on the ecliptic +pole, completing one revolution in about 26,000 years. The +cause of the motion is the torque exerted on the distorted and +spinning Earth by the Sun and the Moon. Consider the effect of the +Sun alone, at or near the northern summer solstice. The Sun +`sees' the top (north pole) of the Earth tilted towards it +(by about $23^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$, the obliquity of the +ecliptic), +and sees the nearer part of the Earth's equatorial bulge +below centre and the further part above centre. +Although the Earth is in free fall, +the gravitational force on the nearer part of the +equatorial bulge is greater than that on the further part, and +so there is a net torque acting +as if to eliminate the tilt. Six months later the same thing +is happening in reverse, except that the torque is still +trying to eliminate the tilt. In between (at the equinoxes) the +torque shrinks to zero. A torque acting on a spinning body +is gyroscopically translated +into a precessional motion of the spin axis at right-angles to the torque, +and this happens to the Earth. +The motion varies during the +year, going through two maxima, but always acts in the +same direction. The Moon produces the same effect, +adding a contribution to the precession which peaks twice +per month. The Moon's proximity to the Earth more than compensates +for its smaller mass and gravitational attraction, so that it +in fact contributes most of the precessional effect. +

+The complex interactions between the three bodies produce a +precessional motion that is wobbly rather than completely smooth. +However, the main 26,000-year component is on such a grand scale that +it dwarfs the remaining terms, the biggest of +which has an amplitude of only $17\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and a period of +about 18.6 years. This difference of scale makes it convenient to treat +these two components of the motion separately. The main 26,000-year +effect is called luni-solar precession; the smaller, +faster, periodic terms are called the nutation. +

+Note that precession and nutation are simply +different frequency components of the same physical effect. It is +a common misconception that precession is caused +by the Sun and nutation is caused by the Moon. In fact +the Moon is responsible for two-thirds of the precession, and, +while it is true that much of the complex detail of the nutation is +a reflection of the intricacies of the lunar orbit, there are +nonetheless important solar terms in the nutation. +

+In addition to and quite separate +from the precession/nutation effect, the orbit of the Earth-Moon system +is not fixed in orientation, a result of the attractions of the +planets. This slow (about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$  per year) +secular rotation of the ecliptic about a slowly-moving diameter is called, +confusingly, planetary +precession and, along with the luni-solar precession is +included in the general precession. The equator and +ecliptic as affected by general precession +are what define the various ``mean'' $[\,\alpha,\delta\,]$ reference frames. +

+The models for precession and nutation come from a combination +of observation and theory, and are subject to continuous +refinement. Nutation models in particular have reached a high +degree of sophistication, taking into account such things as +the non-rigidity of the Earth and the effects of +the planets; SLALIB's nutation +model (IAU 1980) involves 106 terms in each of $\psi$ (longitude) +and $\epsilon$ (obliquity), some as small as + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0001$ . +

+

+ +  + + +
+ +next + +up + +previous +
+ Next: SLALIB support for precession and nutation +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Celestial Coordinate Systems +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node204.html b/src/slalib/sun67.htx/node204.html new file mode 100644 index 0000000..cc880e2 --- /dev/null +++ b/src/slalib/sun67.htx/node204.html @@ -0,0 +1,127 @@ + + + + +SLALIB support for precession and nutation + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Mean Places +
+Up: Precession and Nutation +
+ Previous: Precession and Nutation +

+

+

+SLALIB support for precession and nutation +

+SLALIB offers a choice of three precession models: + +In each case, the named SLALIB routine generates the $(3\times3)$precession +matrix for a given start and finish time. For example, +here is the Fortran code for generating the rotation +matrix which describes the precession between the epochs +J2000 and J1985.372 (IAU 1976 model): +

+            DOUBLE PRECISION PMAT(3,3)
+             :
+            CALL sla_PREC(2000D0,1985.372D0,PMAT)
+
+

+It is instructive to examine the resulting matrix: +

+            +0.9999936402  +0.0032709208  +0.0014214694
+            -0.0032709208  +0.9999946505  -0.0000023247
+            -0.0014214694  -0.0000023248  +0.9999989897
+
+

+Note that the diagonal elements are close to unity, and the +other elements are small. This shows that over an interval as +short as 15 years the precession isn't going to move a +position vector very far (in this case about $0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}2$). +

+For convenience, a direct $[\,\alpha,\delta\,]$ to $[\,\alpha,\delta\,]$ precession routine is +also provided +(sla_PRECES), +suitable for either the old or the new system (but not a +mixture of the two). +

+SLALIB provides only one nutation model, the new, IAU 1980 model, +implemented in the routine +sla_NUTC. +This returns the components of nutation +in longitude and latitude (and also provides the obliquity) from +which a nutation matrix can be generated by calling +sla_DEULER +(and from which the equation of the equinoxes, described +later, can be found). Alternatively, +the nutation matrix can be generated in a single call by using +sla_NUT. +

+A rotation matrix for applying the entire precession/nutation +transformation in one go can be generated by calling +sla_PRENUT. +

+

+ +next + +up + +previous +
+ Next: Mean Places +
+Up: Precession and Nutation +
+ Previous: Precession and Nutation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node205.html b/src/slalib/sun67.htx/node205.html new file mode 100644 index 0000000..6da5021 --- /dev/null +++ b/src/slalib/sun67.htx/node205.html @@ -0,0 +1,92 @@ + + + + +Mean Places + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Epoch +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: SLALIB support for precession and nutation +

+

+

+Mean Places +

+The main effect of the precession/nutation is a steady increase of about +$50\hspace{-0.05em}^{'\hspace{-0.1em}'}$/year in the ecliptic longitudes of the stars. It is therefore +essential, when reporting the position of an astronomical target, to +qualify the coordinates with a date, or epoch. +Specifying the epoch ties down the equator and +equinox which define the $[\,\alpha,\delta\,]$ coordinate system that is +being used. +[*] For simplicity, only +the smooth and steady ``general +precession'' part of the complete precession/nutation effect is +included, thereby defining what is called the mean +equator and equinox for the epoch concerned. We say a star +has a mean place of (for example) +$12^{h}\,07^{m}\,58^{s}.09$ $-19^{\circ}\,44^{'}\,37^{''}.1$ ``with respect to the mean equator +and equinox of epoch J2000''. The short way of saying +this is ``$[\,\alpha,\delta\,]$ equinox J2000'' (not ``$[\,\alpha,\delta\,]$ epoch J2000'', +which means something different to do with +proper motion). +

+

+ +next + +up + +previous +
+ Next: Epoch +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: SLALIB support for precession and nutation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node206.html b/src/slalib/sun67.htx/node206.html new file mode 100644 index 0000000..9a94a3d --- /dev/null +++ b/src/slalib/sun67.htx/node206.html @@ -0,0 +1,125 @@ + + + + +Epoch + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Proper Motion +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Mean Places +

+

+

+Epoch +

+The word ``epoch'' just means a moment in time, and can be supplied +in a variety of forms, using different calendar systems and timescales. +

+For the purpose of specifying the epochs associated with the +mean place of a star, two conventions exist. Both sorts of epoch +superficially resemble years AD but are not tied to the civil +(Gregorian) calendar; to distinguish them from ordinary calendar-years +there is often +a ``.0'' suffix (as in ``1950.0''), although any other fractional +part is perfectly legal (e.g. 1987.5). +

+The older system, +Besselian epoch, is defined in such a way that its units are +tropical years of about 365.2422 days and its timescale is the +obsolete Ephemeris Time. +The start of the Besselian year is the moment +when the ecliptic longitude of the mean Sun is +$280^\circ$; this happens near the start of the +calendar year (which is why $280^\circ$ was chosen). +

+The new system, Julian epoch, was adopted as +part of the IAU 1976 revisions (about which more will be said +in due course) and came formally into use at the +beginning of 1984. It uses the Julian year of exactly +365.25 days; Julian epoch 2000 is defined to be 2000 January 1.5 in the +TT timescale. +

+For specifying mean places, various standard epochs are in use, the +most common ones being Besselian epoch 1950.0 and Julian epoch 2000.0. +To distinguish the two systems, Besselian epochs +are now prefixed ``B'' and Julian epochs are prefixed ``J''. +Epochs without an initial letter can be assumed to be Besselian +if before 1984.0, otherwise Julian. These details are supported by +the SLALIB routines +sla_DBJIN +(decodes numbers from a +character string, accepting an optional leading B or J), +sla_KBJ +(decides whether B or J depending on prefix or range) and +sla_EPCO +(converts one epoch to match another). +

+SLALIB has four routines for converting +Besselian and Julian epochs into other forms. +The functions +sla_EPB2D +and +sla_EPJ2D +convert Besselian and Julian epochs into MJD; the functions +sla_EPB +and +sla_EPJ +do the reverse. For example, to express B1950 as a Julian epoch: +

+            DOUBLE PRECISION sla_EPJ,sla_EPB2D
+             :
+            WRITE (*,'(1X,''J'',F10.5)') sla_EPJ(sla_EPB2D(1950D0))
+
+

(The answer is J1949.99979.) +

+

+ +next + +up + +previous +
+ Next: Proper Motion +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Mean Places +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node207.html b/src/slalib/sun67.htx/node207.html new file mode 100644 index 0000000..6c74c4e --- /dev/null +++ b/src/slalib/sun67.htx/node207.html @@ -0,0 +1,119 @@ + + + + +Proper Motion + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Parallax and Radial Velocity +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Epoch +

+

+

+Proper Motion +

+Stars in catalogues usually have, in addition to the +$[\,\alpha,\delta\,]$ coordinates, a proper motion $[\mu_\alpha,\mu_\delta]$.This is an intrinsic motion +of the star across the background. Very few stars have a +proper motion which exceeds $1\hspace{-0.05em}^{'\hspace{-0.1em}'}$/year, and most are +far below this level. A star observed as part of normal +astronomy research will, as a rule, have a proper motion +which is unknown. +

+Mean $[\,\alpha,\delta\,]$ and rate of change are not sufficient to pin +down a star; the epoch at which the $[\,\alpha,\delta\,]$ was or will +be correct is also needed. Note the distinction +between the epoch which specifies the +coordinate system and the epoch at which the star passed +through the given $[\,\alpha,\delta\,]$. The full specification for a star +is $[\,\alpha,\delta\,]$, proper motions, equinox and epoch (plus something to +identify which set of models for the precession etc. is +being used - see the next section). +For convenience, coordinates given in star catalogues are almost +always adjusted to make the equinox and epoch the same - for +example B1950 in the case of the SAO catalogue. +

+SLALIB provides one routine to handle proper motion on its own, +sla_PM. +Proper motion is also allowed for in various other +routines as appropriate, for example +sla_MAP +and +sla_FK425. +Note that in all SLALIB routines which involve proper motion +the units are radians per year and the +$\alpha$ component is in the form $\dot{\alpha}$ (i.e. big +numbers near the poles). +Some star catalogues have proper motion per century, and +in some catalogues the $\alpha$ component is in the form +$\dot{\alpha}\cos\delta$ (i.e. angle on the sky). +

+

+ +next + +up + +previous +
+ Next: Parallax and Radial Velocity +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Epoch +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node208.html b/src/slalib/sun67.htx/node208.html new file mode 100644 index 0000000..cc2b337 --- /dev/null +++ b/src/slalib/sun67.htx/node208.html @@ -0,0 +1,92 @@ + + + + +Parallax and Radial Velocity + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Aberration +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Proper Motion +

+

+

+Parallax and Radial Velocity +

+For the utmost accuracy and the nearest stars, allowance can +be made for annual parallax and for the effects of perspective +on the proper motion. +

+Parallax is appreciable only for nearby stars; even +the nearest, Proxima Centauri, is displaced from its average +position by less than +an arcsecond as the Earth revolves in its orbit. +

+For stars with a known parallax, knowledge of the radial velocity +allows the proper motion to be expressed as an actual space +motion in 3 dimensions. The proper motion is, +in fact, a snapshot of the transverse component of the +space motion, and in the case of nearby stars will +change with time due to perspective. +

+SLALIB does not provide facilities for handling parallax +and radial-velocity on their own, but their contribution is +allowed for in such routines as +sla_PM, +sla_MAP +and +sla_FK425. +Catalogue mean +places do not include the effects of parallax and are therefore +barycentric; when pointing telescopes etc. it is +usually most efficient to apply the slowly-changing +parallax correction to the mean place of the target early on +and to work with the geocentric mean place. This latter +approach is implied in Figure 1. +

+

+ +next + +up + +previous +
+ Next: Aberration +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Proper Motion +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node209.html b/src/slalib/sun67.htx/node209.html new file mode 100644 index 0000000..4790dda --- /dev/null +++ b/src/slalib/sun67.htx/node209.html @@ -0,0 +1,147 @@ + + + + +Aberration + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Different Sorts of Mean Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Parallax and Radial Velocity +

+

+

+Aberration +

+The finite speed of light combined with the motion of the observer +around the Sun during the year causes apparent displacements of +the positions of the stars. The effect is called +the annual aberration (or ``stellar'' +aberration). Its maximum size, about + $20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ , +occurs for stars $90^{\circ}$ from the point towards which +the Earth is headed as it orbits the Sun; a star exactly in line with +the Earth's motion is not displaced. To receive the light of +a star, the telescope has to be offset slightly in the direction of +the Earth's motion. A familiar analogy is the need to tilt your +umbrella forward when on the move, to avoid getting wet. This +Newtonian model is, +in fact, highly misleading in the context of light as opposed +to rain, but happens to give the same answer as a relativistic +treatment to first order (better than 1 milliarcsecond). +

+Before the IAU 1976 resolutions, different +values for the approximately +

$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ aberration constant were employed +at different times, and this can complicate comparisons +between different catalogues. Another complication comes from +the so-called E-terms of aberration, +that small part of the annual aberration correction that is a +function of the eccentricity of the Earth's orbit. The E-terms, +maximum amplitude about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ , +happen to be approximately constant for a given star, and so they +used to be incorporated in the catalogue $[\,\alpha,\delta\,]$to reduce the labour of converting to and from apparent place. +The E-terms can be removed from a catalogue $[\,\alpha,\delta\,]$ by +calling +sla_SUBET +or applied (for example to allow a pulsar +timing-position to be plotted on a B1950 finding chart) +by calling +sla_ADDET; +the E-terms vector itself can be obtained by calling +sla_ETRMS. +Star positions post IAU 1976 are free of these distortions, and to +apply corrections for annual aberration involves the actual +barycentric velocity of the Earth rather than the use of +canonical circular-orbit models. +

+The annual aberration is the aberration correction for +an imaginary observer at the Earth's centre. +The motion of a real observer around the Earth's rotation axis in +the course of the day makes a small extra contribution to the total +aberration effect called the diurnal aberration. Its +maximum amplitude is about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ . +

+No SLALIB routine is provided for calculating the aberration on +its own, though the required velocity vectors can be +generated using +sla_EVP +and +sla_GEOC. +Annual and diurnal aberration are allowed for where required, for example in +sla_MAP +etc. and +sla_AOP +etc. Note that this sort +of aberration is different from the planetary +aberration, which is the apparent displacement of a solar-system +body, with respect to the ephemeris position, as a consequence +of the motion of both the Earth and the source. The +planetary aberration can be computed either by correcting the +position of the solar-system body for light-time, followed by +the ordinary stellar aberration correction, or more +directly by expressing the position and velocity of the source +in the observer's frame and correcting for light-time alone. +

+

+ +next + +up + +previous +
+ Next: Different Sorts of Mean Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Parallax and Radial Velocity +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node21.html b/src/slalib/sun67.htx/node21.html new file mode 100644 index 0000000..13ef3e2 --- /dev/null +++ b/src/slalib/sun67.htx/node21.html @@ -0,0 +1,264 @@ + + + + +SLA_AOPPA - Appt-to-Obs Parameters + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AOPPAT - Update Appt-to-Obs Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOP - Apparent to Observed +

+

+

SLA_AOPPA - Appt-to-Obs Parameters +   +

+
+
ACTION: +
Pre-compute the set of apparent to observed place parameters +required by the ``quick'' routines sla_AOPQK and sla_OAPQK. +

CALL: +
CALL sla_AOPPA ( + DATE, DUT, ELONGM, PHIM, HM, XP, YP, + TDK, PMB, RH, WL, TLR, AOPRMS) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDUTC date/time (Modified Julian Date, JD-2400000.5)
DUTD$\Delta$UT: UT1-UTC (UTC seconds)
ELONGMDobserver's mean longitude (radians, east +ve)
PHIMDobserver's mean geodetic latitude (radians)
HMDobserver's height above sea level (metres)
XP,YPDpolar motion $[\,x,y\,]$ coordinates (radians)
TDKDlocal ambient temperature (degrees K; std=273.155D0)
PMBDlocal atmospheric pressure (mB; std=1013.25D0)
RHDlocal relative humidity (in the range 0D0-1D0)
WLDeffective wavelength ($\mu{\rm m}$, e.g. 0.55D0)
TLRDtropospheric lapse rate (degrees K per metre, +e.g. 0.0065D0)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
AOPRMSD(14)star-independent apparent-to-observed parameters:
(1)geodetic latitude (radians)
(2,3)sine and cosine of geodetic latitude
(4)magnitude of diurnal aberration vector
(5)height (HM)
(6)ambient temperature (TDK)
(7)pressure (PMB)
(8)relative humidity (RH)
(9)wavelength (WL)
(10)lapse rate (TLR)
(11,12)refraction constants A and B (radians)
(13)longitude + eqn of equinoxes + +``sidereal $\Delta$UT'' (radians)
(14)local apparent sidereal time (radians)
+

+
NOTES: +
+
1. +
It is advisable to take great care with units, as even +unlikely values of the input parameters are accepted and +processed in accordance with the models used. +
2. +
The DATE argument is UTC expressed as an MJD. This is, + strictly speaking, wrong, because of leap seconds. However, + as long as the $\Delta$UT and the UTC are consistent there + are no difficulties, except during a leap second. In this + case, the start of the 61st second of the final minute should + begin a new MJD day and the old pre-leap $\Delta$UT should + continue to be used. As the 61st second completes, the MJD + should revert to the start of the day as, simultaneously, + the $\Delta$UT changes by one second to its post-leap new value. +
3. +
The $\Delta$UT (UT1-UTC) is tabulated in IERS circulars and + elsewhere. It increases by exactly one second at the end of + each UTC leap second, introduced in order to keep $\Delta$UT + within $\pm$$0^{\rm s}\hspace{-0.3em}.9$. The ``sidereal $\Delta$UT'' which forms + part of AOPRMS(13) is the same quantity, but converted from solar + to sidereal seconds and expressed in radians. +
4. +
IMPORTANT - TAKE CARE WITH THE LONGITUDE SIGN CONVENTION. The + longitude required by the present routine is east-positive, + in accordance with geographical convention (and right-handed). + In particular, note that the longitudes returned by the + sla_OBS routine are west-positive (as in the Astronomical + Almanac before 1984) and must be reversed in sign before use in + the present routine. +
5. +
The polar coordinates XP,YP can be obtained from IERS + circulars and equivalent publications. The + maximum amplitude is about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ . If XP,YP values + are unavailable, use XP=YP=0D0. See page B60 of the 1988 + Astronomical Almanac for a definition of the two angles. +
6. +
The height above sea level of the observing station, HM, + can be obtained from the Astronomical Almanac (Section J + in the 1988 edition), or via the routine sla_OBS. If P, + the pressure in mB, is available, an adequate + estimate of HM can be obtained from the following expression: +
HM=-29.3D0*TSL*LOG(P/1013.25D0) +
+ where TSL is the approximate sea-level air temperature in degrees K + (see Astrophysical Quantities, C.W.Allen, 3rd edition, + §52). Similarly, if the pressure P is not known, + it can be estimated from the height of the observing + station, HM as follows: +
P=1013.25D0*EXP(-HM/(29.3D0*TSL)) +
+ Note, however, that the refraction is proportional to the + pressure and that an accurate P value is important for + precise work. +
+
+ +next + +up + +previous +
+ Next: SLA_AOPPAT - Update Appt-to-Obs Parameters +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOP - Apparent to Observed +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node210.html b/src/slalib/sun67.htx/node210.html new file mode 100644 index 0000000..1a8e19e --- /dev/null +++ b/src/slalib/sun67.htx/node210.html @@ -0,0 +1,177 @@ + + + + +Different Sorts of Mean Place + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Mean Place Transformations +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Aberration +

+

+

+Different Sorts of Mean Place +

+A particularly confusing aspect of published mean places is that they +are sensitive to the precise way they were determined. A mean +place is not directly observable, even with fundamental +instruments such as transit circles, and to produce a mean +place will involve relying on some existing star catalogue, +for example the fundamental catalogues FK4 and FK5, +and applying given mathematical models of precession, nutation, +aberration and so on. +Note in particular that no star catalogue, +even a fundamental catalogue such as FK4 or +FK5, defines a coordinate system, strictly speaking; +it is merely a list of star positions and proper motions. +However, once the stars from a given catalogue +are used as position calibrators, e.g. for +transit-circle observations or for plate reductions, then a +broader sense of there being a coordinate grid naturally +arises, and such phrases as ``in the system of +the FK4'' can legitimately be employed. However, +there is no formal link between the +two concepts - no ``standard least squares fit'' between +reality and the inevitably flawed catalogues.[*] All such +catalogues suffer at some level from systematic, zonal distortions +of both the star positions and of the proper motions, +and include measurement errors peculiar to individual +stars. +

+Many of these complications are of little significance except to +specialists. However, observational astronomers cannot +escape exposure to at least the two main varieties of +mean place, loosely called +FK4 and FK5, and should be aware of +certain pitfalls. For most practical purposes the more recent +system, FK5, is free of surprises and tolerates naive +use well. FK4, in contrast, contains two important traps: +

+The change from the old FK4-based system to FK5 +occurred at the beginning +of 1984 as part of a package of resolutions made by the IAU in 1976, +along with the adoption of J2000 as the reference epoch. Star +positions in the newer, FK5, system are free from the E-terms, and +the system is a much better approximation to an +inertial frame (about five times better). +

+It may occasionally be convenient to specify the FK4 fictitious proper +motion directly. In FK4, the centennial proper motion of (for example) +a QSO is: +

$\mu_\alpha=-$$0^{\rm s}\hspace{-0.3em}.015869$+(($0^{\rm s}\hspace{-0.3em}.029032$$~\sin \alpha + +$$0^{\rm s}\hspace{-0.3em}.000340$$~\cos \alpha ) \sin \delta + -$$0^{\rm s}\hspace{-0.3em}.000105$$~\cos \alpha + -$$0^{\rm s}\hspace{-0.3em}.000083$$~\sin \alpha ) \sec \delta $
+$\mu_\delta\,=+$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.43549$ $~\cos \alpha + -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00510$ $~\sin \alpha + + ($ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00158$ $~\sin \alpha + -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00125$ $~\cos \alpha ) \sin \delta + -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00066$ $~\cos \delta $ +

+ +next + +up + +previous +
+ Next: Mean Place Transformations +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Aberration +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node211.html b/src/slalib/sun67.htx/node211.html new file mode 100644 index 0000000..2a8cbee --- /dev/null +++ b/src/slalib/sun67.htx/node211.html @@ -0,0 +1,232 @@ + + + + +Mean Place Transformations + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Mean Place to Apparent Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Different Sorts of Mean Place +

+

+

+Mean Place Transformations +

+Figure 1 is based upon three varieties of mean $[\,\alpha,\delta\,]$ all of which are +of practical significance to observing astronomers in the present era: + +The figure outlines the steps required to convert positions in +any of these systems to a J2000 $[\,\alpha,\delta\,]$ for the current +epoch, as might be required in a telescope-control +program for example. +Most of the steps can be carried out by calling a single +SLALIB routines; there are other SLALIB routines which +offer set-piece end-to-end transformation routines for common cases. +Note, however, that SLALIB does not set out to provide the capability +for arbitrary transformations of star-catalogue data +between all possible systems of mean $[\,\alpha,\delta\,]$.Only in the (common) cases of FK4, equinox and epoch B1950, +to FK5, equinox and epoch J2000, and vice versa are +proper motion, parallax and radial velocity transformed +along with the star position itself, the +focus of SLALIB support. +

+As an example of using SLALIB to transform mean places, here is +a program which implements the top-left path of Figure 1. +An FK4 $[\,\alpha,\delta\,]$ of arbitrary equinox and epoch and with +known proper motion and +parallax is transformed into an FK5 J2000 $[\,\alpha,\delta\,]$ for the current +epoch. As a test star we will use $\alpha=$$16^{h}\,09^{m}\,55^{s}.13$,$\delta=$$-75^{\circ}\,59^{'}\,27^{''}.2$, equinox 1900, epoch 1963.087, +$\mu_\alpha=$$-0^{\rm s}\hspace{-0.3em}.0312$/y, $\mu_\delta=$ $+0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.103$ /y, +parallax = + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.062$ , radial velocity = -34.22 km/s. The +epoch of observation is 1994.35. +

+            IMPLICIT NONE
+            DOUBLE PRECISION AS2R,S2R
+            PARAMETER (AS2R=4.8481368110953599D-6,S2R=7.2722052166430399D-5)
+            INTEGER J,I
+            DOUBLE PRECISION R0,D0,EQ0,EP0,PR,PD,PX,RV,EP1,R1,D1,R2,D2,R3,D3,
+           :                 R4,D4,R5,D5,R6,D6,EP1D,EP1B,W(3),EB(3),PXR,V(3)
+            DOUBLE PRECISION sla_EPB,sla_EPJ2D
+
+      *  RA, Dec etc of example star
+            CALL sla_DTF2R(16,09,55.13D0,R0,J)
+            CALL sla_DAF2R(75,59,27.2D0,D0,J)
+            D0=-D0
+            EQ0=1900D0
+            EP0=1963.087D0
+            PR=-0.0312D0*S2R
+            PD=+0.103D0*AS2R
+            PX=0.062D0
+            RV=-34.22D0
+            EP1=1994.35D0
+
+      *  Epoch of observation as MJD and Besselian epoch
+            EP1D=sla_EPJ2D(EP1)
+            EP1B=sla_EPB(EP1D)
+
+      *  Space motion to the current epoch
+            CALL sla_PM(R0,D0,PR,PD,PX,RV,EP0,EP1B,R1,D1)
+
+      *  Remove E-terms of aberration for the original equinox
+            CALL sla_SUBET(R1,D1,EQ0,R2,D2)
+
+      *  Precess to B1950
+            R3=R2
+            D3=D2
+            CALL sla_PRECES('FK4',EQ0,1950D0,R3,D3)
+
+      *  Add E-terms for the standard equinox B1950
+            CALL sla_ADDET(R3,D3,1950D0,R4,D4)
+
+      *  Transform to J2000, no proper motion
+            CALL sla_FK45Z(R4,D4,EP1B,R5,D5)
+
+      *  Parallax
+            CALL sla_EVP(sla_EPJ2D(EP1),2000D0,W,EB,W,W)
+            PXR=PX*AS2R
+            CALL sla_DCS2C(R5,D5,V)
+            DO I=1,3
+               V(I)=V(I)-PXR*EB(I)
+            END DO
+            CALL sla_DCC2S(V,R6,D6)
+             :
+
+

+It is interesting to look at how the $[\,\alpha,\delta\,]$ changes during the +course of the calculation: +


+		 16 09 55.130 -75 59 27.20 		 		 original equinox and epoch
+		 16 09 54.155 -75 59 23.98 		 		 with space motion
+		 16 09 54.229 -75 59 24.18 		 		 with old E-terms removed
+		 16 16 28.213 -76 06 54.57 		 		 precessed to 1950.0
+		 16 16 28.138 -76 06 54.37 		 		 with new E-terms
+		 16 23 07.901 -76 13 58.87 		 		 J2000, current epoch
+		 16 23 07.907 -76 13 58.92 		 		 including parallax
+
+

+Other remarks about the above (unusually complicated) example: +

+
+ +next + +up + +previous +
+ Next: Mean Place to Apparent Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Different Sorts of Mean Place +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node212.html b/src/slalib/sun67.htx/node212.html new file mode 100644 index 0000000..35a5044 --- /dev/null +++ b/src/slalib/sun67.htx/node212.html @@ -0,0 +1,171 @@ + + + + +Mean Place to Apparent Place + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Apparent Place to Observed Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Mean Place Transformations +

+

+

+Mean Place to Apparent Place +

+The geocentric apparent place of a source, or apparent place +for short, +is the $[\,\alpha,\delta\,]$ if viewed from the centre of the Earth, +with respect to the true equator and equinox of date. +Transformation of an FK5 mean $[\,\alpha,\delta\,]$, equinox J2000, +current epoch, to apparent place involves the following effects: +

+The light deflection is seldom significant. Its value +at the limb of the Sun is about +

$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.74$ ; it falls off rapidly with distance from the +Sun and has shrunk to about +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.02$ at an elongation of $20^\circ$.

+As already described, the annual aberration +is a function of the Earth's velocity +relative to the solar system barycentre (available through the +SLALIB routine +sla_EVP) +and produces shifts of up to about + $20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ . +

+The precession/nutation, from J2000 to the current epoch, is +expressed by a rotation matrix which is available through the +SLALIB routine +sla_PRENUT. +

+The whole mean-to-apparent transformation can be done using the SLALIB +routine +sla_MAP. As a demonstration, here is a program which lists the +North Polar Distance ($90^\circ-\delta$) of Polaris for +the decade of closest approach to the Pole: +

+            IMPLICIT NONE
+            DOUBLE PRECISION PI,PIBY2,D2R,S2R,AS2R
+            PARAMETER (PI=3.141592653589793238462643D0)
+            PARAMETER (D2R=PI/180D0,
+           :           PIBY2=PI/2D0,
+           :           S2R=PI/(12D0*3600D0),
+           :           AS2R=PI/(180D0*3600D0))
+            DOUBLE PRECISION RM,DM,PR,PD,DATE,RA,DA
+            INTEGER J,IDS,IDE,ID,IYMDF(4),I
+            DOUBLE PRECISION sla_EPJ2D
+
+            CALL sla_DTF2R(02,31,49.8131D0,RM,J)
+            CALL sla_DAF2R(89,15,50.661D0,DM,J)
+            PR=+21.7272D0*S2R/100D0
+            PD=-1.571D0*AS2R/100D0
+            WRITE (*,'(1X,'//
+           :            '''Polaris north polar distance (deg) 2096-2105''/)')
+            WRITE (*,'(4X,''Date'',7X''NPD''/)')
+            CALL sla_CLDJ(2096,1,1,DATE,J)
+            IDS=NINT(DATE)
+            CALL sla_CLDJ(2105,12,31,DATE,J)
+            IDE=NINT(DATE)
+            DO ID=IDS,IDE,10
+               DATE=DBLE(ID)
+               CALL sla_DJCAL(0,DATE,IYMDF,J)
+               CALL sla_MAP(RM,DM,PR,PD,0D0,0D0,2000D0,DATE,RA,DA)
+               WRITE (*,'(1X,I4,2I3.2,F9.5)') (IYMDF(I),I=1,3),(PIBY2-DA)/D2R
+            END DO
+
+            END
+
+

+For cases where the transformation has to be repeated for different +times or for more than one star, the straightforward +sla_MAP +approach is apt to be +wasteful as both the Earth velocity and the +precession/nutation matrix can be re-calculated relatively +infrequently without ill effect. A more efficient method is to +perform the target-independent calculations only when necessary, +by calling +sla_MAPPA, +and then to use either +sla_MAPQKZ, +when only the $[\,\alpha,\delta\,]$ is known, or +sla_MAPQK, +when full catalogue positions, including proper motion, parallax and +radial velocity, are available. How frequently to call +sla_MAPPA +depends on the accuracy objectives; once per +night will deliver sub-arcsecond accuracy for example. +

+The routines +sla_AMP +and +sla_AMPQK +allow the reverse transformation, from apparent to mean place. +

+

+ +next + +up + +previous +
+ Next: Apparent Place to Observed Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Mean Place Transformations +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node213.html b/src/slalib/sun67.htx/node213.html new file mode 100644 index 0000000..4d2a0e1 --- /dev/null +++ b/src/slalib/sun67.htx/node213.html @@ -0,0 +1,181 @@ + + + + +Apparent Place to Observed Place + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Refraction +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Mean Place to Apparent Place +

+

+

+Apparent Place to Observed Place +

+The observed place of a source is its position as +seen by a perfect theodolite at the location of the +observer. Transformation of an apparent $[\,\alpha,\delta\,]$ to observed +place involves the following effects: +

+The transformation from apparent $[\,\alpha,\delta\,]$ to +apparent $[\,h,\delta\,]$ is made by allowing for +Earth rotation through the sidereal time, $\theta$: +

\begin{displaymath} +h = \theta - \alpha \end{displaymath}

+For this equation to work, $\alpha$ must be the apparent right +ascension for the time of observation, and $\theta$ must be +the local apparent sidereal time. The latter is obtained +as follows: +
+
1. +
from civil time obtain the coordinated universal time, UTC +(more later on this); +
2. +
add the UT1-UTC (typically a few tenths of a second) to + give the UT; +
3. +
from the UT compute the Greenwich mean sidereal time (using +sla_GMST); +
4. +
add the observer's (east) longitude, giving the local mean + sidereal time; +
5. +
add the equation of the equinoxes (using +sla_EQEQX). +
+The equation of the equinoxes ($=\Delta\psi\cos\epsilon$ plus +small terms) +is the effect of nutation on the sidereal time. +Its value is typically a second or less. It is +interesting to note that if the object of the exercise is to +transform a mean place all the way into an observed place (very +often the case), +then the equation of the +equinoxes and the longitude component of nutation can both be +omitted, removing a great deal of computation. However, SLALIB +follows the normal convention and works via the apparent place. +

+Note that for very precise work the observer's longitude should +be corrected for polar motion. This can be done with +sla_POLMO. +The corrections are always less than about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ , and +are futile unless the position of the observer's telescope is known +to better than a few metres. +

+Tables of observed and +predicted UT1-UTC corrections and polar motion data +are published every few weeks by the International Earth Rotation Service. +

+The transformation from apparent $[\,h,\delta\,]$ to topocentric +$[\,h,\delta\,]$ consists of allowing for +diurnal aberration. This effect, maximum amplitude + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ , +was described earlier. There is no specific SLALIB routine +for computing the diurnal aberration, +though the routines +sla_AOP etc. include it, and the required velocity vector can be +determined by calling +sla_GEOC. +

+The next stage is the major coordinate rotation from local equatorial +coordinates $[\,h,\delta\,]$ into horizon coordinates. The SLALIB routines +sla_E2H +etc. can be used for this. For high-precision +applications the mean geodetic latitude should be corrected for polar +motion. +

+

+ +  + + +
+ +next + +up + +previous +
+ Next: Refraction +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Mean Place to Apparent Place +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node214.html b/src/slalib/sun67.htx/node214.html new file mode 100644 index 0000000..41b8d99 --- /dev/null +++ b/src/slalib/sun67.htx/node214.html @@ -0,0 +1,189 @@ + + + + +Refraction + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Efficiency considerations +
+Up: Apparent Place to Observed Place +
+ Previous: Apparent Place to Observed Place +

+

+

+Refraction +

+The final correction is for atmospheric refraction. +This effect, which depends on local meteorological conditions and +the effective colour of the source/detector combination, +increases the observed elevation of the source by a +significant effect even at moderate zenith distances, and near the +horizon by over $0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$. The amount of refraction can by +computed by calling the SLALIB routine +sla_REFRO; +however, +this requires as input the observed zenith distance, which is what +we are trying to predict. For high precision it is +therefore necessary to iterate, using the topocentric +zenith distance as the initial estimate of the +observed zenith distance. +

+The full +sla_REFRO refraction calculation is onerous, and for +zenith distances of less than, say, $75^\circ$ the following +model can be used instead: +

+

\begin{displaymath} +\zeta _{vac} \approx \zeta _{obs} + + A \tan \zeta _{obs} + + B \tan ^{3}\zeta _{obs} \end{displaymath}

+where $\zeta _{vac}$ is the topocentric +zenith distance (i.e. in vacuo), +$\zeta_{obs}$ is the observed +zenith distance (i.e. affected by refraction), and A and B are +constants, about $60\hspace{-0.05em}^{'\hspace{-0.1em}'}$and + $-0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.06$ respectively for a sea-level site. +The two constants can be calculated for a given set of conditions +by calling either +sla_REFCO or +sla_REFCOQ. +

+sla_REFCO works by calling +sla_REFRO for two zenith distances and fitting A and B +to match. The calculation is onerous, but delivers accurate +results whatever the conditions. +sla_REFCOQ uses a direct formulation of A and B and +is much faster; it is slightly less accurate than +sla_REFCO but more than adequate for most practical purposes. +

+Like the full refraction model, the two-term formulation works in the wrong +direction for our purposes, predicting +the in vacuo (topocentric) zenith distance +given the refracted (observed) zenith distance, +rather than vice versa. The obvious approach of +interchanging $\zeta _{vac}$ and $\zeta_{obs}$ and +reversing the signs, though approximately +correct, gives avoidable errors which are just significant in +some applications; for +example about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ at $70^\circ$ zenith distance. A +much better result can easily be obtained, by using one Newton-Raphson +iteration as follows: +

+

\begin{displaymath} +\zeta _{obs} \approx \zeta _{vac} + - \frac{A \tan \zeta _{va... + ... + {1 + ( A + 3 B \tan ^{2}\zeta _{vac} ) \sec ^{2}\zeta _{vac}}\end{displaymath}

+

+The effect of refraction can be applied to an unrefracted +zenith distance by calling +sla_REFZ or to an unrefracted +$[\,x,y,z\,]$ by calling +sla_REFV. +Over most of the sky these two routines deliver almost identical +results, but beyond $\zeta=83^\circ$sla_REFV +becomes unacceptably inaccurate while +sla_REFZ +remains usable. (However +sla_REFV +is significantly faster, which may be important in some applications.) +SLALIB also provides a routine for computing the airmass, the function +sla_AIRMAS. +

+The refraction ``constants'' returned by +sla_REFCO and +sla_REFCOQ +are slightly affected by colour, especially at the blue end +of the spectrum. Where values for more than one +wavelength are needed, rather than calling +sla_REFCO +several times it is more efficient to call +sla_REFCO +just once, for a selected ``base'' wavelength, and then to call +sla_ATMDSP +once for each wavelength of interest. +

+All the SLALIB refraction routines work for radio wavelengths as well +as the optical/IR band. The radio refraction is very dependent on +humidity, and an accurate value must be supplied. There is no +wavelength dependence, however. The choice of optical/IR or +radio is made by specifying a wavelength greater than $100\mu m$for the radio case. +

+

+ +next + +up + +previous +
+ Next: Efficiency considerations +
+Up: Apparent Place to Observed Place +
+ Previous: Apparent Place to Observed Place +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node215.html b/src/slalib/sun67.htx/node215.html new file mode 100644 index 0000000..020487b --- /dev/null +++ b/src/slalib/sun67.htx/node215.html @@ -0,0 +1,87 @@ + + + + +Efficiency considerations + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: The Hipparcos Catalogue and the ICRS +
+Up: Apparent Place to Observed Place +
+ Previous: Refraction +

+

+

+Efficiency considerations +

+The complete apparent place to observed place transformation +can be carried out by calling +sla_AOP. +For improved efficiency +in cases of more than one star or a sequence of times, the +target-independent calculations can be done once by +calling +sla_AOPPA, +the time can be updated by calling +sla_AOPPAT, +and +sla_AOPQK +can then be used to perform the +apparent-to-observed transformation. The reverse transformation +is available through +sla_OAP +and +sla_OAPQK. +(n.b. These routines use accurate but computationally-expensive +refraction algorithms for zenith distances beyond about $76^\circ$.For many purposes, in-line code tailored to the accuracy requirements +of the application will be preferable, for example ignoring UT1-UTC, +omitting diurnal aberration and using +sla_REFZ +to apply the refraction.) +

+

+ +next + +up + +previous +
+ Next: The Hipparcos Catalogue and the ICRS +
+Up: Apparent Place to Observed Place +
+ Previous: Refraction +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node216.html b/src/slalib/sun67.htx/node216.html new file mode 100644 index 0000000..ab75104 --- /dev/null +++ b/src/slalib/sun67.htx/node216.html @@ -0,0 +1,110 @@ + + + + +The Hipparcos Catalogue and the ICRS + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Timescales +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Efficiency considerations +

+

+

+The Hipparcos Catalogue and the ICRS +

+With effect from the beginning of 1998, the IAU adopted a new +reference system to replace FK5 J2000. The new system, called the +International Celestial Reference System (ICRS), differs profoundly +from all predecessors in that the link with solar-system dynamics +was broken; the ICRS axes are defined in terms of the directions +of a set of extragalactic sources, not in terms of the mean equator and +equinox at a given reference epoch. Although the ICRS and FK5 coordinates +of any given object are almost the same, the orientation of the new frame +was essentially arbitrary, and the close match to FK5 J2000 was contrived +purely for reasons of continuity and convenience. +

+A distinction is made between the reference system (the ICRS) +and frame (ICRF). The ICRS is the set of prescriptions and +conventions together with the modelling required to define, at any +time, a triad of axes. The ICRF is a practical realization, and +currently consists of a catalogue of equatorial coordinates for 608 +extragalactic radio sources observed by VLBI. +

+The best optical realization of the ICRF currently available is the +Hipparcos catalogue. The extragalactic sources were not directly +observable by the Hipparcos satellite and so the link from Hipparcos +to ICRF was established through a variety of indirect techniques: VLBI and +conventional interferometry of radio stars, photographic astrometry +and so on. The Hipparcos frame is aligned to the ICRF to within about +0.5 mas and 0.5 mas/year (at epoch 1991.25). +

+The Hipparcos catalogue includes all of the FK5 stars, which has enabled +the orientation and spin of the latter to be studied. At epoch J2000, +the misalignment of the FK5 frame with respect to Hipparcos +(and hence ICRS) are about 32 mas and 1 mas/year respectively. +Consequently, for many practical purposes, including pointing +telescopes, the IAU 1976-1982 conventions on reference frames and +Earth orientation remain adequate and there is no need to change to +Hipparcos coordinates, new precession/nutation models and so on. +However, for the most exacting astrometric applications, SLALIB +provides some support for Hipparcos coordinates in the form of +four new routines: +sla_FK52H and +sla_H2FK5, +which transform FK5 positions and proper motions to the Hipparcos frame +and vice versa, and +sla_FK5HZ and +sla_HFK5Z, +where the transformations are for stars whose Hipparcos proper motion is +zero. +

+Further information on the ICRS can be found in the paper by M.Feissel +and F.Mignard, Astron.Astrophys. 331, L33-L36 (1988). +

+

+ +next + +up + +previous +
+ Next: Timescales +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Efficiency considerations +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node217.html b/src/slalib/sun67.htx/node217.html new file mode 100644 index 0000000..b6fbe6c --- /dev/null +++ b/src/slalib/sun67.htx/node217.html @@ -0,0 +1,92 @@ + + + + +Timescales + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Atomic Time: TAI +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: The Hipparcos Catalogue and the ICRS +

+

+

+Timescales +

+SLALIB provides for conversion between several timescales, and involves +use of one or two others. The full list is as follows: + +Three obsolete timescales should be mentioned here to avoid confusion. + +
+ +  + + +
+ +next + +up + +previous +
+ Next: Atomic Time: TAI +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: The Hipparcos Catalogue and the ICRS +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node218.html b/src/slalib/sun67.htx/node218.html new file mode 100644 index 0000000..106412e --- /dev/null +++ b/src/slalib/sun67.htx/node218.html @@ -0,0 +1,91 @@ + + + + +Atomic Time: TAI + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Universal Time: UTC, UT1 +
+Up: Timescales +
+ Previous: Timescales +

+

+

+Atomic Time: TAI +

+International Atomic Time TAI is a laboratory timescale. Its +unit is the SI second, which is defined in terms of a +defined number +of wavelengths of the radiation produced by a certain electronic +transition in the caesium 133 atom. It +is realized through a changing +population of high-precision atomic clocks held +at standards institutes in various countries. There is an +elaborate process of continuous intercomparison, leading to +a weighted average of all the clocks involved. +

+Though TAI shares the same second as the more familiar UTC, the +two timescales are noticeably separated in epoch because of the +build-up of leap seconds. At the time of writing, UTC +lags about half a minute behind TAI. +

+For any given date, the difference TAI-UTC +can be obtained by calling the SLALIB routine +sla_DAT. +Note, however, that an up-to-date copy of the routine must be used if +the most recent leap seconds are required. For applications +where this is critical, mechanisms independent of SLALIB +and under local control must +be set up; in such cases +sla_DAT +can be useful as an +independent check, for test dates within the range of the +available version. Up-to-date information on TAI-UTC is available +from ftp://maia.usno.navy.mil/ser7/tai-utc.dat. +

+

+ +next + +up + +previous +
+ Next: Universal Time: UTC, UT1 +
+Up: Timescales +
+ Previous: Timescales +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node219.html b/src/slalib/sun67.htx/node219.html new file mode 100644 index 0000000..4214aaa --- /dev/null +++ b/src/slalib/sun67.htx/node219.html @@ -0,0 +1,184 @@ + + + + +Universal Time: UTC, UT1 + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Sidereal Time: GMST, LAST +
+Up: Timescales +
+ Previous: Atomic Time: TAI +

+

+

+Universal Time: UTC, UT1 +

+Coordinated Universal Time UTC is the basis of civil timekeeping. +Most time zones differ from UTC by an integer number +of hours, though a few (e.g. parts of Canada and Australia) differ +by n+0.5 hours. The UTC second is the same as the SI second, +as for TAI. In the long term, UTC keeps in step with the +Sun. It does so even though the Earth's rotation is slightly +variable (due to large scale movements of water and atmosphere +among other things) by occasionally introducing a leap +second. +

Universal Time UT, or more specifically UT1, +is in effect the mean solar time. It is continuous +(i.e. there are no leap seconds) but has a variable +rate because of the Earth's non-uniform rotation period. It is +needed for computing the sidereal time, an essential part of +pointing a telescope at a celestial source. To obtain UT1, you +have to look up the value of UT1-UTC for the date concerned +in tables published by the International Earth Rotation +Service; this quantity, kept in the range +$\pm$$0^{\rm s}\hspace{-0.3em}.9$ by means of UTC leap +seconds, is then added to the UTC. The quantity UT1-UTC, +which typically changes by 1 or 2 ms per day, +can only be obtained by observation, though seasonal trends +are known and the IERS listings are able to predict some way into +the future with adequate accuracy for pointing telescopes. +

+UTC leap seconds are introduced as necessary, +usually at the end of December or June. +On the average the solar day is slightly longer +than the nominal 86,400 SI seconds and so leap seconds are always positive; +however, provision exists for negative leap seconds if needed. +The form of a leap second can be seen from the +following description of the end of June 1994: +

  + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Figure 1: +Relationship Between Celestial Coordinates
      
   UTCUT1-UTCUT1
      
1994June3023 59 58-0.21823 59 57.782
   23 59 59-0.21823 59 58.782
   23 59 60-0.21823 59 59.782
 July100 00 00+0.78200 00 00.782
   00 00 01+0.78200 00 01.782
+

+Note that UTC has to be expressed as hours, minutes and +seconds (or at least in seconds for a given date) if leap seconds +are to be taken into account. It is improper to express a UTC as a +Julian Date, for example, because there will be an ambiguity +during a leap second (in the above example, +1994 June 30 $23^{h}\,59^{m}\,60^{s}.0$ and +1994 July 1 $00^{h}\,00^{m}\,00^{s}.0$ would both come out as +MJD 49534.00000). Although in the vast majority of +cases this won't matter, there are potential problems in +on-line data acquisition systems and in applications involving +taking the difference between two times. Note that although the routines +sla_DAT +and +sla_DTT +expect UTC in the form of an MJD, the meaning here is really a +whole-number date rather than a time. Though the routines will accept +a fractional part and will almost always function correctly, on a day +which ends with a leap +second incorrect results would be obtained during the leap second +itself because by then the MJD would have moved into the next day. +

+

+ +next + +up + +previous +
+ Next: Sidereal Time: GMST, LAST +
+Up: Timescales +
+ Previous: Atomic Time: TAI +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node22.html b/src/slalib/sun67.htx/node22.html new file mode 100644 index 0000000..4e96061 --- /dev/null +++ b/src/slalib/sun67.htx/node22.html @@ -0,0 +1,119 @@ + + + + +SLA_AOPPAT - Update Appt-to-Obs Parameters + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AOPQK - Quick Appt-to-Observed +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOPPA - Appt-to-Obs Parameters +

+

+

SLA_AOPPAT - Update Appt-to-Obs Parameters +   +

+
+
ACTION: +
Recompute the sidereal time in the apparent to observed place +star-independent parameter block. +

CALL: +
CALL sla_AOPPAT (DATE, AOPRMS) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + +
DATEDUTC date/time (Modified Julian Date, JD-2400000.5)
AOPRMSD(14)star-independent apparent-to-observed parameters:
(1-12)not required
(13)longitude + eqn of equinoxes + +``sidereal $\Delta$UT'' (radians)
(14)not required
+

+
RETURNED: +
+
+ + + + + + + + + + + + + +
AOPRMSD(14)star-independent apparent-to-observed parameters:
(1-13)not changed
(14)local apparent sidereal time (radians)
+

+
NOTE: +
For more information, see sla_AOPPA. +
+
+ +next + +up + +previous +
+ Next: SLA_AOPQK - Quick Appt-to-Observed +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOPPA - Appt-to-Obs Parameters +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node220.html b/src/slalib/sun67.htx/node220.html new file mode 100644 index 0000000..84db99f --- /dev/null +++ b/src/slalib/sun67.htx/node220.html @@ -0,0 +1,96 @@ + + + + +Sidereal Time: GMST, LAST + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Dynamical Time: TT, TDB +
+Up: Timescales +
+ Previous: Universal Time: UTC, UT1 +

+

+

+Sidereal Time: GMST, LAST +

+Sidereal Time is the ``time of day'' relative to the +stars rather than to the Sun. After +one sidereal day the stars come back to the same place in the +sky, apart from sub-arcsecond precession effects. Because the Earth +rotates faster relative to the stars than to the Sun by one day +per year, the sidereal second is shorter than the solar +second; the ratio is about 0.9973. +

+The Greenwich Mean Sidereal Time GMST is +linked to UT1 by a numerical formula which +is implemented in the SLALIB routines +sla_GMST +and +sla_GMSTA. +There are, of course, no leap seconds in GMST, but the second +changes in length along with the UT1 second, and also varies +over long periods of time because of slow changes in the Earth's +orbit. This makes the timescale unsuitable for everything except +predicting the apparent directions of celestial sources. +

+The Local Apparent Sidereal Time LAST is the apparent right +ascension of the local meridian, from which the hour angle of any +star can be determined knowing its $\alpha$. It can be obtained from the +GMST by adding the east longitude (corrected for polar motion +in precise work) and the equation of the equinoxes. The +latter, already described, is an aspect of the nutation effect +and can be predicted by calling the SLALIB routine +sla_EQEQX +or, neglecting certain very small terms, by calling +sla_NUTC +and using the expression $\Delta\psi\cos\epsilon$.

+

+ +next + +up + +previous +
+ Next: Dynamical Time: TT, TDB +
+Up: Timescales +
+ Previous: Universal Time: UTC, UT1 +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node221.html b/src/slalib/sun67.htx/node221.html new file mode 100644 index 0000000..926f2ce --- /dev/null +++ b/src/slalib/sun67.htx/node221.html @@ -0,0 +1,158 @@ + + + + +Dynamical Time: TT, TDB + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Calendars +
+Up: Timescales +
+ Previous: Sidereal Time: GMST, LAST +

+

+

+Dynamical Time: TT, TDB +

+Dynamical time is the independent variable in the theories +which describe the motions of bodies in the solar system. When +you use published formulae which model the position of the +Earth in its orbit, for example, or look up +the Moon's position in a precomputed ephemeris, the date and time +you use must be in terms of one of the dynamical timescales. It +is a common but understandable mistake to use UT directly, in which +case the results will be about 1 minute out (in the present +era). +

+It is not hard to see why such timescales are necessary. +UTC would clearly be unsuitable as the argument of an +ephemeris because of leap seconds. +A solar-system ephemeris based on UT1 or sidereal time would somehow +have to include the unpredictable variations of the Earth's rotation. +TAI would work, but eventually +the ephemeris and the ensemble of atomic clocks would drift apart. +In effect, the ephemeris is a clock, with the bodies of +the solar system the hands. +

+Only two of the dynamical timescales are of any great importance to +observational astronomers, TT and TDB. (The obsolete +timescale ET, ephemeris time, was more or less the same as TT.) +

Terrestrial Time TT is +the theoretical timescale of apparent geocentric ephemerides of solar +system bodies. It applies, in principle, +to an Earthbound clock, at sea-level, and for practical purposes +it is tied to +Atomic Time TAI through the formula TT = TAI + $32^{\rm s}\hspace{-0.3em}.184$.In practice, therefore, the units of TT are ordinary SI seconds, and +the offset of $32^{\rm s}\hspace{-0.3em}.184$ with respect to TAI is fixed. +The SLALIB routine +sla_DTT +returns TT-UTC for a given UTC +(n.b. sla_DTT +calls +sla_DAT, +and the latter must be an up-to-date version if recent leap seconds are +to be taken into account). +

Barycentric Dynamical Time TDB differs from TT by an amount which +cycles back and forth by a millisecond or two due to +relativistic effects. The variation is +negligible for most purposes, but unless taken into +account would swamp +long-term analysis of pulse arrival times from the +millisecond pulsars. It is a consequence of +the TT clock being on the Earth rather than in empty +space: the ellipticity of +the Earth's orbit means that the TT clock's speed and +gravitational potential vary slightly +during the course of the year, and as a consequence +its rate as seen from an outside observer +varies due to transverse Doppler effect and gravitational +redshift. By definition, TDB and TT differ only +by periodic terms, and the main effect +is a sinusoidal variation of amplitude $0^{\rm s}\hspace{-0.3em}.0016$; the +largest planetary terms are nearly two orders of magnitude +smaller. The SLALIB routine +sla_RCC +provides a model of +TDB-TT accurate to a few nanoseconds. +There are other dynamical timescales, not supported by +SLALIB routines, which include allowance also for the secular terms. +These timescales gain on TT and TDB by about $0^{\rm s}\hspace{-0.3em}.0013$/day. +

+For most purposes the more accessible TT is the timescale to use, +for example when calling +sla_PRENUT +to generate a precession/nutation matrix or when calling +sla_EVP +to predict the +Earth's position and velocity. For some purposes TDB is the +correct timescale, for example when interrogating the JPL planetary +ephemeris (see Starlink User Note 87), though in most cases +TT will be near enough and will involve less computation. +

+Investigations of topocentric solar-system phenomena such as +occultations and eclipses require solar time as well as dynamical +time. TT/TDB/ET is all that is required in order to compute the geocentric +circumstances, but if horizon coordinates or geocentric parallax +are to be tackled UT is also needed. A rough estimate +of $\Delta {\rm T} = {\rm ET} - {\rm UT}$ is +available via the routine +sla_DT. +For a given epoch (e.g. 1650) this returns an approximation +to $\Delta {\rm T}$ in seconds. +

+

+ +next + +up + +previous +
+ Next: Calendars +
+Up: Timescales +
+ Previous: Sidereal Time: GMST, LAST +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node222.html b/src/slalib/sun67.htx/node222.html new file mode 100644 index 0000000..7cc8f58 --- /dev/null +++ b/src/slalib/sun67.htx/node222.html @@ -0,0 +1,113 @@ + + + + +Calendars + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Geocentric Coordinates +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Dynamical Time: TT, TDB +

+

+

+Calendars +

+The ordinary Gregorian Calendar Date, +together with a time of day, can be +used to express an epoch in any desired timescale. For many purposes, +however, a continuous count of days is more convenient, and for +this purpose the system of Julian Day Number can be used. +JD zero is located about 7000 years ago, well before the +historical era, and is formally defined in terms of Greenwich noon; +Julian Day Number 2449444 began at noon on 1994 April 1. Julian Date +is the same system but with a fractional part appended; +Julian Date 2449443.5 was the midnight on which 1994 April 1 +commenced. Because of the unwieldy size of Julian Dates +and the awkwardness of the half-day offset, it is +accepted practice to remove the leading `24' and the trailing `.5', +producing what is called the Modified Julian Date: +MJD = JD-2400000.5. SLALIB routines use MJD, as opposed to +JD, throughout, largely to avoid loss of precision. +1994 April 1 commenced at MJD 49443.0. +

+Despite JD (and hence MJD) being defined in terms of (in effect) +UT, the system can be used in conjunction with other timescales +such as TAI, TT and TDB (and even sidereal time through the +concept of Greenwich Sidereal Date). However, it is improper +to express a UTC as a JD or MJD because of leap seconds. +

+SLALIB has six routines for converting to and from dates in +the Gregorian calendar. The routines +sla_CLDJ +and +sla_CALDJ +both convert a calendar date into an MJD, the former interpreting +years between 0 and 99 as 1st century and the latter as late 20th or +early 21st century. The routines sla_DJCL +and +sla_DJCAL +both convert an MJD into calendar year, month, day and fraction of a day; +the latter performs rounding to a specified precision, important +to avoid dates like `94 04 01.***' appearing in messages. +Some of SLALIB's low-precision ephemeris routines +(sla_EARTH, +sla_MOON +and +sla_ECOR) +work in terms of year plus day-in-year (where +day 1 = January 1st, at least for the modern era). +This form of date can be generated by +calling +sla_CALYD +(which defaults years 0-99 into 1950-2049) +or +sla_CLYD +(which covers the full range from prehistoric times). +

+

+ +next + +up + +previous +
+ Next: Geocentric Coordinates +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Dynamical Time: TT, TDB +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node223.html b/src/slalib/sun67.htx/node223.html new file mode 100644 index 0000000..497a385 --- /dev/null +++ b/src/slalib/sun67.htx/node223.html @@ -0,0 +1,139 @@ + + + + +Geocentric Coordinates + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Ephemerides +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Calendars +

+

+

+Geocentric Coordinates +

+The location of the observer on the Earth is significant in a +number of ways. The most obvious, of course, is the effect of latitude +on the observed $[\,Az,El~]$ of a star. Less obvious is the need to +allow for geocentric parallax when finding the Moon with a +telescope (and when doing high-precision work involving the +Sun or planets), and the need to correct observed radial +velocities and apparent pulsar periods for the effects +of the Earth's rotation. +

+The SLALIB routine +sla_OBS +supplies details of groundbased observatories from an internal +list. This is useful when writing applications that apply to +more than one observatory; the user can enter a brief name, +or browse through a list, and be spared the trouble of typing +in the full latitude, longitude etc. The following +Fortran code returns the full name, longitude and latitude +of a specified observatory: +

+            CHARACTER IDENT*10,NAME*40
+            DOUBLE PRECISION W,P,H
+             :
+            CALL sla_OBS(0,IDENT,NAME,W,P,H)
+            IF (NAME.EQ.'?') ...             (not recognized)
+
+

(Beware of the longitude sign convention, which is west +ve +for historical reasons.) The following lists all +the supported observatories: +

+             :
+            INTEGER N
+             :
+            N=1
+            NAME=' '
+            DO WHILE (NAME.NE.'?')
+               CALL sla_OBS(N,IDENT,NAME,W,P,H)
+               IF (NAME.NE.'?') THEN
+                  WRITE (*,'(1X,I3,4X,A,4X,A)') N,IDENT,NAME
+                  N=N+1
+               END IF
+            END DO
+
+

+The routine +sla_GEOC +converts a geodetic latitude +(one referred to the local horizon) to a geocentric position, +taking into account the Earth's oblateness and also the height +above sea level of the observer. The results are expressed in +vector form, namely as the distance of the observer from +the spin axis and equator respectively. The geocentric +latitude can be found be evaluating ATAN2 of the +two numbers. A full 3-D vector description of the position +and velocity of the observer is available through the routine +sla_PVOBS. +For a specified geodetic latitude, height above +sea level, and local sidereal time, +sla_PVOBS +generates a 6-element vector containing the position and +velocity with respect to the true equator and equinox of +date (i.e. compatible with apparent $[\,\alpha,\delta\,]$). For +some applications it will be necessary to convert to a +mean $[\,\alpha,\delta\,]$ frame (notably FK5, J2000) by multiplying +elements 1-3 and 4-6 respectively with the appropriate +precession matrix. (In theory an additional correction to the +velocity vector is needed to allow for differential precession, +but this correction is always negligible.) +

+See also the discussion of the routine +sla_RVEROT, +later. +

+

+ +next + +up + +previous +
+ Next: Ephemerides +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Calendars +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node224.html b/src/slalib/sun67.htx/node224.html new file mode 100644 index 0000000..4cb8678 --- /dev/null +++ b/src/slalib/sun67.htx/node224.html @@ -0,0 +1,617 @@ + + + + +Ephemerides + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Radial Velocity and Light-Time Corrections +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Geocentric Coordinates +

+

+

+Ephemerides +

+SLALIB includes routines for generating positions and +velocities of Solar-System bodies. The accuracy objectives are +modest, and the SLALIB facilities do not attempt +to compete with precomputed ephemerides such as +those provided by JPL, or with models containing +thousands of terms. It is also worth noting +that SLALIB's very accurate star coordinate conversion +routines are not strictly applicable to solar-system cases, +though they are adequate for most practical purposes. +

+Earth/Sun ephemerides can be generated using the routine +sla_EVP, +which predicts Earth position and velocity with respect to both the +solar-system barycentre and the +Sun. Maximum velocity error is 0.42 metres per second; maximum +heliocentric position error is 1600 km (about $2\hspace{-0.05em}^{'\hspace{-0.1em}'}$), with +barycentric position errors about 4 times worse. +(The Sun's position as +seen from the Earth can, of course, be obtained simply by +reversing the signs of the Cartesian components of the +Earth:Sun vector.) +

+Geocentric Moon ephemerides are available from +sla_DMOON, +which predicts the Moon's position and velocity with respect to +the Earth's centre. Direction accuracy is usually better than +10 km ($5\hspace{-0.05em}^{'\hspace{-0.1em}'}$) and distance accuracy a little worse. +

+Lower-precision but faster predictions for the Sun and Moon +can be made by calling +sla_EARTH +and +sla_MOON. +Both are single precision and accept dates in the form of +year, day-in-year and fraction of day +(starting from a calendar date you need to call +sla_CLYD +or +sla_CALYD +to get the required year and day). +The +sla_EARTH +routine returns the heliocentric position and velocity +of the Earth's centre for the mean equator and +equinox of date. The accuracy is better than 20,000 km in position +and 10 metres per second in speed. +The +position and velocity of the Moon with respect to the +Earth's centre for the mean equator and ecliptic of date +can be obtained by calling +sla_MOON. +The positional accuracy is better than $30\hspace{-0.05em}^{'\hspace{-0.1em}'}$ in direction +and 1000 km in distance. +

+Approximate ephemerides for all the major planets +can be generated by calling +sla_PLANET +or +sla_RDPLAN. These routines offer arcminute accuracy (much +better for the inner planets and for Pluto) over a span of several +millennia (but only $\pm100$ years for Pluto). +The routine +sla_PLANET produces heliocentric position and +velocity in the form of equatorial $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ for the +mean equator and equinox of J2000. The vectors +produced by +sla_PLANET +can be used in a variety of ways according to the +requirements of the application concerned. The routine +sla_RDPLAN +uses +sla_PLANET +and +sla_DMOON +to deal with the common case of predicting +a planet's apparent $[\,\alpha,\delta\,]$ and angular size as seen by a +terrestrial observer. +

+Note that in predicting the position in the sky of a solar-system body +it is necessary to allow for geocentric parallax. This correction +is essential in the case of the Moon, where the observer's +position on the Earth can affect the Moon's $[\,\alpha,\delta\,]$ by up to +$1^\circ$. The calculation can most conveniently be done by calling +sla_PVOBS and subtracting the resulting 6-vector from the +one produced by +sla_DMOON, as is demonstrated by the following example: +

+      *  Demonstrate the size of the geocentric parallax correction
+      *  in the case of the Moon.  The test example is for the AAT,
+      *  before midnight, in summer, near first quarter.
+
+            IMPLICIT NONE
+            CHARACTER NAME*40,SH,SD
+            INTEGER J,I,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION SLONGW,SLAT,H,DJUTC,FDUTC,DJUT1,DJTT,STL,
+           :                 RMATN(3,3),PMM(6),PMT(6),RM,DM,PVO(6),TL
+            DOUBLE PRECISION sla_DTT,sla_GMST,sla_EQEQX,sla_DRANRM
+
+      *  Get AAT longitude and latitude in radians and height in metres
+            CALL sla_OBS(0,'AAT',NAME,SLONGW,SLAT,H)
+
+      *  UTC (1992 January 13, 11 13 59) to MJD
+            CALL sla_CLDJ(1992,1,13,DJUTC,J)
+            CALL sla_DTF2D(11,13,59.0D0,FDUTC,J)
+            DJUTC=DJUTC+FDUTC
+
+      *  UT1 (UT1-UTC value of -0.152 sec is from IERS Bulletin B)
+            DJUT1=DJUTC+(-0.152D0)/86400D0
+
+      *  TT
+            DJTT=DJUTC+sla_DTT(DJUTC)/86400D0
+
+      *  Local apparent sidereal time
+            STL=sla_GMST(DJUT1)-SLONGW+sla_EQEQX(DJTT)
+
+      *  Geocentric position/velocity of Moon (mean of date)
+            CALL sla_DMOON(DJTT,PMM)
+
+      *  Nutation to true equinox of date
+            CALL sla_NUT(DJTT,RMATN)
+            CALL sla_DMXV(RMATN,PMM,PMT)
+            CALL sla_DMXV(RMATN,PMM(4),PMT(4))
+
+      *  Report geocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,'' geocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+
+      *  Geocentric position of observer (true equator and equinox of date)
+            CALL sla_PVOBS(SLAT,H,STL,PVO)
+
+      *  Place origin at observer
+            DO I=1,6
+               PMT(I)=PMT(I)-PVO(I)
+            END DO
+
+      *  Allow for planetary aberration
+            TL=499.004782D0*SQRT(PMT(1)**2+PMT(2)**2+PMT(3)**2)
+            DO I=1,3
+               PMT(I)=PMT(I)-TL*PMT(I+3)
+            END DO
+
+      *  Report topocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,''topocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+            END
+
+

+The output produced is as follows: +

+       geocentric:  +03 06 55.59 +15 03 39.0
+      topocentric:  +03 09 23.79 +15 40 51.5
+
+

(An easier but +less instructive method of estimating the topocentric apparent place of the +Moon is to call the routine +sla_RDPLAN.) +

+As an example of using +sla_PLANET, +the following program estimates the geocentric separation +between Venus and Jupiter during a close conjunction +in 2BC, which is a star-of-Bethlehem candidate: +

+      *  Compute time and minimum geocentric apparent separation
+      *  between Venus and Jupiter during the close conjunction of 2 BC.
+
+            IMPLICIT NONE
+
+            DOUBLE PRECISION SEPMIN,DJD0,FD,DJD,DJDM,DF,PV(6),RMATP(3,3),
+           :                 PVM(6),PVE(6),TL,RV,DV,RJ,DJ,SEP
+            INTEGER IHOUR,IMIN,J,I,IHMIN,IMMIN
+            DOUBLE PRECISION sla_EPJ,sla_DSEP
+
+
+      *  Search for closest approach on the given day
+            DJD0=1720859.5D0
+            SEPMIN=1D10
+            DO IHOUR=20,22
+               DO IMIN=0,59
+                  CALL sla_DTF2D(IHOUR,IMIN,0D0,FD,J)
+
+      *        Julian date and MJD
+                  DJD=DJD0+FD
+                  DJDM=DJD-2400000.5D0
+
+      *        Earth to Moon (mean of date)
+                  CALL sla_DMOON(DJDM,PV)
+
+      *        Precess Moon position to J2000
+                  CALL sla_PRECL(sla_EPJ(DJDM),2000D0,RMATP)
+                  CALL sla_DMXV(RMATP,PV,PVM)
+
+      *        Sun to Earth-Moon Barycentre (mean J2000)
+                  CALL sla_PLANET(DJDM,3,PVE,J)
+
+      *        Correct from EMB to Earth
+                  DO I=1,3
+                     PV(I)=PVE(I)-0.012150581D0*PVM(I)
+                  END DO
+
+      *        Sun to Venus
+                  CALL sla_PLANET(DJDM,2,PV,J)
+
+      *        Earth to Venus
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+
+      *        Light time to Venus (sec)
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+
+      *        Extrapolate backwards in time by that much
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+
+      *       To RA,Dec
+                  CALL sla_DCC2S(PV,RV,DV)
+
+      *        Same for Jupiter
+                  CALL sla_PLANET(DJDM,5,PV,J)
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+                  CALL sla_DCC2S(PV,RJ,DJ)
+
+      *        Separation (arcsec)
+                  SEP=sla_DSEP(RV,DV,RJ,DJ)
+
+      *        Keep if smallest so far
+                  IF (SEP.LT.SEPMIN) THEN
+                     IHMIN=IHOUR
+                     IMMIN=IMIN
+                     SEPMIN=SEP
+                  END IF
+               END DO
+            END DO
+
+      *  Report
+            WRITE (*,'(1X,I2.2,'':'',I2.2,F6.1)') IHMIN,IMMIN,
+           :                                      206264.8062D0*SEPMIN
+
+            END
+
+

+The output produced (the Ephemeris Time on the day in question, and +the closest approach in arcseconds) is as follows: +

+      21:19  33.7
+
+

+For comparison, accurate predictions based on the JPL DE102 ephemeris +give a separation about $8\hspace{-0.05em}^{'\hspace{-0.1em}'}$ less than +the above estimate, occurring about half an hour earlier +(see Sky and Telescope, April 1987, p357). +

+The following program demonstrates +sla_RDPLAN. +

+      *  For a given date, time and geographical location, output
+      *  a table of planetary positions and diameters.
+
+            IMPLICIT NONE
+            CHARACTER PNAMES(0:9)*7,B*80,S
+            INTEGER I,NP,IY,J,IM,ID,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION R2AS,FD,DJM,ELONG,PHI,RA,DEC,DIAM
+            PARAMETER (R2AS=206264.80625D0)
+            DATA PNAMES / 'Sun','Mercury','Venus','Moon','Mars','Jupiter',
+           :              'Saturn','Uranus','Neptune', 'Pluto' /
+
+
+      *  Loop until 'end' typed
+            B=' '
+            DO WHILE (B.NE.'END'.AND.B.NE.'end')
+
+      *     Get date, time and observer's location
+               PRINT *,'Date? (Y,M,D, Gregorian)'
+               READ (*,'(A)') B
+               IF (B.NE.'END'.AND.B.NE.'end') THEN
+                  I=1
+                  CALL sla_INTIN(B,I,IY,J)
+                  CALL sla_INTIN(B,I,IM,J)
+                  CALL sla_INTIN(B,I,ID,J)
+                  PRINT *,'Time? (H,M,S, dynamical)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,FD,J)
+                  FD=FD*2.3873241463784300365D0
+                  CALL sla_CLDJ(IY,IM,ID,DJM,J)
+                  DJM=DJM+FD
+                  PRINT *,'Longitude? (D,M,S, east +ve)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,ELONG,J)
+                  PRINT *,'Latitude? (D,M,S, (geodetic)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,PHI,J)
+
+      *        Loop planet by planet
+                  DO NP=0,8
+
+      *           Get RA,Dec and diameter
+                     CALL sla_RDPLAN(DJM,NP,ELONG,PHI,RA,DEC,DIAM)
+
+      *           One line of report
+                     CALL sla_DR2TF(2,RA,S,IHMSF)
+                     CALL sla_DR2AF(1,DEC,S,IDMSF)
+                     WRITE (*,
+           : '(1X,A,2X,3I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1,F8.1)')
+           :                          PNAMES(NP),IHMSF,S,IDMSF,R2AS*DIAM
+
+      *           Next planet
+                  END DO
+                  PRINT *,' '
+               END IF
+
+      *     Next case
+            END DO
+
+            END
+
+Entering the following data (for 1927 June 29 at $5^{\rm h}\,25^{\rm m}$ ET +and the position of Preston, UK.): +
+      1927 6 29
+      5 25
+      -2 42
+      53 46
+
+produces the following report: +
+      Sun       06 28 14.03  +23 17 17.5  1887.8
+      Mercury   08 08 58.62  +19 20 57.3     9.3
+      Venus     09 38 53.64  +15 35 32.9    22.8
+      Moon      06 28 18.30  +23 18 37.3  1903.9
+      Mars      09 06 49.34  +17 52 26.7     4.0
+      Jupiter   00 11 12.06  -00 10 57.5    41.1
+      Saturn    16 01 43.34  -18 36 55.9    18.2
+      Uranus    00 13 33.53  +00 39 36.0     3.5
+      Neptune   09 49 35.75  +13 38 40.8     2.2
+      Pluto     07 05 29.50  +21 25 04.2      .1
+
+Inspection of the Sun and Moon data reveals that +a total solar eclipse is in progress. +

+SLALIB also provides for the case where orbital elements (with respect +to the J2000 equinox and ecliptic) +are available. This allows predictions to be made for minor-planets and +(if you ignore non-gravitational effects) +comets. Furthermore, if major-planet elements for an epoch close to the date +in question are available, more accurate predictions can be made than +are offered by +sla_RDPLAN and +sla_PLANET. +

+The SLALIB planetary-prediction +routines that work with orbital elements are +sla_PLANTE (the orbital-elements equivalent of +sla_RDPLAN), which predicts the topocentric $[\,\alpha,\delta\,]$, and +sla_PLANEL (the orbital-elements equivalent of +sla_PLANET), which predicts the heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ with respect to the +J2000 equinox and equator. In addition, the routine +sla_PV2EL does the inverse of +sla_PLANEL, transforming $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ into osculating elements. +

+Osculating elements describe the unperturbed 2-body orbit. This is +a good approximation to the actual orbit for a few weeks either +side of the specified epoch, outside which perturbations due to +the other bodies of the Solar System lead to +increasing errors. Given a minor planet's osculating elements for +a particular date, predictions for a date even just +100 days earlier or later +are likely to be in error by several arcseconds. +These errors can +be reduced if new elements are generated which take account of +the perturbations of the major planets, and this is what the routine +sla_PERTEL does. Once +sla_PERTEL has been called, to provide osculating elements +close to the required date, the elements can be passed to +sla_PLANEL or +sla_PLANTE in the normal way. Predictions of arcsecond accuracy +over a span of a decade or more are available using this +technique. +

+Three different combinations of orbital elements are +provided for, matching the usual conventions +for major planets, minor planets and +comets respectively. The choice is made through the +argument JFORM: +
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
JFORM=1JFORM=2JFORM=3
t0t0T
iii
$\Omega$$\Omega$$\Omega$
$\varpi$$\omega$$\omega$
aaq
eee
LM 
n  
+
+
+
+
+
+
+The symbols have the following meanings: +


+		 t0 epoch at which the elements were correct
+		 T epoch of perihelion passage
+		 i inclination of the orbit
+		 $\Omega$ longitude of the ascending node
+		 $\varpi$ longitude of perihelion ($\varpi = \Omega + \omega$)		 $\omega$ argument of perihelion
+		 a semi-major axis of the orbital ellipse
+		 q perihelion distance
+		 e orbital eccentricity
+		 L mean longitude ($L = \varpi + M$)		 M mean anomaly
+		 n mean motion 
+
+

+The mean motion, n, tells sla_PLANEL the mass of the planet. +If it is not available, it should be claculated +from n2 a3 = k2 (1+m), where k = 0.01720209895 and +m is the mass of the planet ($M_\odot = 1$); a is in AU. +

+Conventional elements are not the only way of specifying an orbit. +The $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ state vector is an equally valid specification, +and the so-called method of universal variables allows +orbital calculations to be made directly, bypassing angular +quantities and avoiding Kepler's Equation. The universal-variables +approach has various advantages, including better handling of +near-parabolic cases and greater efficiency. +SLALIB uses universal variables for its internal +calculations and also offers a number of routines which +applications can call. +

+The universal elements are the $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ and its epoch, plus the mass +of the body. The SLALIB routines supplement these elements with +certain redundant values in order to +avoid unnecessary recomputation when the elements are next used. +

+The routines +sla_EL2UE and +sla_UE2EL transform conventional elements into the +universal form and vice versa. +The routine +sla_PV2UE takes an $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ and forms the set of universal +elements; +sla_UE2PV takes a set of universal elements and predicts the $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ for a specified epoch. +The routine +sla_PERTUE provides updated universal elements, +taking into account perturbations from the major planets. +

+

+ +next + +up + +previous +
+ Next: Radial Velocity and Light-Time Corrections +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Geocentric Coordinates +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node225.html b/src/slalib/sun67.htx/node225.html new file mode 100644 index 0000000..ce716c7 --- /dev/null +++ b/src/slalib/sun67.htx/node225.html @@ -0,0 +1,143 @@ + + + + +Radial Velocity and Light-Time Corrections + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Focal-Plane Astrometry +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Ephemerides +

+

+

+Radial Velocity and Light-Time Corrections +

+When publishing high-resolution spectral observations +it is necessary to refer them to a specified standard of rest. +This involves knowing the component in the direction of the +source of the velocity of the observer. SLALIB provides a number +of routines for this purpose, allowing observations to be +referred to the Earth's centre, the Sun, a Local Standard of Rest +(either dynamical or kinematical), the centre of the Galaxy, and +the mean motion of the Local Group. +

+The routine +sla_RVEROT +corrects for the diurnal rotation of +the observer around the Earth's axis. This is always less than 0.5 km/s. +

+No specific routine is provided to correct a radial velocity +from geocentric to heliocentric, but this can easily be done by calling +sla_EVP +as follows (array declarations etc. omitted): +

+             :
+      *  Star vector, J2000
+            CALL sla_DCS2C(RM,DM,V)
+
+      *  Earth/Sun velocity and position, J2000
+            CALL sla_EVP(TDB,2000D0,DVB,DPB,DVH,DPH)
+
+      *  Radial velocity correction due to Earth orbit (km/s)
+            VCORB = -sla_DVDV(V,DVH)*149.597870D6
+             :
+
+

+The maximum value of this correction is the Earth's orbital speed +of about 30 km/s. A related routine, +sla_ECOR, +computes the light-time correction with respect to the Sun. It +would be used when reducing observations of a rapid variable-star +for instance. +Note, however, that the accuracy objectives for pulsar work are +beyond the scope of these SLALIB routines, and even the superior +sla_EVP +routine is unsuitable for arrival-time calculations of better +than 25 millisecond accuracy. +

+To remove the intrinsic $\sim20$ km/s motion of the Sun relative +to other stars in the solar neighbourhood, +a velocity correction to a +local standard of rest (LSR) is required. There are +opportunities for mistakes here. There are two sorts of LSR, +dynamical and kinematical, and +multiple definitions exist for the latter. The +dynamical LSR is a point near the Sun which is in a circular +orbit around the Galactic centre; the Sun has a ``peculiar'' +motion relative to the dynamical LSR. A kinematical LSR is +the mean standard of rest of specified star catalogues or stellar +populations, and its precise definition depends on which +catalogues or populations were used and how the analysis was +carried out. The Sun's motion with respect to a kinematical +LSR is called the ``standard'' solar motion. Radial +velocity corrections to the dynamical LSR are produced by the routine +sla_RVLSRD +and to the adopted kinematical LSR by +sla_RVLSRK. +See the individual specifications for these routines for the +precise definition of the LSR in each case. +

+For extragalactic sources, the centre of the Galaxy can be used as +a standard of rest. The radial velocity correction from the +dynamical LSR to the Galactic centre can be obtained by calling +sla_RVGALC. +Its maximum value is 220 km/s. +

+For very distant sources it is appropriate to work relative +to the mean motion of the Local Group. The routine for +computing the radial velocity correction in this case is +sla_RVLG. +Note that in this case the correction is with respect to the +dynamical LSR, not the Galactic centre as might be expected. +This conforms to the IAU definition, and confers immunity from +revisions of the Galactic rotation speed. +

+

+ +next + +up + +previous +
+ Next: Focal-Plane Astrometry +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Ephemerides +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node226.html b/src/slalib/sun67.htx/node226.html new file mode 100644 index 0000000..41baa89 --- /dev/null +++ b/src/slalib/sun67.htx/node226.html @@ -0,0 +1,212 @@ + + + + +Focal-Plane Astrometry + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Numerical Methods +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Radial Velocity and Light-Time Corrections +

+

+

+Focal-Plane Astrometry +

+The relationship between the position of a star image in +the focal plane of a telescope and the star's celestial +coordinates is usually described in terms of the tangent plane +or gnomonic projection. This is the projection produced +by a pin-hole camera and is a good approximation to the projection +geometry of a traditional large f-ratio astrographic refractor. +SLALIB includes a group of routines which transform +star positions between their observed places on the celestial +sphere and their $[\,x,y\,]$ coordinates in the tangent plane. The +spherical coordinate system does not have to be $[\,\alpha,\delta\,]$ but +usually is. The so-called standard coordinates of a star +are the tangent plane $[\,x,y\,]$, in radians, with respect to an origin +at the tangent point, with the y-axis pointing north and +the x-axis pointing east (in the direction of increasing $\alpha$). +The factor relating the standard coordinates to +the actual $[\,x,y\,]$ coordinates in, say, millimetres is simply +the focal length of the telescope. +

+Given the $[\,\alpha,\delta\,]$ of the plate centre (the tangent point) +and the $[\,\alpha,\delta\,]$ of a star within the field, the standard +coordinates can be determined by calling +sla_S2TP +(single precision) or +sla_DS2TP +(double precision). The reverse transformation, where the +$[\,x,y\,]$ is known and we wish to find the $[\,\alpha,\delta\,]$, is carried out by calling +sla_TP2S +or +sla_DTP2S. +Occasionally we know the both the $[\,x,y\,]$ and the $[\,\alpha,\delta\,]$ of a +star and need to deduce the $[\,\alpha,\delta\,]$ of the tangent point; +this can be done by calling +sla_TPS2C +or +sla_DTPS2C. +(All of these transformations apply not just to $[\,\alpha,\delta\,]$ but to +other spherical coordinate systems, of course.) +Equivalent (and faster) +routines are provided which work directly in $[\,x,y,z\,]$ instead of +spherical coordinates: +sla_V2TP and +sla_DV2TP, +sla_TP2V and +sla_DTP2V, +sla_TPV2C and +sla_DTPV2C. +

+Even at the best of times, the tangent plane projection is merely an +approximation. Some telescopes and cameras exhibit considerable pincushion +or barrel distortion and some have a curved focal surface. +For example, neither Schmidt cameras nor (especially) +large reflecting telescopes with wide-field corrector lenses +are adequately modelled by tangent-plane geometry. In such +cases, however, it is still possible to do most of the work +using the (mathematically convenient) tangent-plane +projection by inserting an extra step which applies or +removes the distortion peculiar to the system concerned. +A simple r1=r0(1+Kr02) law works well in the +majority of cases; r0 is the radial distance in the +tangent plane, r1 is the radial distance after adding +the distortion, and K is a constant which depends on the +telescope ($\theta$ is unaffected). The routine +sla_PCD +applies the distortion to an $[\,x,y\,]$ and +sla_UNPCD +removes it. For $[\,x,y\,]$ in radians, K values range from -1/3 for the +tiny amount of barrel distortion in Schmidt geometry to several +hundred for the serious pincushion distortion +produced by wide-field correctors in big reflecting telescopes +(the AAT prime focus triplet corrector is about K=+178.6). +

+SLALIB includes a group of routines which can be put together +to build a simple plate-reduction program. The heart of the group is +sla_FITXY, +which fits a linear model to relate two sets of $[\,x,y\,]$ coordinates, +in the case of a plate reduction the measured positions of the +images of a set of +reference stars and the standard +coordinates derived from their catalogue positions. The +model is of the form: + +

+xp = a + bxm + cym +

+ +

+yp = d + exm + fym +

+

+where the p subscript indicates ``predicted'' coordinates +(the model's approximation to the ideal ``expected'' coordinates) and the +m subscript indicates ``measured coordinates''. The +six coefficients a-f can optionally be +constrained to represent a ``solid body rotation'' free of +any squash or shear distortions. Without this constraint +the model can, to some extent, accommodate effects like refraction, +allowing mean places to be used directly and +avoiding the extra complications of a +full mean-apparent-observed transformation for each star. +Having obtained the linear model, +sla_PXY +can be used to process the set of measured and expected +coordinates, giving the predicted coordinates and determining +the RMS residuals in x and y. +The routine +sla_XY2XY +transforms one $[\,x,y\,]$ into another using the linear model. A model +can be inverted by calling +sla_INVF, +and decomposed into zero points, scales, x/y nonperpendicularity +and orientation by calling +sla_DCMPF. +

+

+ +next + +up + +previous +
+ Next: Numerical Methods +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Radial Velocity and Light-Time Corrections +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node227.html b/src/slalib/sun67.htx/node227.html new file mode 100644 index 0000000..9ed563a --- /dev/null +++ b/src/slalib/sun67.htx/node227.html @@ -0,0 +1,230 @@ + + + + +Numerical Methods + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SUMMARY OF CALLS +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Focal-Plane Astrometry +

+

+

+Numerical Methods +

+SLALIB contains a small number of simple, general-purpose +numerical-methods routines. They have no specific +connection with positional astronomy but have proved useful in +applications to do with simulation and fitting. +

+At the heart of many simulation programs is the generation of +pseudo-random numbers, evenly distributed in a given range: +sla_RANDOM +does this. Pseudo-random normal deviates, or ``Gaussian +residuals'', are often required to simulate noise and +can be generated by means of the function +sla_GRESID. +Neither routine will pass super-sophisticated +statistical tests, but they work adequately for most +practical purposes and avoid the need to call non-standard +library routines peculiar to one sort of computer. +

+Applications which perform a least-squares fit using a traditional +normal-equations methods can accomplish the required matrix-inversion +by calling either +sla_SMAT +(single precision) or +sla_DMAT +(double). A generally better way to perform such fits is +to use singular value decomposition. SLALIB provides a routine +to do the decomposition itself, +sla_SVD, +and two routines to use the results: +sla_SVDSOL +generates the solution, and +sla_SVDCOV +produces the covariance matrix. +A simple demonstration of the use of the SLALIB SVD +routines is given below. It generates 500 simulated data +points and fits them to a model which has 4 unknown coefficients. +(The arrays in the example are sized to accept up to 1000 +points and 20 unknowns.) The model is: + +

+y = C1 +C2x +C3sinx +C4cosx +

+The test values for the four coefficients are +$C_1\!=\!+50.0$,$C_2\!=\!-2.0$,$C_3\!=\!-10.0$ and +$C_4\!=\!+25.0$.Gaussian noise, $\sigma=5.0$, is added to each ``observation''. +

+            IMPLICIT NONE
+
+      *  Sizes of arrays, physical and logical
+            INTEGER MP,NP,NC,M,N
+            PARAMETER (MP=1000,NP=10,NC=20,M=500,N=4)
+
+      *  The unknowns we are going to solve for
+            DOUBLE PRECISION C1,C2,C3,C4
+            PARAMETER (C1=50D0,C2=-2D0,C3=-10D0,C4=25D0)
+
+      *  Arrays
+            DOUBLE PRECISION A(MP,NP),W(NP),V(NP,NP),
+           :                 WORK(NP),B(MP),X(NP),CVM(NC,NC)
+
+            DOUBLE PRECISION VAL,BF1,BF2,BF3,BF4,SD2,D,VAR
+            REAL sla_GRESID
+            INTEGER I,J
+
+      *  Fill the design matrix
+            DO I=1,M
+
+      *     Dummy independent variable
+               VAL=DBLE(I)/10D0
+
+      *     The basis functions
+               BF1=1D0
+               BF2=VAL
+               BF3=SIN(VAL)
+               BF4=COS(VAL)
+
+      *     The observed value, including deliberate Gaussian noise
+               B(I)=C1*BF1+C2*BF2+C3*BF3+C4*BF4+DBLE(sla_GRESID(5.0))
+
+      *     Fill one row of the design matrix
+               A(I,1)=BF1
+               A(I,2)=BF2
+               A(I,3)=BF3
+               A(I,4)=BF4
+            END DO
+
+      *  Factorize the design matrix, solve and generate covariance matrix
+            CALL sla_SVD(M,N,MP,NP,A,W,V,WORK,J)
+            CALL sla_SVDSOL(M,N,MP,NP,B,A,W,V,WORK,X)
+            CALL sla_SVDCOV(N,NP,NC,W,V,WORK,CVM)
+
+      *  Compute the variance
+            SD2=0D0
+            DO I=1,M
+               VAL=DBLE(I)/10D0
+               BF1=1D0
+               BF2=VAL
+               BF3=SIN(VAL)
+               BF4=COS(VAL)
+               D=B(I)-(X(1)*BF1+X(2)*BF2+X(3)*BF3+X(4)*BF4)
+               SD2=SD2+D*D
+            END DO
+            VAR=SD2/DBLE(M)
+
+      *  Report the RMS and the solution
+            WRITE (*,'(1X,''RMS ='',F5.2/)') SQRT(VAR)
+            DO I=1,N
+               WRITE (*,'(1X,''C'',I1,'' ='',F7.3,'' +/-'',F6.3)')
+           :                                         I,X(I),SQRT(VAR*CVM(I,I))
+            END DO
+            END
+
+

+The program produces the following output: +

+            RMS = 4.88
+
+            C1 = 50.192 +/- 0.439
+            C2 = -2.002 +/- 0.015
+            C3 = -9.771 +/- 0.310
+            C4 = 25.275 +/- 0.310
+
+

+In this above example, essentially +identical results would be obtained if the more +commonplace normal-equations method had been used, and the large +$1000\times20$ array would have been avoided. However, the SVD method +comes into its own when the opportunity is taken to edit the W-matrix +(the so-called ``singular values'') in order to control +possible ill-conditioning. The procedure involves replacing with +zeroes any W-elements smaller than a nominated value, for example +0.001 times the largest W-element. Small W-elements indicate +ill-conditioning, which in the case of the normal-equations +method would produce spurious large coefficient values and +possible arithmetic overflows. Using SVD, the effect on the solution +of setting suspiciously small W-elements to zero is to restrain +the offending coefficients from moving very far. The +fact that action was taken can be reported to show the program user that +something is amiss. Furthermore, if element W(J) was set to zero, +the row numbers of the two biggest elements in the Jth column of the +V-matrix identify the pair of solution coefficients that are +dependent. +

+A more detailed description of SVD and its use in least-squares +problems would be out of place here, and the reader is urged +to refer to the relevant sections of the book Numerical Recipes +(Press et al., Cambridge University Press, 1987). +

+The routines +sla_COMBN +and +sla_PERMUT +are useful for problems which involve combinations (different subsets) +and permutations (different orders). +Both return the next in a sequence of results, cycling through all the +possible results as the routine is called repeatedly. +

+
+

+

+ +next + +up + +previous +
+ Next: SUMMARY OF CALLS +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Focal-Plane Astrometry +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node228.html b/src/slalib/sun67.htx/node228.html new file mode 100644 index 0000000..f21ae0e --- /dev/null +++ b/src/slalib/sun67.htx/node228.html @@ -0,0 +1,696 @@ + + + + +SUMMARY OF CALLS + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: About this document ... +
+Up: SLALIB Positional Astronomy Library +
+ Previous: Numerical Methods +

+

+

+SUMMARY OF CALLS +

+The basic trigonometrical and numerical facilities are supplied in both single +and double precision versions. +Most of the more esoteric position and time routines use double precision +arguments only, even in cases where single precision would normally be adequate +in practice. +Certain routines with modest accuracy objectives are supplied in +single precision versions only. +In the calling sequences which follow, no attempt has been made +to distinguish between single and double precision argument names, +and frequently the same name is used on different occasions to +mean different things. +However, none of the routines uses a mixture of single and +double precision arguments; each routine is either wholly +single precision or wholly double precision. +

+In the classified list, below, +subroutine subprograms are those whose names and argument lists +are preceded by `CALL', whereas function subprograms are +those beginning `R=' (when the result is REAL) or `D=' (when +the result is DOUBLE PRECISION). +

+The list is, of course, merely for quick reference; inexperienced +users must refer to the detailed specifications given later. +In particular, don't guess whether arguments are single or +double precision; the result could be a program that happens to +works on one sort of machine but not on another. +

+
String Decoding

+
Sexagesimal Conversions +
Angles, Vectors and Rotation Matrices +
Calendars +
Timescales +
Precession and Nutation +
Proper Motion +
FK4/FK5/Hipparcos Conversions +
Elliptic Aberration +
Geographical and Geocentric Coordinates +
Apparent and Observed Place +
Azimuth and Elevation +
Refraction and Air Mass +
Ecliptic Coordinates +
Galactic Coordinates +
Supergalactic Coordinates +
Ephemerides +
Astrometry +
Numerical Methods +
Real-time +
+ +next + +up + +previous +
+ Next: About this document ... +
+Up: SLALIB Positional Astronomy Library +
+ Previous: Numerical Methods +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node229.html b/src/slalib/sun67.htx/node229.html new file mode 100644 index 0000000..ac949b4 --- /dev/null +++ b/src/slalib/sun67.htx/node229.html @@ -0,0 +1,65 @@ + + + + +About this document ... + + + + + + + + + + +
+next + +up + +previous +
+Up: SLALIB Positional Astronomy Library +
+ Previous: SUMMARY OF CALLS +

+

+

+About this document ... +

+

+This document was generated using the +LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997) +

+Copyright © 1993, 1994, 1995, 1996, 1997, +Nikos Drakos, +Computer Based Learning Unit, University of Leeds. +

+The command line arguments were:
+ latex2html -init_file .star2html-init -no_subdir -no_auto_link /home/user1/dec/ptw/hypertext/sun67_htx//sun67.tex. +

+The translation was initiated by Pat Wallace on 10/12/1999 +

+next + +up + +previous +
+Up: SLALIB Positional Astronomy Library +
+ Previous: SUMMARY OF CALLS +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node23.html b/src/slalib/sun67.htx/node23.html new file mode 100644 index 0000000..dfb0e24 --- /dev/null +++ b/src/slalib/sun67.htx/node23.html @@ -0,0 +1,278 @@ + + + + +SLA_AOPQK - Quick Appt-to-Observed + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ATMDSP - Atmospheric Dispersion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOPPAT - Update Appt-to-Obs Parameters +

+

+

SLA_AOPQK - Quick Appt-to-Observed +   +

+
+
ACTION: +
Quick apparent to observed place (but see Note 8, below). +
CALL: +
CALL sla_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
RAP,DAPDgeocentric apparent $[\,\alpha,\delta\,]$ (radians)
AOPRMSD(14)star-independent apparent-to-observed parameters:
(1)geodetic latitude (radians)
(2,3)sine and cosine of geodetic latitude
(4)magnitude of diurnal aberration vector
(5)height (metres)
(6)ambient temperature (degrees K)
(7)pressure (mB)
(8)relative humidity (0-1)
(9)wavelength ($\mu{\rm m}$)
(10)lapse rate (degrees K per metre)
(11,12)refraction constants A and B (radians)
(13)longitude + eqn of equinoxes + +``sidereal $\Delta$UT'' (radians)
(14)local apparent sidereal time (radians)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
AOBDobserved azimuth (radians: N=0, E=$90^{\circ}$)
ZOBDobserved zenith distance (radians)
HOBDobserved Hour Angle (radians)
DOBDobserved Declination (radians)
ROBDobserved Right Ascension (radians)
+

+
NOTES: +
+
1. +
This routine returns zenith distance rather than elevation +in order to reflect the fact that no allowance is made for +depression of the horizon. +
2. +
The accuracy of the result is limited by the corrections for + refraction. Providing the meteorological parameters are + known accurately and there are no gross local effects, the + predicted azimuth and elevation should be within about +

$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ for $\zeta<70^{\circ}$. Even + at a topocentric zenith distance of + $90^{\circ}$, the accuracy in elevation should be better than + 1 arcminute; useful results are available for a further + $3^{\circ}$, beyond which the sla_REFRO routine returns a + fixed value of the refraction. The complementary + routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK) + are self-consistent to better than 1 microarcsecond all over + the celestial sphere. +

3. +
It is advisable to take great care with units, as even + unlikely values of the input parameters are accepted and + processed in accordance with the models used. +
4. +
Apparent $[\,\alpha,\delta\,]$ means the geocentric apparent right ascension + and declination, which is obtained from a catalogue mean place + by allowing for space motion, parallax, precession, nutation, + annual aberration, and the Sun's gravitational lens effect. For + star positions in the FK5 system (i.e. J2000), these effects can + be applied by means of the sla_MAP etc. routines. Starting from + other mean place systems, additional transformations will be + needed; for example, FK4 (i.e. B1950) mean places would first + have to be converted to FK5, which can be done with the + sla_FK425 etc. routines. +
5. +
Observed $[\,Az,El~]$ means the position that would be seen by a + perfect theodolite located at the observer. This is obtained + from the geocentric apparent $[\,\alpha,\delta\,]$ by allowing for Earth + orientation and diurnal aberration, rotating from equator + to horizon coordinates, and then adjusting for refraction. + The $[\,h,\delta\,]$ is obtained by rotating back into equatorial + coordinates, using the geodetic latitude corrected for polar + motion, and is the position that would be seen by a perfect + equatorial located at the observer and with its polar axis + aligned to the Earth's axis of rotation (n.b. not to the + refracted pole). Finally, the $\alpha$ is obtained by subtracting + the h from the local apparent ST. +
6. +
To predict the required setting of a real telescope, the + observed place produced by this routine would have to be + adjusted for the tilt of the azimuth or polar axis of the + mounting (with appropriate corrections for mount flexures), + for non-perpendicularity between the mounting axes, for the + position of the rotator axis and the pointing axis relative + to it, for tube flexure, for gear and encoder errors, and + finally for encoder zero points. Some telescopes would, of + course, exhibit other properties which would need to be + accounted for at the appropriate point in the sequence. +
7. +
The star-independent apparent-to-observed-place parameters + in AOPRMS may be computed by means of the sla_AOPPA routine. + If nothing has changed significantly except the time, the + sla_AOPPAT routine may be used to perform the requisite + partial recomputation of AOPRMS. +
8. +
The ``sidereal $\Delta$UT'' which forms part of AOPRMS(13) + is UT1-UTC converted from solar to + sidereal seconds and expressed in radians. +
9. +
At zenith distances beyond about $76^\circ$, the need for + special care with the corrections for refraction causes a + marked increase in execution time. Moreover, the effect + gets worse with increasing zenith distance. Adroit + programming in the calling application may allow the + problem to be reduced. Prepare an alternative AOPRMS array, + computed for zero air-pressure; this will disable the + refraction corrections and cause rapid execution. Using + this AOPRMS array, a preliminary call to the present routine + will, depending on the application, produce a rough position + which may be enough to establish whether the full, slow + calculation (using the real AOPRMS array) is worthwhile. + For example, there would be no need for the full calculation + if the preliminary call had already established that the + source was well below the elevation limits for a particular + telescope. +
10. +
The azimuths etc. used by the present routine are with + respect to the celestial pole. Corrections to the terrestrial pole + can be computed using sla_POLMO. +
+
+ +next + +up + +previous +
+ Next: SLA_ATMDSP - Atmospheric Dispersion +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOPPAT - Update Appt-to-Obs Parameters +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node24.html b/src/slalib/sun67.htx/node24.html new file mode 100644 index 0000000..aecbb98 --- /dev/null +++ b/src/slalib/sun67.htx/node24.html @@ -0,0 +1,213 @@ + + + + +SLA_ATMDSP - Atmospheric Dispersion + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_AV2M - Rotation Matrix from Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOPQK - Quick Appt-to-Observed +

+

+

SLA_ATMDSP - Atmospheric Dispersion +   +

+
+
ACTION: +
Apply atmospheric-dispersion adjustments to refraction coefficients. +
CALL: +
CALL sla_ATMDSP (TDK, PMB, RH, WL1, A1, B1, WL2, A2, B2) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
TDKDambient temperature at the observer (degrees K)
PMBDpressure at the observer (mB)
RHDrelative humidity at the observer (range 0-1)
WL1Dbase wavelength ($\mu{\rm m}$)
A1Drefraction coefficient A for wavelength WL1 (radians)
B1Drefraction coefficient B for wavelength WL1 (radians)
WL2Dwavelength for which adjusted A,B required ($\mu{\rm m}$)
+

+
RETURNED: +
+
+ + + + + + + + + +
A2Drefraction coefficient A for wavelength WL2 (radians)
B2Drefraction coefficient B for wavelength WL2 (radians)
+

+
NOTES: +
+
1. +
To use this routine, first call sla_REFCO specifying WL1 as the +wavelength. This yields refraction coefficients A1, B1, correct +for that wavelength. Subsequently, calls to sla_ATMDSP specifying + different wavelengths will produce new, slightly adjusted + refraction coefficients A2, B2, which apply to the specified wavelength. +
2. +
Most of the atmospheric dispersion happens between $0.7\,\mu{\rm m}$ and the UV atmospheric cutoff, and the effect increases strongly + towards the UV end. For this reason a blue reference wavelength + is recommended, for example $0.4\,\mu{\rm m}$.
3. +
The accuracy, for this set of conditions:
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
height above sea level 2000m
latitude $29^\circ$
pressure 793mB
temperature $290^\circ$K
humidity 0.5 (50%)
lapse rate $0.0065^\circ m^{-1}$
reference wavelength $0.4\,\mu{\rm m}$
star elevation $15^\circ$
+
+
+is about 2.5mas RMS between 0.3 and $1.0\,\mu{\rm m}$, and stays + within 4mas for the whole range longward of $0.3\,\mu{\rm m}$ (compared with a total dispersion from 0.3 to $20\,\mu{\rm m}$ of about $11\hspace{-0.05em}^{'\hspace{-0.1em}'}$). These errors are typical for ordinary + conditions; in extreme conditions values a few times this size + may occur. +
4. +
If either wavelength exceeds $100\,\mu{\rm m}$, the radio case + is assumed and the returned refraction coefficients are the + same as the given ones. +
5. +
The algorithm consists of calculation of the refractivity of the + air at the observer for the two wavelengths, using the methods + of the sla_REFRO routine, and then scaling of the two refraction + coefficients according to classical refraction theory. This + amounts to scaling the A coefficient in proportion to $(\mu-1)$ and + the B coefficient almost in the same ratio (see R.M.Green, + Spherical Astronomy, Cambridge University Press, 1985). +
+
+ +next + +up + +previous +
+ Next: SLA_AV2M - Rotation Matrix from Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AOPQK - Quick Appt-to-Observed +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node25.html b/src/slalib/sun67.htx/node25.html new file mode 100644 index 0000000..f557394 --- /dev/null +++ b/src/slalib/sun67.htx/node25.html @@ -0,0 +1,103 @@ + + + + +SLA_AV2M - Rotation Matrix from Axial Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_BEAR - Direction Between Points on a Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ATMDSP - Atmospheric Dispersion +

+

+

SLA_AV2M - Rotation Matrix from Axial Vector +   +

+
+
ACTION: +
Form the rotation matrix corresponding to a given axial vector +(single precision). +

CALL: +
CALL sla_AV2M (AXVEC, RMAT) +

+

+
GIVEN: +
+
+ + + + + +
AXVECR(3)axial vector (radians)
+

+
RETURNED: +
+
+ + + + + +
RMATR(3,3)rotation matrix
+

+
NOTES: +
+
1. +
A rotation matrix describes a rotation about some arbitrary axis. +The axis is called the Euler axis, and the angle through which the +reference frame rotates is called the Euler angle. The axial + vector supplied to this routine has the same direction as the + Euler axis, and its magnitude is the Euler angle in radians. +
2. +
If AXVEC is null, the unit matrix is returned. +
3. +
The reference frame rotates clockwise as seen looking along + the axial vector from the origin. +
+
+ +next + +up + +previous +
+ Next: SLA_BEAR - Direction Between Points on a Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ATMDSP - Atmospheric Dispersion +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node26.html b/src/slalib/sun67.htx/node26.html new file mode 100644 index 0000000..8296b32 --- /dev/null +++ b/src/slalib/sun67.htx/node26.html @@ -0,0 +1,123 @@ + + + + +SLA_BEAR - Direction Between Points on a Sphere + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CAF2R - Deg,Arcmin,Arcsec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AV2M - Rotation Matrix from Axial Vector +

+

+

SLA_BEAR - Direction Between Points on a Sphere +   +

+
+
ACTION: +
Returns the bearing (position angle) of one point on a +sphere seen from another (single precision). +

CALL: +
R = sla_BEAR (A1, B1, A2, B2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
A1,B1Rspherical coordinates of one point
A2,B2Rspherical coordinates of the other point
+

+
RETURNED: +
+
+ + + + + +
sla_BEARRbearing from first point to second
+

+
NOTES: +
+
1. +
The spherical coordinates are $[\,\alpha,\delta\,]$,$[\lambda,\phi]$ etc., in radians. +
2. +
The result is the bearing (position angle), in radians, + of point [A2,B2] as seen + from point [A1,B1]. It is in the range $\pm \pi$. The sense + is such that if [A2,B2] + is a small distance due east of [A1,B1] the result + is about $+\pi/2$. Zero is returned + if the two points are coincident. +
3. +
If either B-coordinate is outside the range $\pm\pi/2$, the + result may correspond to ``the long way round''. +
4. +
The routine sla_PAV performs an equivalent function except + that the points are specified in the form of Cartesian unit + vectors. +
+
+ +next + +up + +previous +
+ Next: SLA_CAF2R - Deg,Arcmin,Arcsec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_AV2M - Rotation Matrix from Axial Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node27.html b/src/slalib/sun67.htx/node27.html new file mode 100644 index 0000000..6c176b5 --- /dev/null +++ b/src/slalib/sun67.htx/node27.html @@ -0,0 +1,122 @@ + + + + +SLA_CAF2R - Deg,Arcmin,Arcsec to Radians + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CALDJ - Calendar Date to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_BEAR - Direction Between Points on a Sphere +

+

+

SLA_CAF2R - Deg,Arcmin,Arcsec to Radians +   +

+
+
ACTION: +
Convert degrees, arcminutes, arcseconds to radians +(single precision). +

CALL: +
CALL sla_CAF2R (IDEG, IAMIN, ASEC, RAD, J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IDEGIdegrees
IAMINIarcminutes
ASECRarcseconds
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
RADRangle in radians
JIstatus:
1 = IDEG outside range 0-359
2 = IAMIN outside range 0-59
3 = ASEC outside range 0-59.999$\cdots$
+

+
NOTES: +
+
1. +
The result is computed even if any of the range checks fail. +
2. +
The sign must be dealt with outside this routine. +
+
+ +next + +up + +previous +
+ Next: SLA_CALDJ - Calendar Date to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_BEAR - Direction Between Points on a Sphere +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node28.html b/src/slalib/sun67.htx/node28.html new file mode 100644 index 0000000..33bc93d --- /dev/null +++ b/src/slalib/sun67.htx/node28.html @@ -0,0 +1,128 @@ + + + + +SLA_CALDJ - Calendar Date to MJD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CALYD - Calendar to Year, Day +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CAF2R - Deg,Arcmin,Arcsec to Radians +

+

+

SLA_CALDJ - Calendar Date to MJD +   +

+
+
ACTION: +
Gregorian Calendar to Modified Julian Date, with century default. +
CALL: +
CALL sla_CALDJ (IY, IM, ID, DJM, J) +

+

+
GIVEN: +
+
+ + + + + +
IY,IM,IDIyear, month, day in Gregorian calendar
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
DJMDmodified Julian Date (JD-2400000.5) for $0^{\rm h}$
JIstatus:
0 = OK
1 = bad year (MJD not computed)
2 = bad month (MJD not computed)
3 = bad day (MJD computed)
+

+
NOTES: +
+
1. +
This routine supports the century default feature. +Acceptable years are: +
    +
  • 00-49, interpreted as 2000-2049, +
  • 50-99, interpreted as 1950-1999, and +
  • 100 upwards, interpreted literally. +
+ For 1-100AD use the routine sla_CLDJ instead. +
2. +
For year nBC use IY = -(n-1). +
3. +
When an invalid year or month is supplied (status J = 1 or 2) + the MJD is not computed. When an invalid day is supplied + (status J = 3) the MJD is computed. +
+
+ +next + +up + +previous +
+ Next: SLA_CALYD - Calendar to Year, Day +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CAF2R - Deg,Arcmin,Arcsec to Radians +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node29.html b/src/slalib/sun67.htx/node29.html new file mode 100644 index 0000000..f831e5a --- /dev/null +++ b/src/slalib/sun67.htx/node29.html @@ -0,0 +1,140 @@ + + + + +SLA_CALYD - Calendar to Year, Day + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CC2S - Cartesian to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CALDJ - Calendar Date to MJD +

+

+

SLA_CALYD - Calendar to Year, Day +   +

+
+
ACTION: +
Gregorian calendar date to year and day in year, in a Julian +calendar aligned to the 20th/21st century Gregorian calendar, + with century default. +

CALL: +
CALL sla_CALYD (IY, IM, ID, NY, ND, J) +

+

+
GIVEN: +
+
+ + + + + +
IY,IM,IDIyear, month, day in Gregorian calendar: +year may optionally omit the century
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NYIyear (re-aligned Julian calendar)
NDIday in year (1 = January 1st)
JIstatus:
0 = OK
1 = bad year (before -4711)
2 = bad month
3 = bad day
+

+
NOTES: +
+
1. +
This routine supports the century default feature. +Acceptable years are: +
    +
  • 00-49, interpreted as 2000-2049, +
  • 50-99, interpreted as 1950-1999, and +
  • other years after -4712 , interpreted literally. +
+ Use sla_CLYD for years before 100AD. +
2. +
The purpose of sla_CALDJ is to support + sla_EARTH, sla_MOON and sla_ECOR. +
3. +
Between 1900 March 1 and 2100 February 28 it returns answers + which are consistent with the ordinary Gregorian calendar. + Outside this range there will be a discrepancy which increases + by one day for every non-leap century year. +
4. +
When an invalid year or month is supplied (status J = 1 or J = 2) + the results are not computed. When a day is + supplied which is outside the conventional range (status J = 3) + the results are computed. +
+
+ +next + +up + +previous +
+ Next: SLA_CC2S - Cartesian to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CALDJ - Calendar Date to MJD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node3.html b/src/slalib/sun67.htx/node3.html new file mode 100644 index 0000000..886a149 --- /dev/null +++ b/src/slalib/sun67.htx/node3.html @@ -0,0 +1,76 @@ + + + + +Purpose + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Example Application +
+Up: INTRODUCTION +
+ Previous: INTRODUCTION +

+

+

+Purpose +

+SLALIB[*] +is a library of routines +intended to make accurate and reliable positional-astronomy +applications easier to write. +Most SLALIB routines are concerned with astronomical position and time, but a +number have wider trigonometrical, numerical or general applications. +The applications ASTROM, COCO, RV and TPOINT +all make extensive use of the SLALIB +routines, as do a number of telescope control systems around the world. +The SLALIB versions currently in service are written in +Fortran 77 and run on VAX/VMS, several Unix platforms and PC. +A generic ANSI C version is also available from the author; it is +functionally similar to the Fortran version upon which the present +document concentrates. +

+

+ +next + +up + +previous +
+ Next: Example Application +
+Up: INTRODUCTION +
+ Previous: INTRODUCTION +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node30.html b/src/slalib/sun67.htx/node30.html new file mode 100644 index 0000000..21b121e --- /dev/null +++ b/src/slalib/sun67.htx/node30.html @@ -0,0 +1,103 @@ + + + + +SLA_CC2S - Cartesian to Spherical + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CC62S - Cartesian 6-Vector to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CALYD - Calendar to Year, Day +

+

+

SLA_CC2S - Cartesian to Spherical +   +

+
+
ACTION: +
Cartesian coordinates to spherical coordinates (single precision). +
CALL: +
CALL sla_CC2S (V, A, B) +

+

+
GIVEN: +
+
+ + + + + +
VR(3)$[\,x,y,z\,]$ vector
+

+
RETURNED: +
+
+ + + + + +
A,BRspherical coordinates in radians
+

+
NOTES: +
+
1. +
The spherical coordinates are longitude (+ve anticlockwise +looking from the +ve latitude pole) and latitude. The +Cartesian coordinates are right handed, with the x-axis + at zero longitude and latitude, and the z-axis at the + +ve latitude pole. +
2. +
If V is null, zero A and B are returned. +
3. +
At either pole, zero A is returned. +
+
+ +next + +up + +previous +
+ Next: SLA_CC62S - Cartesian 6-Vector to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CALYD - Calendar to Year, Day +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node31.html b/src/slalib/sun67.htx/node31.html new file mode 100644 index 0000000..1877958 --- /dev/null +++ b/src/slalib/sun67.htx/node31.html @@ -0,0 +1,114 @@ + + + + +SLA_CC62S - Cartesian 6-Vector to Spherical + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CD2TF - Days to Hour,Min,Sec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CC2S - Cartesian to Spherical +

+

+

SLA_CC62S - Cartesian 6-Vector to Spherical +   +

+
+
ACTION: +
Conversion of position & velocity in Cartesian coordinates +to spherical coordinates (single precision). +

CALL: +
CALL sla_CC62S (V, A, B, R, AD, BD, RD) +

+

+
GIVEN: +
+
+ + + + + +
VR(6)$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
ARlongitude (radians) - for example $\alpha$
BRlatitude (radians) - for example $\delta$
RRradial coordinate
ADRlongitude derivative (radians per unit time)
BDRlatitude derivative (radians per unit time)
RDRradial derivative
+
+ +next + +up + +previous +
+ Next: SLA_CD2TF - Days to Hour,Min,Sec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CC2S - Cartesian to Spherical +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node32.html b/src/slalib/sun67.htx/node32.html new file mode 100644 index 0000000..9d7f8ab --- /dev/null +++ b/src/slalib/sun67.htx/node32.html @@ -0,0 +1,115 @@ + + + + +SLA_CD2TF - Days to Hour,Min,Sec + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CLDJ - Calendar to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CC62S - Cartesian 6-Vector to Spherical +

+

+

SLA_CD2TF - Days to Hour,Min,Sec +   +

+
+
ACTION: +
Convert an interval in days to hours, minutes, seconds +(single precision). +

CALL: +
CALL sla_CD2TF (NDP, DAYS, SIGN, IHMSF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of seconds
DAYSRinterval in days
+

+
RETURNED: +
+
+ + + + + + + + + +
SIGNC`+' or `-'
IHMSFI(4)hours, minutes, seconds, fraction
+

+
NOTES: +
+
1. +
NDP less than zero is interpreted as zero. +
2. +
The largest useful value for NDP is determined by the size of +DAYS, the format of REAL floating-point numbers on the target + machine, and the risk of overflowing IHMSF(4). For example, + on a VAX computer, for DAYS up to 1.0, the available floating-point + precision corresponds roughly to NDP=3. This is well below + the ultimate limit of NDP=9 set by the capacity of the 32-bit + integer IHMSF(4). +
3. +
The absolute value of DAYS may exceed 1.0. In cases where it + does not, it is up to the caller to test for and handle the + case where DAYS is very nearly 1.0 and rounds up to 24 hours, + by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero. +
+
+ +next + +up + +previous +
+ Next: SLA_CLDJ - Calendar to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CC62S - Cartesian 6-Vector to Spherical +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node33.html b/src/slalib/sun67.htx/node33.html new file mode 100644 index 0000000..556eb23 --- /dev/null +++ b/src/slalib/sun67.htx/node33.html @@ -0,0 +1,128 @@ + + + + +SLA_CLDJ - Calendar to MJD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CLYD - Calendar to Year, Day +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CD2TF - Days to Hour,Min,Sec +

+

+

SLA_CLDJ - Calendar to MJD +   +

+
+
ACTION: +
Gregorian Calendar to Modified Julian Date. +
CALL: +
CALL sla_CLDJ (IY, IM, ID, DJM, J) +

+

+
GIVEN: +
+
+ + + + + +
IY,IM,IDIyear, month, day in Gregorian calendar
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
DJMDmodified Julian Date (JD-2400000.5) for $0^{\rm h}$
JIstatus:
0 = OK
1 = bad year
2 = bad month
3 = bad day
+

+
NOTES: +
+
1. +
When an invalid year or month is supplied (status J = 1 or 2) +the MJD is not computed. When an invalid day is supplied +(status J = 3) the MJD is computed. +
2. +
The year must be -4699 (i.e. 4700BC) or later. + For year nBC use IY = -(n-1). +
3. +
An alternative to the present routine is sla_CALDJ, which + accepts a year with the century missing. +
+

+
REFERENCE: +
The algorithm is derived from that of Hatcher, +Q.Jl.R.astr.Soc. (1984) 25, 53-55. +
+
+ +next + +up + +previous +
+ Next: SLA_CLYD - Calendar to Year, Day +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CD2TF - Days to Hour,Min,Sec +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node34.html b/src/slalib/sun67.htx/node34.html new file mode 100644 index 0000000..266f38a --- /dev/null +++ b/src/slalib/sun67.htx/node34.html @@ -0,0 +1,129 @@ + + + + +SLA_CLYD - Calendar to Year, Day + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_COMBN - Next Combination +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CLDJ - Calendar to MJD +

+

+

SLA_CLYD - Calendar to Year, Day +   +

+
+
ACTION: +
Gregorian calendar date to year and day in year, in a Julian +calendar aligned to the 20th/21st century Gregorian calendar. +

CALL: +
CALL sla_CLYD (IY, IM, ID, NY, ND, J) +

+

+
GIVEN: +
+
+ + + + + +
IY,IM,IDIyear, month, day in Gregorian calendar
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NYIyear (re-aligned Julian calendar)
NDIday in year (1 = January 1st)
JIstatus:
0 = OK
1 = bad year (before -4711)
2 = bad month
3 = bad day
+

+
NOTES: +
+
1. +
The purpose of sla_CLYD is to support sla_EARTH, +sla_MOON and sla_ECOR. +
2. +
Between 1900 March 1 and 2100 February 28 it returns answers + which are consistent with the ordinary Gregorian calendar. + Outside this range there will be a discrepancy which increases + by one day for every non-leap century year. +
3. +
When an invalid year or month is supplied (status J = 1 or J = 2) + the results are not computed. When a day is + supplied which is outside the conventional range (status J = 3) + the results are computed. +
+
+ +next + +up + +previous +
+ Next: SLA_COMBN - Next Combination +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CLDJ - Calendar to MJD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node35.html b/src/slalib/sun67.htx/node35.html new file mode 100644 index 0000000..8723385 --- /dev/null +++ b/src/slalib/sun67.htx/node35.html @@ -0,0 +1,142 @@ + + + + +SLA_COMBN - Next Combination + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CR2AF - Radians to Deg,Arcmin,Arcsec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CLYD - Calendar to Year, Day +

+

+

SLA_COMBN - Next Combination +   +

+
+
ACTION: +
Generate the next combination, a subset of a specified size chosen +from a specified number of items. +

CALL: +
CALL sla_COMBN (NSEL, NCAND, LIST, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NSELInumber of items (subset size)
NCANDInumber of candidates (set size)
+

+
GIVEN and RETURNED: +
+
+ + + + + +
LISTI(NSEL)latest combination, LIST(1)=0 to initialize
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + +
JIstatus:
-1 = illegal NSEL or NCAND
0 = OK
+1 = no more combinations available
+

+
NOTES: +
+
1. +
NSEL and NCAND must both be at least 1, and NSEL must be less +than or equal to NCAND. +
2. +
This routine returns, in the LIST array, a subset of NSEL integers + chosen from the range 1 to NCAND inclusive, in ascending order. + Before calling the routine for the first time, the caller must set + the first element of the LIST array to zero (any value less than 1 + will do) to cause initialization. +
3. +
The first combination to be generated is: +
LIST(1)=1, LIST(2)=2, ..., LIST(NSEL)=NSEL +
+ This is also the combination returned for the ``finished'' (J=1) case. + The final permutation to be generated is: +
LIST(1)=NCAND, LIST(2)=NCAND-1, ...,
+                                LIST(NSEL)=NCAND-NSEL+1 +
+
4. +
If the ``finished'' (J=1) status is ignored, the routine + continues to deliver combinations, the pattern repeating + every NCAND!/(NSEL!(NCAND-NSEL)!) calls. +
5. +
The algorithm is by R.F.Warren-Smith (private communication). +
+
+ +next + +up + +previous +
+ Next: SLA_CR2AF - Radians to Deg,Arcmin,Arcsec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CLYD - Calendar to Year, Day +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node36.html b/src/slalib/sun67.htx/node36.html new file mode 100644 index 0000000..0932642 --- /dev/null +++ b/src/slalib/sun67.htx/node36.html @@ -0,0 +1,122 @@ + + + + +SLA_CR2AF - Radians to Deg,Arcmin,Arcsec + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CR2TF - Radians to Hour,Min,Sec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_COMBN - Next Combination +

+

+

SLA_CR2AF - Radians to Deg,Arcmin,Arcsec +   +

+
+
ACTION: +
Convert an angle in radians to degrees, arcminutes, +arcseconds (single precision). +

CALL: +
CALL sla_CR2AF (NDP, ANGLE, SIGN, IDMSF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of arcseconds
ANGLERangle in radians
+

+
RETURNED: +
+
+ + + + + + + + + +
SIGNC`+' or `-'
IDMSFI(4)degrees, arcminutes, arcseconds, fraction
+

+
NOTES: +
+
1. +
NDP less than zero is interpreted as zero. +
2. +
The largest useful value for NDP is determined by the size of +ANGLE, the format of REAL floating-point numbers on the target + machine, and the risk of overflowing IDMSF(4). For example, + on a VAX computer, for ANGLE up to $2\pi$, the available floating-point + precision corresponds roughly to NDP=3. This is well below + the ultimate limit of NDP=9 set by the capacity of the 32-bit + integer IHMSF(4). +
3. +
The absolute value of ANGLE may exceed $2\pi$. In cases where it + does not, it is up to the caller to test for and handle the + case where ANGLE is very nearly $2\pi$ and rounds up to $360^{\circ}$, by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero. +
+
+ +next + +up + +previous +
+ Next: SLA_CR2TF - Radians to Hour,Min,Sec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_COMBN - Next Combination +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node37.html b/src/slalib/sun67.htx/node37.html new file mode 100644 index 0000000..cd25af4 --- /dev/null +++ b/src/slalib/sun67.htx/node37.html @@ -0,0 +1,121 @@ + + + + +SLA_CR2TF - Radians to Hour,Min,Sec + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CS2C - Spherical to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CR2AF - Radians to Deg,Arcmin,Arcsec +

+

+

SLA_CR2TF - Radians to Hour,Min,Sec +   +

+
+
ACTION: +
Convert an angle in radians to hours, minutes, seconds +(single precision). +

CALL: +
CALL sla_CR2TF (NDP, ANGLE, SIGN, IHMSF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of seconds
ANGLERangle in radians
+

+
RETURNED: +
+
+ + + + + + + + + +
SIGNC`+' or `-'
IHMSFI(4)hours, minutes, seconds, fraction
+

+
NOTES: +
+
1. +
NDP less than zero is interpreted as zero. +
2. +
The largest useful value for NDP is determined by the size of +ANGLE, the format of REAL floating-point numbers on the target + machine, and the risk of overflowing IHMSF(4). For example, + on a VAX computer, for ANGLE up to $2\pi$, the available floating-point + precision corresponds roughly to NDP=3. This is well below + the ultimate limit of NDP=9 set by the capacity of the 32-bit + integer IHMSF(4). +
3. +
The absolute value of ANGLE may exceed $2\pi$. In cases where it + does not, it is up to the caller to test for and handle the + case where ANGLE is very nearly $2\pi$ and rounds up to 24 hours, + by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero. +
+
+ +next + +up + +previous +
+ Next: SLA_CS2C - Spherical to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CR2AF - Radians to Deg,Arcmin,Arcsec +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node38.html b/src/slalib/sun67.htx/node38.html new file mode 100644 index 0000000..93d4f63 --- /dev/null +++ b/src/slalib/sun67.htx/node38.html @@ -0,0 +1,99 @@ + + + + +SLA_CS2C - Spherical to Cartesian + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CS2C6 - Spherical Pos/Vel to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CR2TF - Radians to Hour,Min,Sec +

+

+

SLA_CS2C - Spherical to Cartesian +   +

+
+
ACTION: +
Spherical coordinates to Cartesian coordinates (single precision). +
CALL: +
CALL sla_CS2C (A, B, V) +

+

+
GIVEN: +
+
+ + + + + +
A,BRspherical coordinates in radians: $[\,\alpha,\delta\,]$ etc.
+

+
RETURNED: +
+
+ + + + + +
VR(3)$[\,x,y,z\,]$ unit vector
+

+
NOTE: +
The spherical coordinates are longitude (+ve anticlockwise +looking from the +ve latitude pole) and latitude. The + Cartesian coordinates are right handed, with the x-axis + at zero longitude and latitude, and the z-axis at the + +ve latitude pole. +
+
+ +next + +up + +previous +
+ Next: SLA_CS2C6 - Spherical Pos/Vel to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CR2TF - Radians to Hour,Min,Sec +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node39.html b/src/slalib/sun67.htx/node39.html new file mode 100644 index 0000000..51bbf4f --- /dev/null +++ b/src/slalib/sun67.htx/node39.html @@ -0,0 +1,114 @@ + + + + +SLA_CS2C6 - Spherical Pos/Vel to Cartesian + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CTF2D - Hour,Min,Sec to Days +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CS2C - Spherical to Cartesian +

+

+

SLA_CS2C6 - Spherical Pos/Vel to Cartesian +   +

+
+
ACTION: +
Conversion of position & velocity in spherical coordinates +to Cartesian coordinates (single precision). +

CALL: +
CALL sla_CS2C6 (A, B, R, AD, BD, RD, V) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
ARlongitude (radians) - for example $\alpha$
BRlatitude (radians) - for example $\delta$
RRradial coordinate
ADRlongitude derivative (radians per unit time)
BDRlatitude derivative (radians per unit time)
RDRradial derivative
+

+
RETURNED: +
+
+ + + + + +
VR(6)$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$
+
+ +next + +up + +previous +
+ Next: SLA_CTF2D - Hour,Min,Sec to Days +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CS2C - Spherical to Cartesian +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node4.html b/src/slalib/sun67.htx/node4.html new file mode 100644 index 0000000..81c9586 --- /dev/null +++ b/src/slalib/sun67.htx/node4.html @@ -0,0 +1,131 @@ + + + + +Example Application + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Scope +
+Up: INTRODUCTION +
+ Previous: Purpose +

+

+

+Example Application +

+Here is a simple example of an application program written +using SLALIB calls: +

+         PROGRAM FK4FK5
+   *
+   *  Read a B1950 position from I/O unit 5 and reply on I/O unit 6
+   *  with the J2000 equivalent.  Enter a period to quit.
+   *
+         IMPLICIT NONE
+         CHARACTER C*80,S
+         INTEGER I,J,IHMSF(4),IDMSF(4)
+         DOUBLE PRECISION R4,D4,R5,D5
+         LOGICAL BAD
+
+   *   Loop until a period is entered
+         C = ' '
+         DO WHILE (C(:1).NE.'.')
+
+   *     Read h m s d ' "
+            READ (5,'(A)') C
+            IF (C(:1).NE.'.') THEN
+               BAD = .TRUE.
+
+   *        Decode the RA
+               I = 1
+               CALL sla_DAFIN(C,I,R4,J)
+               IF (J.EQ.0) THEN
+                  R4 = 15D0*R4
+
+   *           Decode the Dec
+                  CALL sla_DAFIN(C,I,D4,J)
+                  IF (J.EQ.0) THEN
+
+   *              FK4 to FK5
+                     CALL sla_FK45Z(R4,D4,1950D0,R5,D5)
+
+   *              Format and output the result
+                     CALL sla_DR2TF(2,R5,S,IHMSF)
+                     CALL sla_DR2AF(1,D5,S,IDMSF)
+                     WRITE (6,
+        :       '(1X,I2.2,2I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1)')
+        :                                                     IHMSF,S,IDMSF
+                     BAD = .FALSE.
+                  END IF
+               END IF
+               IF (BAD) WRITE (6,'(1X,''?'')')
+            END IF
+         END DO
+
+         END
+
+In this example, SLALIB not only provides the complicated FK4 to +FK5 transformation but also +simplifies the tedious and error-prone tasks +of decoding and formatting angles +expressed as hours, minutes etc. The +example incorporates range checking, and avoids the +notorious ``minus zero'' problem (an often-perpetrated bug where +declinations between $0^{\circ}$ and $-1^{\circ}$ lose their minus +sign). +With a little extra elaboration and a few more calls to SLALIB, +defaulting can be provided (enabling unused fields to +be replaced with commas to avoid retyping), proper motions +can be handled, different epochs can be specified, and +so on. See the program COCO (SUN/56) for further ideas. +

+

+ +next + +up + +previous +
+ Next: Scope +
+Up: INTRODUCTION +
+ Previous: Purpose +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node40.html b/src/slalib/sun67.htx/node40.html new file mode 100644 index 0000000..438541e --- /dev/null +++ b/src/slalib/sun67.htx/node40.html @@ -0,0 +1,125 @@ + + + + +SLA_CTF2D - Hour,Min,Sec to Days + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_CTF2R - Hour,Min,Sec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CS2C6 - Spherical Pos/Vel to Cartesian +

+

+

SLA_CTF2D - Hour,Min,Sec to Days +   +

+
+
ACTION: +
Convert hours, minutes, seconds to days (single precision). +
CALL: +
CALL sla_CTF2D (IHOUR, IMIN, SEC, DAYS, J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IHOURIhours
IMINIminutes
SECRseconds
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
DAYSRinterval in days
JIstatus:
0 = OK
1 = IHOUR outside range 0-23
2 = IMIN outside range 0-59
3 = SEC outside range 0-59.999$\cdots$
+

+
NOTES: +
+
1. +
The result is computed even if any of the range checks fail. +
2. +
The sign must be dealt with outside this routine. +
+
+ +next + +up + +previous +
+ Next: SLA_CTF2R - Hour,Min,Sec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CS2C6 - Spherical Pos/Vel to Cartesian +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node41.html b/src/slalib/sun67.htx/node41.html new file mode 100644 index 0000000..bf3cf62 --- /dev/null +++ b/src/slalib/sun67.htx/node41.html @@ -0,0 +1,125 @@ + + + + +SLA_CTF2R - Hour,Min,Sec to Radians + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DAF2R - Deg,Arcmin,Arcsec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CTF2D - Hour,Min,Sec to Days +

+

+

SLA_CTF2R - Hour,Min,Sec to Radians +   +

+
+
ACTION: +
Convert hours, minutes, seconds to radians (single precision). +
CALL: +
CALL sla_CTF2R (IHOUR, IMIN, SEC, RAD, J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IHOURIhours
IMINIminutes
SECRseconds
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
RADRangle in radians
JIstatus:
0 = OK
1 = IHOUR outside range 0-23
2 = IMIN outside range 0-59
3 = SEC outside range 0-59.999$\cdots$
+

+
NOTES: +
+
1. +
The result is computed even if any of the range checks fail. +
2. +
The sign must be dealt with outside this routine. +
+
+ +next + +up + +previous +
+ Next: SLA_DAF2R - Deg,Arcmin,Arcsec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CTF2D - Hour,Min,Sec to Days +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node42.html b/src/slalib/sun67.htx/node42.html new file mode 100644 index 0000000..faed2a4 --- /dev/null +++ b/src/slalib/sun67.htx/node42.html @@ -0,0 +1,122 @@ + + + + +SLA_DAF2R - Deg,Arcmin,Arcsec to Radians + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DAFIN - Sexagesimal character string to angle +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CTF2R - Hour,Min,Sec to Radians +

+

+

SLA_DAF2R - Deg,Arcmin,Arcsec to Radians +   +

+
+
ACTION: +
Convert degrees, arcminutes, arcseconds to radians +(double precision). +

CALL: +
CALL sla_DAF2R (IDEG, IAMIN, ASEC, RAD, J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IDEGIdegrees
IAMINIarcminutes
ASECDarcseconds
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
RADDangle in radians
JIstatus:
1 = IDEG outside range 0-359
2 = IAMIN outside range 0-59
3 = ASEC outside range 0-59.999$\cdots$
+

+
NOTES: +
+
1. +
The result is computed even if any of the range checks fail. +
2. +
The sign must be dealt with outside this routine. +
+
+ +next + +up + +previous +
+ Next: SLA_DAFIN - Sexagesimal character string to angle +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_CTF2R - Hour,Min,Sec to Radians +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node43.html b/src/slalib/sun67.htx/node43.html new file mode 100644 index 0000000..8559153 --- /dev/null +++ b/src/slalib/sun67.htx/node43.html @@ -0,0 +1,229 @@ + + + + +SLA_DAFIN - Sexagesimal character string to angle + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DAT - TAI-UTC +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAF2R - Deg,Arcmin,Arcsec to Radians +

+

+

SLA_DAFIN - Sexagesimal character string to angle +   +

+
+
ACTION: +
Decode a free-format sexagesimal string (degrees, arcminutes, +arcseconds) into a double precision floating point + number (radians). +

CALL: +
CALL sla_DAFIN (STRING, NSTRT, DRESLT, JF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
STRINGC*(*)string containing deg, arcmin, arcsec fields
NSTRTIpointer to start of decode (beginning of STRING = 1)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NSTRTIadvanced past the decoded angle
DRESLTDangle in radians
JFIstatus:
0 = OK
+1 = default, DRESLT unchanged (note 2)
-1 = bad degrees (note 3)
-2 = bad arcminutes (note 3)
-3 = bad arcseconds (note 3)
+

+
EXAMPLE +
:
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
argumentbeforeafter
   
STRING'-57 17 44.806 12 34 56.7'unchanged
NSTRT116 (i.e. pointing to 12...)
RESLT--1.00000D0
JF- 
+
A further call to sla_DAFIN, without adjustment of NSTRT, will + decode the second angle, $12^{\circ}\,34^{'}\,56^{''}.7$.
+

+
NOTES: +
+
1. +
The first three ``fields'' in STRING are degrees, arcminutes, +arcseconds, separated by spaces or commas. The degrees field +may be signed, but not the others. The decoding is carried + out by the sla_DFLTIN routine and is free-format. +
2. +
Successive fields may be absent, defaulting to zero. For + zero status, the only combinations allowed are degrees alone, + degrees and arcminutes, and all three fields present. If all + three fields are omitted, a status of +1 is returned and DRESLT is + unchanged. In all other cases DRESLT is changed. +
3. +
Range checking: +
    +
  • The degrees field is not range checked. However, it is + expected to be integral unless the other two fields are absent. +
  • The arcminutes field is expected to be 0-59, and integral if + the arcseconds field is present. If the arcseconds field + is absent, the arcminutes is expected to be 0-59.9999... +
  • The arcseconds field is expected to be 0-59.9999... +
  • Decoding continues even when a check has failed. Under these + circumstances the field takes the supplied value, defaulting to + zero, and the result DRESLT is computed and returned. +
+
4. +
Further fields after the three expected ones are not treated as + an error. The pointer NSTRT is left in the correct state for + further decoding with the present routine or with sla_DFLTIN + etc. See the example, above. +
5. +
If STRING contains hours, minutes, seconds instead of + degrees etc, + or if the required units are turns (or days) instead of radians, + the result DRESLT should be multiplied as follows:
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
for STRINGto obtainmultiply DRESLT by
   
${\circ}$  '  ''radians1.0D0
${\circ}$  '  ''turns$1/{2 \pi} = 0.1591549430918953358$D0
h m sradians15.0D0
h m sdays$15/{2\pi} = 2.3873241463784300365$D0
+
+ +next + +up + +previous +
+ Next: SLA_DAT - TAI-UTC +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAF2R - Deg,Arcmin,Arcsec to Radians +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node44.html b/src/slalib/sun67.htx/node44.html new file mode 100644 index 0000000..791aba6 --- /dev/null +++ b/src/slalib/sun67.htx/node44.html @@ -0,0 +1,109 @@ + + + + +SLA_DAT - TAI-UTC + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DAV2M - Rotation Matrix from Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAFIN - Sexagesimal character string to angle +

+

+

SLA_DAT - TAI-UTC +   +

+
+
ACTION: +
Increment to be applied to Coordinated Universal Time UTC to give +International Atomic Time TAI. +

CALL: +
D = sla_DAT (UTC) +

+

+
GIVEN: +
+
+ + + + + +
UTCDUTC date as a modified JD (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
sla_DATDTAI-UTC in seconds
+

+
NOTES: +
+
1. +
The UTC is specified to be a date rather than a time to indicate +that care needs to be taken not to specify an instant which lies +within a leap second. Though in most cases UTC can include the + fractional part, correct behaviour on the day of a leap second + can be guaranteed only up to the end of the second + $23^{\rm h}\,59^{\rm m}\,59^{\rm s}$.
2. +
UTC began at 1960 January 1. To specify a UTC prior to this + date would be meaningless; in such cases the parameters + for the year 1960 are used by default. +
3. +
This routine has to be updated on each occasion that a + leap second is announced, and programs using it relinked. + Refer to the program source code for information on when the + most recent leap second was added. +
+
+ +next + +up + +previous +
+ Next: SLA_DAV2M - Rotation Matrix from Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAFIN - Sexagesimal character string to angle +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node45.html b/src/slalib/sun67.htx/node45.html new file mode 100644 index 0000000..4e11c46 --- /dev/null +++ b/src/slalib/sun67.htx/node45.html @@ -0,0 +1,103 @@ + + + + +SLA_DAV2M - Rotation Matrix from Axial Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DBEAR - Direction Between Points on a Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAT - TAI-UTC +

+

+

SLA_DAV2M - Rotation Matrix from Axial Vector +   +

+
+
ACTION: +
Form the rotation matrix corresponding to a given axial vector +(double precision). +

CALL: +
CALL sla_DAV2M (AXVEC, RMAT) +

+

+
GIVEN: +
+
+ + + + + +
AXVECD(3)axial vector (radians)
+

+
RETURNED: +
+
+ + + + + +
RMATD(3,3)rotation matrix
+

+
NOTES: +
+
1. +
A rotation matrix describes a rotation about some arbitrary axis. +The axis is called the Euler axis, and the angle through which the +reference frame rotates is called the Euler angle. The axial + vector supplied to this routine has the same direction as the + Euler axis, and its magnitude is the Euler angle in radians. +
2. +
If AXVEC is null, the unit matrix is returned. +
3. +
The reference frame rotates clockwise as seen looking along + the axial vector from the origin. +
+
+ +next + +up + +previous +
+ Next: SLA_DBEAR - Direction Between Points on a Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAT - TAI-UTC +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node46.html b/src/slalib/sun67.htx/node46.html new file mode 100644 index 0000000..39a1ffd --- /dev/null +++ b/src/slalib/sun67.htx/node46.html @@ -0,0 +1,123 @@ + + + + +SLA_DBEAR - Direction Between Points on a Sphere + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DBJIN - Decode String to B/J Epoch (DP) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAV2M - Rotation Matrix from Axial Vector +

+

+

SLA_DBEAR - Direction Between Points on a Sphere +   +

+
+
ACTION: +
Returns the bearing (position angle) of one point on a +sphere relative to another (double precision). +

CALL: +
D = sla_DBEAR (A1, B1, A2, B2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
A1,B1Dspherical coordinates of one point
A2,B2Dspherical coordinates of the other point
+

+
RETURNED: +
+
+ + + + + +
sla_DBEARDbearing from first point to second
+

+
NOTES: +
+
1. +
The spherical coordinates are $[\,\alpha,\delta\,]$,$[\lambda,\phi]$ etc., in radians. +
2. +
The result is the bearing (position angle), in radians, + of point [A2,B2] as seen + from point [A1,B1]. It is in the range $\pm \pi$. The sense + is such that if [A2,B2] + is a small distance due east of [A1,B1] the result + is about $+\pi/2$. Zero is returned + if the two points are coincident. +
3. +
If either B-coordinate is outside the range $\pm\pi/2$, the + result may correspond to ``the long way round''. +
4. +
The routine sla_DPAV performs an equivalent function except + that the points are specified in the form of Cartesian unit + vectors. +
+
+ +next + +up + +previous +
+ Next: SLA_DBJIN - Decode String to B/J Epoch (DP) +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DAV2M - Rotation Matrix from Axial Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node47.html b/src/slalib/sun67.htx/node47.html new file mode 100644 index 0000000..5d8e877 --- /dev/null +++ b/src/slalib/sun67.htx/node47.html @@ -0,0 +1,157 @@ + + + + +SLA_DBJIN - Decode String to B/J Epoch (DP) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DC62S - Cartesian 6-Vector to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DBEAR - Direction Between Points on a Sphere +

+

+

SLA_DBJIN - Decode String to B/J Epoch (DP) +   +

+
+
ACTION: +
Decode a character string into a DOUBLE PRECISION number, +with special provision for Besselian and Julian epochs. + The string syntax is as for sla_DFLTIN, prefixed by + an optional `B' or `J'. +

CALL: +
CALL sla_DBJIN (STRING, NSTRT, DRESLT, J1, J2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
STRINGCstring containing field to be decoded
NSTRTIpointer to first character of field in string
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NSTRTIincremented past the decoded field
DRESLTDresult
J1IDFLTIN status:
-1 = -OK
0 = +OK
1 = null field
2 = error
J2Isyntax flag:
0 = normal DFLTIN syntax
1 = `B' or `b'
2 = `J' or `j'
+

+
NOTES: +
+
1. +
The purpose of the syntax extensions is to help cope with mixed +FK4 and FK5 data, allowing fields such as `B1950' or `J2000' +to be decoded. +
2. +
In addition to the syntax accepted by sla_DFLTIN, + the following two extensions are recognized by sla_DBJIN: +
+
(a) +
A valid non-null field preceded by the character `B' +(or `b') is accepted. +
(b) +
A valid non-null field preceded by the character `J' + (or `j') is accepted. +
+
3. +
The calling program is told of the `B' or `J' through an + supplementary status argument. The rest of + the arguments are as for sla_DFLTIN. +
+
+ +next + +up + +previous +
+ Next: SLA_DC62S - Cartesian 6-Vector to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DBEAR - Direction Between Points on a Sphere +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node48.html b/src/slalib/sun67.htx/node48.html new file mode 100644 index 0000000..95057e4 --- /dev/null +++ b/src/slalib/sun67.htx/node48.html @@ -0,0 +1,110 @@ + + + + +SLA_DC62S - Cartesian 6-Vector to Spherical + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DCC2S - Cartesian to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DBJIN - Decode String to B/J Epoch (DP) +

+

+

SLA_DC62S - Cartesian 6-Vector to Spherical +   +

+
+
ACTION: +
Conversion of position & velocity in Cartesian coordinates +to spherical coordinates (double precision). +

CALL: +
CALL sla_DC62S (V, A, B, R, AD, BD, RD) +

+

+
GIVEN: +
+
+ + + + + +
VD(6)$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
ADlongitude (radians)
BDlatitude (radians)
RDradial coordinate
ADDlongitude derivative (radians per unit time)
BDDlatitude derivative (radians per unit time)
RDDradial derivative
+
+ +next + +up + +previous +
+ Next: SLA_DCC2S - Cartesian to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DBJIN - Decode String to B/J Epoch (DP) +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node49.html b/src/slalib/sun67.htx/node49.html new file mode 100644 index 0000000..86f582e --- /dev/null +++ b/src/slalib/sun67.htx/node49.html @@ -0,0 +1,103 @@ + + + + +SLA_DCC2S - Cartesian to Spherical + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DCMPF - Interpret Linear Fit +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DC62S - Cartesian 6-Vector to Spherical +

+

+

SLA_DCC2S - Cartesian to Spherical +   +

+
+
ACTION: +
Cartesian coordinates to spherical coordinates (double precision). +
CALL: +
CALL sla_DCC2S (V, A, B) +

+

+
GIVEN: +
+
+ + + + + +
VD(3)$[\,x,y,z\,]$ vector
+

+
RETURNED: +
+
+ + + + + +
A,BDspherical coordinates in radians
+

+
NOTES: +
+
1. +
The spherical coordinates are longitude (+ve anticlockwise +looking from the +ve latitude pole) and latitude. The +Cartesian coordinates are right handed, with the x-axis + at zero longitude and latitude, and the z-axis at the + +ve latitude pole. +
2. +
If V is null, zero A and B are returned. +
3. +
At either pole, zero A is returned. +
+
+ +next + +up + +previous +
+ Next: SLA_DCMPF - Interpret Linear Fit +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DC62S - Cartesian 6-Vector to Spherical +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node5.html b/src/slalib/sun67.htx/node5.html new file mode 100644 index 0000000..3920866 --- /dev/null +++ b/src/slalib/sun67.htx/node5.html @@ -0,0 +1,83 @@ + + + + +Scope + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Objectives +
+Up: INTRODUCTION +
+ Previous: Example Application +

+

+

+Scope +

+SLALIB contains 183 routines covering the following topics: + +
+ +next + +up + +previous +
+ Next: Objectives +
+Up: INTRODUCTION +
+ Previous: Example Application +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node50.html b/src/slalib/sun67.htx/node50.html new file mode 100644 index 0000000..555de30 --- /dev/null +++ b/src/slalib/sun67.htx/node50.html @@ -0,0 +1,166 @@ + + + + +SLA_DCMPF - Interpret Linear Fit + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DCS2C - Spherical to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DCC2S - Cartesian to Spherical +

+

+

SLA_DCMPF - Interpret Linear Fit +   +

+
+
ACTION: +
Decompose an $[\,x,y\,]$ linear fit into its constituent parameters: +zero points, scales, nonperpendicularity and orientation. +

CALL: +
CALL sla_DCMPF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT) +

+

+
GIVEN: +
+
+ + + + + +
COEFFSD(6)transformation coefficients (see note)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
XZDx zero point
YZDy zero point
XSDx scale
YSDy scale
PERPDnonperpendicularity (radians)
ORIENTDorientation (radians)
+

+
NOTES: +
+
1. +
The model relates two sets of $[\,x,y\,]$ coordinates as follows. +Naming the six elements of COEFFS a,b,c,d,e & f, +the model transforms coordinates $[x_{1},y_{1}\,]$ into coordinates + $[x_{2},y_{2}\,]$ as follows: +
x2 = a + bx1 + cy1
+ y2 = d + ex1 + fy1
+ The sla_DCMPF routine decomposes this transformation + into four steps: +
+
(a) +
Zero points: +
$x' = x_{1} + {\rm XZ}$
+ $y' = y_{1} + {\rm YZ}$
+
(b) +
Scales: +
$x'' = x' {\rm XS}$
+ $y'' = y' {\rm YS}$
+
(c) +
Nonperpendicularity: +
$x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$
+ $y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$
+
(d) +
Orientation: +
$x_{2} = + x''' \cos {\rm ORIENT} + + y''' \sin {\rm ORIENT}$
+ $y_{2} = - x''' \sin {\rm ORIENT} + + y''' \cos {\rm ORIENT}$
+
2. +
See also sla_FITXY, sla_PXY, sla_INVF, sla_XY2XY. +
+
+ +next + +up + +previous +
+ Next: SLA_DCS2C - Spherical to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DCC2S - Cartesian to Spherical +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node51.html b/src/slalib/sun67.htx/node51.html new file mode 100644 index 0000000..1a8cb1b --- /dev/null +++ b/src/slalib/sun67.htx/node51.html @@ -0,0 +1,99 @@ + + + + +SLA_DCS2C - Spherical to Cartesian + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DD2TF - Days to Hour,Min,Sec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DCMPF - Interpret Linear Fit +

+

+

SLA_DCS2C - Spherical to Cartesian +   +

+
+
ACTION: +
Spherical coordinates to Cartesian coordinates (double precision). +
CALL: +
CALL sla_DCS2C (A, B, V) +

+

+
GIVEN: +
+
+ + + + + +
A,BDspherical coordinates in radians: $[\,\alpha,\delta\,]$ etc.
+

+
RETURNED: +
+
+ + + + + +
VD(3)$[\,x,y,z\,]$ unit vector
+

+
NOTE: +
The spherical coordinates are longitude (+ve anticlockwise +looking from the +ve latitude pole) and latitude. The + Cartesian coordinates are right handed, with the x-axis + at zero longitude and latitude, and the z-axis at the + +ve latitude pole. +
+
+ +next + +up + +previous +
+ Next: SLA_DD2TF - Days to Hour,Min,Sec +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DCMPF - Interpret Linear Fit +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node52.html b/src/slalib/sun67.htx/node52.html new file mode 100644 index 0000000..52cca63 --- /dev/null +++ b/src/slalib/sun67.htx/node52.html @@ -0,0 +1,115 @@ + + + + +SLA_DD2TF - Days to Hour,Min,Sec + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DE2H - to Az,El +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DCS2C - Spherical to Cartesian +

+

+

SLA_DD2TF - Days to Hour,Min,Sec +   +

+
+
ACTION: +
Convert an interval in days into hours, minutes, seconds +(double precision). +

CALL: +
CALL sla_DD2TF (NDP, DAYS, SIGN, IHMSF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of seconds
DAYSDinterval in days
+

+
RETURNED: +
+
+ + + + + + + + + +
SIGNC`+' or `-'
IHMSFI(4)hours, minutes, seconds, fraction
+

+
NOTES: +
+
1. +
NDP less than zero is interpreted as zero. +
2. +
The largest useful value for NDP is determined by the size +of DAYS, the format of DOUBLE PRECISION floating-point numbers + on the target machine, and the risk of overflowing IHMSF(4). + For example, on a VAX computer, for DAYS up to 1D0, the available + floating-point precision corresponds roughly to NDP=12. However, + the practical limit is NDP=9, set by the capacity of the 32-bit + integer IHMSF(4). +
3. +
The absolute value of DAYS may exceed 1D0. In cases where it + does not, it is up to the caller to test for and handle the + case where DAYS is very nearly 1D0 and rounds up to 24 hours, + by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero. +
+
+ +next + +up + +previous +
+ Next: SLA_DE2H - to Az,El +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DCS2C - Spherical to Cartesian +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node53.html b/src/slalib/sun67.htx/node53.html new file mode 100644 index 0000000..05a6c56 --- /dev/null +++ b/src/slalib/sun67.htx/node53.html @@ -0,0 +1,145 @@ + + + + +SLA_DE2H - to Az,El + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DEULER - Euler Angles to Rotation Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DD2TF - Days to Hour,Min,Sec +

+

+

    +
+SLA_DE2H - $h,\delta$ to Az,El +

+
+
ACTION: +
Equatorial to horizon coordinates +(double precision). +

CALL: +
CALL sla_DE2H (HA, DEC, PHI, AZ, EL) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
HADhour angle (radians)
DECDdeclination (radians)
PHIDlatitude (radians)
+

+
RETURNED: +
+
+ + + + + + + + + +
AZDazimuth (radians)
ELDelevation (radians)
+

+
NOTES: +
+
1. +
Azimuth is returned in the range $0\!-\!2\pi$; north is zero, +and east is $+\pi/2$. Elevation is returned in the range +$\pm \pi$.
2. +
The latitude must be geodetic. In critical applications, + corrections for polar motion should be applied. +
3. +
In some applications it will be important to specify the + correct type of hour angle and declination in order to + produce the required type of azimuth and elevation. In + particular, it may be important to distinguish between + elevation as affected by refraction, which would + require the observed $[\,h,\delta\,]$, and the elevation + in vacuo, which would require the topocentric + $[\,h,\delta\,]$. If the effects of diurnal aberration can be neglected, the + apparent $[\,h,\delta\,]$ may be used instead of the topocentric + $[\,h,\delta\,]$.
4. +
No range checking of arguments is carried out. +
5. +
In applications which involve many such calculations, rather + than calling the present routine it will be more efficient to + use inline code, having previously computed fixed terms such + as sine and cosine of latitude, and (for tracking a star) + sine and cosine of declination. +
+
+ +next + +up + +previous +
+ Next: SLA_DEULER - Euler Angles to Rotation Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DD2TF - Days to Hour,Min,Sec +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node54.html b/src/slalib/sun67.htx/node54.html new file mode 100644 index 0000000..1fc9a2a --- /dev/null +++ b/src/slalib/sun67.htx/node54.html @@ -0,0 +1,127 @@ + + + + +SLA_DEULER - Euler Angles to Rotation Matrix + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DFLTIN - Decode a Double Precision Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DE2H - to Az,El +

+

+

SLA_DEULER - Euler Angles to Rotation Matrix +   +

+
+
ACTION: +
Form a rotation matrix from the Euler angles - three +successive rotations about specified Cartesian axes + (double precision). +

CALL: +
CALL sla_DEULER (ORDER, PHI, THETA, PSI, RMAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
ORDERCspecifies about which axes the rotations occur
PHID1st rotation (radians)
THETAD2nd rotation (radians)
PSID3rd rotation (radians)
+

+
RETURNED: +
+
+ + + + + +
RMATD(3,3)rotation matrix
+

+
NOTES: +
+
1. +
A rotation is positive when the reference frame rotates +anticlockwise as seen looking towards the origin from the +positive region of the specified axis. +
2. +
The characters of ORDER define which axes the three successive + rotations are about. A typical value is `ZXZ', indicating that + RMAT is to become the direction cosine matrix corresponding to + rotations of the reference frame through PHI radians about the + old z-axis, followed by THETA radians about the resulting + x-axis, + then PSI radians about the resulting z-axis. +
3. +
The axis names can be any of the following, in any order or + combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal + axis labelling/numbering conventions apply; the xyz ($\equiv123$) triad is right-handed. Thus, the `ZXZ' example given above + could be written `zxz' or `313' (or even `ZxZ' or `3xZ'). ORDER + is terminated by length or by the first unrecognized character. + Fewer than three rotations are acceptable, in which case the later + angle arguments are ignored. Zero rotations produces a unit RMAT. +
+
+ +next + +up + +previous +
+ Next: SLA_DFLTIN - Decode a Double Precision Number +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DE2H - to Az,El +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node55.html b/src/slalib/sun67.htx/node55.html new file mode 100644 index 0000000..390f876 --- /dev/null +++ b/src/slalib/sun67.htx/node55.html @@ -0,0 +1,200 @@ + + + + +SLA_DFLTIN - Decode a Double Precision Number + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DH2E - Az,El to +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DEULER - Euler Angles to Rotation Matrix +

+

+

SLA_DFLTIN - Decode a Double Precision Number +   +

+
+
ACTION: +
Convert free-format input into double precision floating point. +
CALL: +
CALL sla_DFLTIN (STRING, NSTRT, DRESLT, JFLAG) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
STRINGCstring containing number to be decoded
NSTRTIpointer to where decoding is to commence
DRESLTDcurrent value of result
+

+
RETURNED: +
+
+ + + + + + + + + + + + + +
NSTRTIadvanced to next number
DRESLTDresult
JFLAGIstatus: -1 = -OK, 0 = +OK, 1 = null result, 2 = error
+

+
NOTES: +
+
1. +
The reason sla_DFLTIN has separate `OK' status values +for + and - is to enable minus zero to be detected. +This is of crucial importance + when decoding mixed-radix numbers. For example, an angle + expressed as degrees, arcminutes and arcseconds may have a + leading minus sign but a zero degrees field. +
2. +
A TAB is interpreted as a space, and lowercase characters are + interpreted as uppercase. n.b. The test for TAB is + ASCII-specific. +
3. +
The basic format is the sequence of fields $\pm n.n x \pm n$, where $\pm$ is a sign + character `+' or `-', n means a string of decimal digits, + `.' is a decimal point, and x, which indicates an exponent, + means `D' or `E'. Various combinations of these fields can be + omitted, and embedded blanks are permissible in certain places. +
4. +
Spaces: +
    +
  • Leading spaces are ignored. +
  • Embedded spaces are allowed only after +, -, D or E, + and after the decimal point if the first sequence of + digits is absent. +
  • Trailing spaces are ignored; the first signifies + end of decoding and subsequent ones are skipped. +
+
5. +
Delimiters: +
    +
  • Any character other than +,-,0-9,.,D,E or space may be + used to signal the end of the number and terminate decoding. +
  • Comma is recognized by sla_DFLTIN as a special case; it + is skipped, leaving the pointer on the next character. See + 13, below. +
  • Decoding will in all cases terminate if end of string + is reached. +
+
6. +
Both signs are optional. The default is +. +
7. +
The mantissa n.n defaults to unity. +
8. +
The exponent $x\!\pm\!n$ defaults to `D0'. +
9. +
The strings of decimal digits may be of any length. +
10. +
The decimal point is optional for whole numbers. +
11. +
A null result occurs when the string of characters + being decoded does not begin with +,-,0-9,.,D or E, or + consists entirely of spaces. When this condition is + detected, JFLAG is set to 1 and DRESLT is left untouched. +
12. +
NSTRT = 1 for the first character in the string. +
13. +
On return from sla_DFLTIN, NSTRT is set ready for the next + decode - following trailing blanks and any comma. If a + delimiter other than comma is being used, NSTRT must be + incremented before the next call to sla_DFLTIN, otherwise + all subsequent calls will return a null result. +
14. +
Errors (JFLAG=2) occur when: +
    +
  • a +, -, D or E is left unsatisfied; or +
  • the decimal point is present without at least + one decimal digit before or after it; or +
  • an exponent more than 100 has been presented. +
+
15. +
When an error has been detected, NSTRT is left + pointing to the character following the last + one used before the error came to light. This + may be after the point at which a more sophisticated + program could have detected the error. For example, + sla_DFLTIN does not detect that `1D999' is unacceptable + (on a computer where this is so) until the entire number + has been decoded. +
16. +
Certain highly unlikely combinations of mantissa and + exponent can cause arithmetic faults during the + decode, in some cases despite the fact that they + together could be construed as a valid number. +
17. +
Decoding is left to right, one pass. +
18. +
See also sla_FLOTIN and sla_INTIN. +
+
+ +next + +up + +previous +
+ Next: SLA_DH2E - Az,El to +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DEULER - Euler Angles to Rotation Matrix +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node56.html b/src/slalib/sun67.htx/node56.html new file mode 100644 index 0000000..e71b073 --- /dev/null +++ b/src/slalib/sun67.htx/node56.html @@ -0,0 +1,146 @@ + + + + +SLA_DH2E - Az,El to + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DIMXV - Apply 3D Reverse Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DFLTIN - Decode a Double Precision Number +

+

+

    +
+SLA_DH2E - Az,El to $h,\delta$

+
+
ACTION: +
Horizon to equatorial coordinates +(double precision). +

CALL: +
CALL sla_DH2E (AZ, EL, PHI, HA, DEC) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
AZDazimuth (radians)
ELDelevation (radians)
PHIDlatitude (radians)
+

+
RETURNED: +
+
+ + + + + + + + + +
HADhour angle (radians)
DECDdeclination (radians)
+

+
NOTES: +
+
1. +
The sign convention for azimuth is north zero, east $+\pi/2$.
2. +
HA is returned in the range $\pm \pi$. Declination is returned +in the range $\pm \pi$.
3. +
The latitude is (in principle) geodetic. In critical + applications, corrections for polar motion should be applied + (see sla_POLMO). +
4. +
In some applications it will be important to specify the + correct type of elevation in order to produce the required + type of $[\,h,\delta\,]$. In particular, it may be important to + distinguish between the elevation as affected by refraction, + which will yield the observed $[\,h,\delta\,]$, and the elevation + in vacuo, which will yield the topocentric + $[\,h,\delta\,]$. If the + effects of diurnal aberration can be neglected, the + topocentric $[\,h,\delta\,]$ may be used as an approximation to the + apparent $[\,h,\delta\,]$.
5. +
No range checking of arguments is carried out. +
6. +
In applications which involve many such calculations, rather + than calling the present routine it will be more efficient to + use inline code, having previously computed fixed terms such + as sine and cosine of latitude. +
+
+ +next + +up + +previous +
+ Next: SLA_DIMXV - Apply 3D Reverse Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DFLTIN - Decode a Double Precision Number +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node57.html b/src/slalib/sun67.htx/node57.html new file mode 100644 index 0000000..df5870d --- /dev/null +++ b/src/slalib/sun67.htx/node57.html @@ -0,0 +1,118 @@ + + + + +SLA_DIMXV - Apply 3D Reverse Rotation + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DJCAL - MJD to Gregorian for Output +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DH2E - Az,El to +

+

+

SLA_DIMXV - Apply 3D Reverse Rotation +   +

+
+
ACTION: +
Multiply a 3-vector by the inverse of a rotation +matrix (double precision). +

CALL: +
CALL sla_DIMXV (DM, VA, VB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DMD(3,3)rotation matrix
VAD(3)vector to be rotated
+

+
RETURNED: +
+
+ + + + + +
VBD(3)result vector
+

+
NOTES: +
+
1. +
This routine performs the operation: +
b = M$^{T}\cdot$a +
+ where a and b are the 3-vectors VA and VB + respectively, and M is the $3\times3$ matrix DM. +
2. +
The main function of this routine is apply an inverse + rotation; under these circumstances, ${\bf \rm M}$ is + orthogonal, with its inverse the same as its transpose. +
3. +
To comply with the ANSI Fortran 77 standard, VA and VB must + not be the same array. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
+
+ +next + +up + +previous +
+ Next: SLA_DJCAL - MJD to Gregorian for Output +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DH2E - Az,El to +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node58.html b/src/slalib/sun67.htx/node58.html new file mode 100644 index 0000000..78f70fa --- /dev/null +++ b/src/slalib/sun67.htx/node58.html @@ -0,0 +1,112 @@ + + + + +SLA_DJCAL - MJD to Gregorian for Output + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DJCL - MJD to Year,Month,Day,Frac +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DIMXV - Apply 3D Reverse Rotation +

+

+

SLA_DJCAL - MJD to Gregorian for Output +   +

+
+
ACTION: +
Modified Julian Date to Gregorian Calendar Date, expressed +in a form convenient for formatting messages (namely + rounded to a specified precision, and with the fields + stored in a single array). +

CALL: +
CALL sla_DJCAL (NDP, DJM, IYMDF, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of days in fraction
DJMDmodified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + + + + + +
IYMDFI(4)year, month, day, fraction in Gregorian calendar
JIstatus: nonzero = out of range
+

+
NOTES: +
+
1. +
Any date after 4701BC March 1 is accepted. +
2. +
NDP should be 4 or less to avoid overflow on machines which +use 32-bit integers. +
+

+
REFERENCE: +
The algorithm is derived from that of Hatcher, +Q.Jl.R.astr.Soc. (1984) 25, 53-55. +
+
+ +next + +up + +previous +
+ Next: SLA_DJCL - MJD to Year,Month,Day,Frac +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DIMXV - Apply 3D Reverse Rotation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node59.html b/src/slalib/sun67.htx/node59.html new file mode 100644 index 0000000..1d0b789 --- /dev/null +++ b/src/slalib/sun67.htx/node59.html @@ -0,0 +1,117 @@ + + + + +SLA_DJCL - MJD to Year,Month,Day,Frac + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DM2AV - Rotation Matrix to Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DJCAL - MJD to Gregorian for Output +

+

+

SLA_DJCL - MJD to Year,Month,Day,Frac +   +

+
+
ACTION: +
Modified Julian Date to Gregorian year, month, day, +and fraction of a day. +

CALL: +
CALL sla_DJCL (DJM, IY, IM, ID, FD, J) +

+

+
GIVEN: +
+
+ + + + + +
DJMDmodified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IYIyear
IMImonth
IDIday
FDDfraction of day
JIstatus:
0 = OK
-1 = unacceptable date (before 4701BC March 1)
+

+
REFERENCE: +
The algorithm is derived from that of Hatcher, +Q.Jl.R.astr.Soc. (1984) 25, 53-55. +
+
+ +next + +up + +previous +
+ Next: SLA_DM2AV - Rotation Matrix to Axial Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DJCAL - MJD to Gregorian for Output +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node6.html b/src/slalib/sun67.htx/node6.html new file mode 100644 index 0000000..c90fd51 --- /dev/null +++ b/src/slalib/sun67.htx/node6.html @@ -0,0 +1,116 @@ + + + + +Objectives + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Fortran Version +
+Up: INTRODUCTION +
+ Previous: Scope +

+

+

+Objectives +

+SLALIB was designed to give application programmers +a basic set of positional-astronomy tools which were +accurate and easy to use. To this end, the library is: + +A few caveats: + +
+ +next + +up + +previous +
+ Next: Fortran Version +
+Up: INTRODUCTION +
+ Previous: Scope +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node60.html b/src/slalib/sun67.htx/node60.html new file mode 100644 index 0000000..db12402 --- /dev/null +++ b/src/slalib/sun67.htx/node60.html @@ -0,0 +1,107 @@ + + + + +SLA_DM2AV - Rotation Matrix to Axial Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DMAT - Solve Simultaneous Equations +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DJCL - MJD to Year,Month,Day,Frac +

+

+

SLA_DM2AV - Rotation Matrix to Axial Vector +   +

+
+
ACTION: +
From a rotation matrix, determine the corresponding axial vector +(double precision). +

CALL: +
CALL sla_DM2AV (RMAT, AXVEC) +

+

+
GIVEN: +
+
+ + + + + +
RMATD(3,3)rotation matrix
+

+
RETURNED: +
+
+ + + + + +
AXVECD(3)axial vector (radians)
+

+
NOTES: +
+
1. +
A rotation matrix describes a rotation about some arbitrary axis. +The axis is called the Euler axis, and the angle through +which the reference frame rotates is called the Euler angle. + The axial vector returned by this routine has the same + direction as the Euler axis, and its magnitude is the Euler angle + in radians. +
2. +
The magnitude and direction of the axial vector can be separated + by means of the routine sla_DVN. +
3. +
The reference frame rotates clockwise as seen looking along + the axial vector from the origin. +
4. +
If RMAT is null, so is the result. +
+
+ +next + +up + +previous +
+ Next: SLA_DMAT - Solve Simultaneous Equations +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DJCL - MJD to Year,Month,Day,Frac +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node61.html b/src/slalib/sun67.htx/node61.html new file mode 100644 index 0000000..b72e3ac --- /dev/null +++ b/src/slalib/sun67.htx/node61.html @@ -0,0 +1,152 @@ + + + + +SLA_DMAT - Solve Simultaneous Equations + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DMOON - Approx Moon Pos/Vel +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DM2AV - Rotation Matrix to Axial Vector +

+

+

SLA_DMAT - Solve Simultaneous Equations +   +

+
+
ACTION: +
Matrix inversion and solution of simultaneous equations +(double precision). +

CALL: +
CALL sla_DMAT (N, A, Y, D, JF, IW) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
NInumber of unknowns
AD(N,N)matrix
YD(N)vector
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + +
AD(N,N)matrix inverse
YD(N)solution
DDdeterminant
JFIsingularity flag: 0=OK
IWI(N)workspace
+

+
NOTES: +
+
1. +
For the set of n simultaneous linear equations in n unknowns: +
A$\cdot$y = x +
+ where: +
    +
  • A is a non-singular $n \times n$ matrix, +
  • y is the vector of n unknowns, and +
  • x is the known vector, +
+ sla_DMAT computes: +
    +
  • the inverse of matrix A, +
  • the determinant of matrix A, and +
  • the vector of n unknowns y. +
+ Argument N is the order n, A (given) is the matrix A, + Y (given) is the vector x and Y (returned) + is the vector y. + The argument A (returned) is the inverse matrix A-1, + and D is det(A). +
2. +
JF is the singularity flag. If the matrix is non-singular, + JF=0 is returned. If the matrix is singular, JF=-1 + and D=0D0 are returned. In the latter case, the contents + of array A on return are undefined. +
3. +
The algorithm is Gaussian elimination with partial pivoting. + This method is very fast; some much slower algorithms can give + better accuracy, but only by a small factor. +
4. +
This routine replaces the obsolete sla_DMATRX. +
+
+ +next + +up + +previous +
+ Next: SLA_DMOON - Approx Moon Pos/Vel +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DM2AV - Rotation Matrix to Axial Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node62.html b/src/slalib/sun67.htx/node62.html new file mode 100644 index 0000000..dedceda --- /dev/null +++ b/src/slalib/sun67.htx/node62.html @@ -0,0 +1,154 @@ + + + + +SLA_DMOON - Approx Moon Pos/Vel + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DMXM - Multiply Matrices +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMAT - Solve Simultaneous Equations +

+

+

SLA_DMOON - Approx Moon Pos/Vel +   +

+
+
ACTION: +
Approximate geocentric position and velocity of the Moon +(double precision). +

CALL: +
CALL sla_DMOON (DATE, PV) +

+

+
GIVEN: +
+
+ + + + + +
DATEDTDB (loosely ET) as a Modified Julian Date (JD-2400000.5) +
+

+
RETURNED: +
+
+ + + + + +
PVD(6)Moon $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, mean equator and equinox +of date (AU, AU s-1)
+

+
NOTES: +
+
1. +
This routine is a full implementation of the algorithm +published by Meeus (see reference). +
2. +
Meeus quotes accuracies of $10\hspace{-0.05em}^{'\hspace{-0.1em}'}$ in longitude, + $3\hspace{-0.05em}^{'\hspace{-0.1em}'}$ in latitude and + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ arcsec in HP + (equivalent to about 20 km in distance). Comparison with + JPL DE200 over the interval 1960-2025 gives RMS errors of +

$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.7$ and 83 mas/hour in longitude, +

$2\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ arcsec and 48 mas/hour in latitude, + 11 km and 81 mm/s in distance. + The maximum errors over the same interval are + $18\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.50$ /hour in longitude, + $11\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.24$ /hour in latitude, + 40 km and 0.29 m/s in distance. +

3. +
The original algorithm is expressed in terms of the obsolete + timescale Ephemeris Time. Either TDB or TT can be used, + but not UT without incurring significant errors ($30\hspace{-0.05em}^{'\hspace{-0.1em}'}$ at + the present time) due to the Moon's + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ /s movement. +
4. +
The algorithm is based on pre IAU 1976 standards. However, + the result has been moved onto the new (FK5) equinox, an + adjustment which is in any case much smaller than the + intrinsic accuracy of the procedure. +
5. +
Velocity is obtained by a complete analytical differentiation + of the Meeus model. +
+

+
REFERENCE: +
Meeus, l'Astronomie, June 1984, p348. +
+
+ +next + +up + +previous +
+ Next: SLA_DMXM - Multiply Matrices +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMAT - Solve Simultaneous Equations +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node63.html b/src/slalib/sun67.htx/node63.html new file mode 100644 index 0000000..9d19b4d --- /dev/null +++ b/src/slalib/sun67.htx/node63.html @@ -0,0 +1,106 @@ + + + + +SLA_DMXM - Multiply Matrices + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DMXV - Apply 3D Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMOON - Approx Moon Pos/Vel +

+

+

    +
+SLA_DMXM - Multiply $3\times3$ Matrices +

+
+
ACTION: +
Product of two $3\times3$ matrices (double precision). +
CALL: +
CALL sla_DMXM (A, B, C) +

+

+
GIVEN: +
+
+ + + + + + + + + +
AD(3,3)matrix A
BD(3,3)matrix B
+

+
RETURNED: +
+
+ + + + + +
CD(3,3)matrix result: A$\times$B
+

+
NOTE: +
To comply with the ANSI Fortran 77 standard, A, B and C must +be different arrays. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
+
+ +next + +up + +previous +
+ Next: SLA_DMXV - Apply 3D Rotation +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMOON - Approx Moon Pos/Vel +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node64.html b/src/slalib/sun67.htx/node64.html new file mode 100644 index 0000000..b6a0e15 --- /dev/null +++ b/src/slalib/sun67.htx/node64.html @@ -0,0 +1,115 @@ + + + + +SLA_DMXV - Apply 3D Rotation + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DPAV - Position-Angle Between Two Directions +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMXM - Multiply Matrices +

+

+

SLA_DMXV - Apply 3D Rotation +   +

+
+
ACTION: +
Multiply a 3-vector by a rotation matrix (double precision). +
CALL: +
CALL sla_DMXV (DM, VA, VB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DMD(3,3)rotation matrix
VAD(3)vector to be rotated
+

+
RETURNED: +
+
+ + + + + +
VBD(3)result vector
+

+
NOTES: +
+
1. +
This routine performs the operation: +
b = M$\cdot$a +
+ where a and b are the 3-vectors VA and VB + respectively, and M is the $3\times3$ matrix DM. +
2. +
The main function of this routine is apply a + rotation; under these circumstances, M is a + proper real orthogonal matrix. +
3. +
To comply with the ANSI Fortran 77 standard, VA and VB must + not be the same array. The routine is, in fact, coded + so as to work properly on the VAX and many other systems even + if this rule is violated, something that is not, however, + recommended. +
+
+ +next + +up + +previous +
+ Next: SLA_DPAV - Position-Angle Between Two Directions +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMXM - Multiply Matrices +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node65.html b/src/slalib/sun67.htx/node65.html new file mode 100644 index 0000000..de89921 --- /dev/null +++ b/src/slalib/sun67.htx/node65.html @@ -0,0 +1,117 @@ + + + + +SLA_DPAV - Position-Angle Between Two Directions + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DR2AF - Radians to Deg,Min,Sec,Frac +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMXV - Apply 3D Rotation +

+

+

SLA_DPAV - Position-Angle Between Two Directions +   +

+
+
ACTION: +
Returns the bearing (position angle) of one celestial +direction with respect to another (double precision). +

CALL: +
D = sla_DPAV (V1, V2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
V1D(3)direction cosines of one point
V2D(3)directions cosines of the other point
+

+
RETURNED: +
+
+ + + + + +
sla_DPAVDposition-angle of 2nd point with respect to 1st
+

+
NOTES: +
+
1. +
The coordinate frames correspond to $[\,\alpha,\delta\,]$,$[\lambda,\phi]$ etc.. +
2. +
The result is the bearing (position angle), in radians, + of point V2 as seen + from point V1. It is in the range $\pm \pi$. The sense + is such that if V2 + is a small distance due east of V1 the result + is about $+\pi/2$. Zero is returned + if the two points are coincident. +
3. +
The routine sla_DBEAR performs an equivalent function except + that the points are specified in the form of spherical coordinates. +
+
+ +next + +up + +previous +
+ Next: SLA_DR2AF - Radians to Deg,Min,Sec,Frac +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DMXV - Apply 3D Rotation +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node66.html b/src/slalib/sun67.htx/node66.html new file mode 100644 index 0000000..c4b2639 --- /dev/null +++ b/src/slalib/sun67.htx/node66.html @@ -0,0 +1,122 @@ + + + + +SLA_DR2AF - Radians to Deg,Min,Sec,Frac + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DR2TF - Radians to Hour,Min,Sec,Frac +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DPAV - Position-Angle Between Two Directions +

+

+

SLA_DR2AF - Radians to Deg,Min,Sec,Frac +   +

+
+
ACTION: +
Convert an angle in radians to degrees, arcminutes, arcseconds, +fraction (double precision). +

CALL: +
CALL sla_DR2AF (NDP, ANGLE, SIGN, IDMSF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of arcseconds
ANGLEDangle in radians
+

+
RETURNED: +
+
+ + + + + + + + + +
SIGNC`+' or `-'
IDMSFI(4)degrees, arcminutes, arcseconds, fraction
+

+
NOTES: +
+
1. +
NDP less than zero is interpreted as zero. +
2. +
The largest useful value for NDP is determined by the size +of ANGLE, the format of DOUBLE PRECISION floating-point numbers + on the target machine, and the risk of overflowing IDMSF(4). + For example, on a VAX computer, for ANGLE up to $2\pi$, the available + floating-point precision corresponds roughly to NDP=12. However, + the practical limit is NDP=9, set by the capacity of the 32-bit + integer IDMSF(4). +
3. +
The absolute value of ANGLE may exceed $2\pi$. In cases where it + does not, it is up to the caller to test for and handle the + case where ANGLE is very nearly $2\pi$ and rounds up to $360^{\circ}$, by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero. +
+
+ +next + +up + +previous +
+ Next: SLA_DR2TF - Radians to Hour,Min,Sec,Frac +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DPAV - Position-Angle Between Two Directions +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node67.html b/src/slalib/sun67.htx/node67.html new file mode 100644 index 0000000..f5e0648 --- /dev/null +++ b/src/slalib/sun67.htx/node67.html @@ -0,0 +1,121 @@ + + + + +SLA_DR2TF - Radians to Hour,Min,Sec,Frac + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DRANGE - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DR2AF - Radians to Deg,Min,Sec,Frac +

+

+

SLA_DR2TF - Radians to Hour,Min,Sec,Frac +   +

+
+
ACTION: +
Convert an angle in radians to hours, minutes, seconds, +fraction (double precision). +

CALL: +
CALL sla_DR2TF (NDP, ANGLE, SIGN, IHMSF) +

+

+
GIVEN: +
+
+ + + + + + + + + +
NDPInumber of decimal places of seconds
ANGLEDangle in radians
+

+
RETURNED: +
+
+ + + + + + + + + +
SIGNC`+' or `-'
IHMSFI(4)hours, minutes, seconds, fraction
+

+
NOTES: +
+
1. +
NDP less than zero is interpreted as zero. +
2. +
The largest useful value for NDP is determined by the size +of ANGLE, the format of DOUBLE PRECISION floating-point numbers + on the target machine, and the risk of overflowing IHMSF(4). + For example, on a VAX computer, for ANGLE up to $2\pi$, the available + floating-point precision corresponds roughly to NDP=12. However, + the practical limit is NDP=9, set by the capacity of the 32-bit + integer IHMSF(4). +
3. +
The absolute value of ANGLE may exceed $2\pi$. In cases where it + does not, it is up to the caller to test for and handle the + case where ANGLE is very nearly $2\pi$ and rounds up to 24 hours, + by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero. +
+
+ +next + +up + +previous +
+ Next: SLA_DRANGE - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DR2AF - Radians to Deg,Min,Sec,Frac +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node68.html b/src/slalib/sun67.htx/node68.html new file mode 100644 index 0000000..477164f --- /dev/null +++ b/src/slalib/sun67.htx/node68.html @@ -0,0 +1,93 @@ + + + + +SLA_DRANGE - Put Angle into Range + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DRANRM - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DR2TF - Radians to Hour,Min,Sec,Frac +

+

+

    +
+SLA_DRANGE - Put Angle into Range $\pm \pi$

+
+
ACTION: +
Normalize an angle into the range $\pm \pi$ (double precision). +
CALL: +
D = sla_DRANGE (ANGLE) +

+

+
GIVEN: +
+
+ + + + + +
ANGLEDangle in radians
+

+
RETURNED: +
+
+ + + + + +
sla_DRANGEDANGLE expressed in the range $\pm \pi$.
+
+ +next + +up + +previous +
+ Next: SLA_DRANRM - Put Angle into Range +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DR2TF - Radians to Hour,Min,Sec,Frac +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node69.html b/src/slalib/sun67.htx/node69.html new file mode 100644 index 0000000..02f5415 --- /dev/null +++ b/src/slalib/sun67.htx/node69.html @@ -0,0 +1,93 @@ + + + + +SLA_DRANRM - Put Angle into Range + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DS2C6 - Spherical Pos/Vel to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DRANGE - Put Angle into Range +

+

+

    +
+SLA_DRANRM - Put Angle into Range $0\!-\!2\pi$

+
+
ACTION: +
Normalize an angle into the range $0\!-\!2\pi$(double precision). +

CALL: +
D = sla_DRANRM (ANGLE) +

+

+
GIVEN: +
+
+ + + + + +
ANGLEDangle in radians
+

+
RETURNED: +
+
+ + + + + +
sla_DRANRMDANGLE expressed in the range $0\!-\!2\pi$
+
+ +next + +up + +previous +
+ Next: SLA_DS2C6 - Spherical Pos/Vel to Cartesian +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DRANGE - Put Angle into Range +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node7.html b/src/slalib/sun67.htx/node7.html new file mode 100644 index 0000000..e75fbed --- /dev/null +++ b/src/slalib/sun67.htx/node7.html @@ -0,0 +1,76 @@ + + + + +Fortran Version + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: C Version +
+Up: INTRODUCTION +
+ Previous: Objectives +

+

+

+Fortran Version +

+The Fortran versions of SLALIB use ANSI Fortran 77 with a few +commonplace extensions. Just three out of the 183 routines require +platform-specific techniques and accordingly are supplied +in different forms. +SLALIB has been implemented on the following platforms: +VAX/VMS, +PC (Microsoft Fortran, Linux), +DECstation (Ultrix), +DEC Alpha (DEC Unix), +Sun (SunOS, Solaris), +Hewlett Packard (HP-UX), +CONVEX, +Perkin-Elmer and +Fujitsu. +

+

+ +next + +up + +previous +
+ Next: C Version +
+Up: INTRODUCTION +
+ Previous: Objectives +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node70.html b/src/slalib/sun67.htx/node70.html new file mode 100644 index 0000000..b1ebf8a --- /dev/null +++ b/src/slalib/sun67.htx/node70.html @@ -0,0 +1,114 @@ + + + + +SLA_DS2C6 - Spherical Pos/Vel to Cartesian + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DS2TP - Spherical to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DRANRM - Put Angle into Range +

+

+

SLA_DS2C6 - Spherical Pos/Vel to Cartesian +   +

+
+
ACTION: +
Conversion of position & velocity in spherical coordinates +to Cartesian coordinates (double precision). +

CALL: +
CALL sla_DS2C6 (A, B, R, AD, BD, RD, V) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
ADlongitude (radians) - for example $\alpha$
BDlatitude (radians) - for example $\delta$
RDradial coordinate
ADDlongitude derivative (radians per unit time)
BDDlatitude derivative (radians per unit time)
RDDradial derivative
+

+
RETURNED: +
+
+ + + + + +
VD(6)$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$
+
+ +next + +up + +previous +
+ Next: SLA_DS2TP - Spherical to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DRANRM - Put Angle into Range +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node71.html b/src/slalib/sun67.htx/node71.html new file mode 100644 index 0000000..8703383 --- /dev/null +++ b/src/slalib/sun67.htx/node71.html @@ -0,0 +1,129 @@ + + + + +SLA_DS2TP - Spherical to Tangent Plane + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DSEP - Angle Between 2 Points on Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DS2C6 - Spherical Pos/Vel to Cartesian +

+

+

SLA_DS2TP - Spherical to Tangent Plane +   +

+
+
ACTION: +
Projection of spherical coordinates onto the tangent plane +(double precision). +

CALL: +
CALL sla_DS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
RA,DECDspherical coordinates of star (radians)
RAZ,DECZDspherical coordinates of tangent point (radians)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
XI,ETADtangent plane coordinates (radians)
JIstatus:
0 = OK, star on tangent plane
1 = error, star too far from axis
2 = error, antistar on tangent plane
3 = error, antistar too far from axis
+

+
NOTES: +
+
1. +
The projection is called the gnomonic projection; the +Cartesian coordinates $[\,\xi,\eta\,]$ are called +standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
2. +
When working in $[\,x,y,z\,]$ rather than spherical coordinates, the + equivalent Cartesian routine sla_DV2TP is available. +
+
+ +next + +up + +previous +
+ Next: SLA_DSEP - Angle Between 2 Points on Sphere +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DS2C6 - Spherical Pos/Vel to Cartesian +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node72.html b/src/slalib/sun67.htx/node72.html new file mode 100644 index 0000000..b127b82 --- /dev/null +++ b/src/slalib/sun67.htx/node72.html @@ -0,0 +1,100 @@ + + + + +SLA_DSEP - Angle Between 2 Points on Sphere + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DT - Approximate ET minus UT +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DS2TP - Spherical to Tangent Plane +

+

+

SLA_DSEP - Angle Between 2 Points on Sphere +   +

+
+
ACTION: +
Angle between two points on a sphere (double precision). +
CALL: +
D = sla_DSEP (A1, B1, A2, B2) +

+

+
GIVEN: +
+
+ + + + + + + + + +
A1,B1Dspherical coordinates of one point (radians)
A2,B2Dspherical coordinates of the other point (radians)
+

+
RETURNED: +
+
+ + + + + +
sla_DSEPDangle between [A1,B1] and [A2,B2] in radians
+

+
NOTES: +
+
1. +
The spherical coordinates are right ascension and declination, +longitude and latitude, etc., in radians. +
2. +
The result is always positive. +
+
+ +next + +up + +previous +
+ Next: SLA_DT - Approximate ET minus UT +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DS2TP - Spherical to Tangent Plane +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node73.html b/src/slalib/sun67.htx/node73.html new file mode 100644 index 0000000..fca730c --- /dev/null +++ b/src/slalib/sun67.htx/node73.html @@ -0,0 +1,131 @@ + + + + +SLA_DT - Approximate ET minus UT + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTF2D - Hour,Min,Sec to Days +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DSEP - Angle Between 2 Points on Sphere +

+

+

SLA_DT - Approximate ET minus UT +   +

+
+
ACTION: +
Estimate $\Delta$T, the offset between dynamical time +and Universal Time, for a given historical epoch. +

CALL: +
D = sla_DT (EPOCH) +

+

+
GIVEN: +
+
+ + + + + +
EPOCHD(Julian) epoch (e.g. 1850D0)
+

+
RETURNED: +
+
+ + + + + +
sla_DTDapproximate ET-UT (after 1984, TT-UT1) in seconds
+

+
NOTES: +
+
1. +
Depending on the epoch, one of three parabolic approximations +is used: +

+before AD 979 		 Stephenson & Morrison's 390 BC to AD 948 model
+		 AD 979 to AD 1708 		 Stephenson & Morrison's AD 948 to AD 1600 model
+		 after AD 1708 		 McCarthy & Babcock's post-1650 model
+
+ The breakpoints are chosen to ensure continuity: they occur + at places where the adjacent models give the same answer as + each other. +
2. +
The accuracy is modest, with errors of up to $20^{\rm s}$ during + the interval since 1650, rising to perhaps $30^{\rm m}$ by 1000 BC. Comparatively accurate values from AD 1600 + are tabulated in + the Astronomical Almanac (see section K8 of the 1995 + edition). +
3. +
The use of DOUBLE PRECISION for both argument and result is + simply for compatibility with other SLALIB time routines. +
4. +
The models used are based on a lunar tidal acceleration value + of + $-26\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00$ per century. +
+

+
REFERENCE: +
Seidelmann, P.K. (ed), 1992. Explanatory +Supplement to the Astronomical Almanac, ISBN 0-935702-68-7. + This contains references to the papers by Stephenson & Morrison + and by McCarthy & Babcock which describe the models used here. +
+
+ +next + +up + +previous +
+ Next: SLA_DTF2D - Hour,Min,Sec to Days +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DSEP - Angle Between 2 Points on Sphere +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node74.html b/src/slalib/sun67.htx/node74.html new file mode 100644 index 0000000..88700cd --- /dev/null +++ b/src/slalib/sun67.htx/node74.html @@ -0,0 +1,125 @@ + + + + +SLA_DTF2D - Hour,Min,Sec to Days + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTF2R - Hour,Min,Sec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DT - Approximate ET minus UT +

+

+

SLA_DTF2D - Hour,Min,Sec to Days +   +

+
+
ACTION: +
Convert hours, minutes, seconds to days (double precision). +
CALL: +
CALL sla_DTF2D (IHOUR, IMIN, SEC, DAYS, J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IHOURIhours
IMINIminutes
SECDseconds
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
DAYSDinterval in days
JIstatus:
0 = OK
1 = IHOUR outside range 0-23
2 = IMIN outside range 0-59
3 = SEC outside range 0-59.999$\cdots$
+

+
NOTES: +
+
1. +
The result is computed even if any of the range checks fail. +
2. +
The sign must be dealt with outside this routine. +
+
+ +next + +up + +previous +
+ Next: SLA_DTF2R - Hour,Min,Sec to Radians +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DT - Approximate ET minus UT +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node75.html b/src/slalib/sun67.htx/node75.html new file mode 100644 index 0000000..535d444 --- /dev/null +++ b/src/slalib/sun67.htx/node75.html @@ -0,0 +1,125 @@ + + + + +SLA_DTF2R - Hour,Min,Sec to Radians + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTP2S - Tangent Plane to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTF2D - Hour,Min,Sec to Days +

+

+

SLA_DTF2R - Hour,Min,Sec to Radians +   +

+
+
ACTION: +
Convert hours, minutes, seconds to radians (double precision). +
CALL: +
CALL sla_DTF2R (IHOUR, IMIN, SEC, RAD, J) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IHOURIhours
IMINIminutes
SECDseconds
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
RADDangle in radians
JIstatus:
0 = OK
1 = IHOUR outside range 0-23
2 = IMIN outside range 0-59
3 = SEC outside range 0-59.999$\cdots$
+

+
NOTES: +
+
1. +
The result is computed even if any of the range checks fail. +
2. +
The sign must be dealt with outside this routine. +
+
+ +next + +up + +previous +
+ Next: SLA_DTP2S - Tangent Plane to Spherical +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTF2D - Hour,Min,Sec to Days +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node76.html b/src/slalib/sun67.htx/node76.html new file mode 100644 index 0000000..46c4f7a --- /dev/null +++ b/src/slalib/sun67.htx/node76.html @@ -0,0 +1,109 @@ + + + + +SLA_DTP2S - Tangent Plane to Spherical + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTP2V - Tangent Plane to Direction Cosines +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTF2R - Hour,Min,Sec to Radians +

+

+

SLA_DTP2S - Tangent Plane to Spherical +   +

+
+
ACTION: +
Transform tangent plane coordinates into spherical +coordinates (double precision) +

CALL: +
CALL sla_DTP2S (XI, ETA, RAZ, DECZ, RA, DEC) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETADtangent plane rectangular coordinates (radians)
RAZ,DECZDspherical coordinates of tangent point (radians)
+

+
RETURNED: +
+
+ + + + + +
RA,DECDspherical coordinates (radians)
+

+
NOTES: +
+
1. +
The projection is called the gnomonic projection; the +Cartesian coordinates $[\,\xi,\eta\,]$ are called +standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
2. +
When working in $[\,x,y,z\,]$ rather than spherical coordinates, the + equivalent Cartesian routine sla_DTP2V is available. +
+
+ +next + +up + +previous +
+ Next: SLA_DTP2V - Tangent Plane to Direction Cosines +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTF2R - Hour,Min,Sec to Radians +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node77.html b/src/slalib/sun67.htx/node77.html new file mode 100644 index 0000000..522e009 --- /dev/null +++ b/src/slalib/sun67.htx/node77.html @@ -0,0 +1,117 @@ + + + + +SLA_DTP2V - Tangent Plane to Direction Cosines + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTPS2C - Plate centre from and +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTP2S - Tangent Plane to Spherical +

+

+

SLA_DTP2V - Tangent Plane to Direction Cosines +   +

+
+
ACTION: +
Given the tangent-plane coordinates of a star and the direction +cosines of the tangent point, determine the direction cosines + of the star + (double precision). +

CALL: +
CALL sla_DTP2V (XI, ETA, V0, V) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETADtangent plane coordinates of star (radians)
V0D(3)direction cosines of tangent point
+

+
RETURNED: +
+
+ + + + + +
VD(3)direction cosines of star
+

+
NOTES: +
+
1. +
If vector V0 is not of unit length, the returned vector V will +be wrong. +
2. +
If vector V0 points at a pole, the returned vector V will be + based on the arbitrary assumption that $\alpha=0$ at + the tangent point. +
3. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
4. +
This routine is the Cartesian equivalent of the routine sla_DTP2S. +
+
+ +next + +up + +previous +
+ Next: SLA_DTPS2C - Plate centre from and +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTP2S - Tangent Plane to Spherical +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node78.html b/src/slalib/sun67.htx/node78.html new file mode 100644 index 0000000..61458ac --- /dev/null +++ b/src/slalib/sun67.htx/node78.html @@ -0,0 +1,168 @@ + + + + +SLA_DTPS2C - Plate centre from and + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTPV2C - Plate centre from and x,y,z +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTP2V - Tangent Plane to Direction Cosines +

+

+

    +
+SLA_DTPS2C - Plate centre from $\xi,\eta$ and $\alpha,\delta$

+
+
ACTION: +
From the tangent plane coordinates of a star of known $[\,\alpha,\delta\,]$,determine the $[\,\alpha,\delta\,]$ of the tangent point (double precision) +

CALL: +
CALL sla_DTPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETADtangent plane rectangular coordinates (radians)
RA,DECDspherical coordinates (radians)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
RAZ1,DECZ1Dspherical coordinates of tangent point, +solution 1
RAZ2,DECZ2Dspherical coordinates of tangent point, +solution 2
NInumber of solutions:
0 = no solutions returned (note 2)
1 = only the first solution is useful (note 3)
2 = there are two useful solutions (note 3)
+

+
NOTES: +
+
1. +
The RAZ1 and RAZ2 values returned are in the range $0\!-\!2\pi$.
2. +
Cases where there is no solution can only arise near the poles. +For example, it is clearly impossible for a star at the pole + itself to have a non-zero $\xi$ value, and hence it is + meaningless to ask where the tangent point would have to be + to bring about this combination of $\xi$ and $\delta$.
3. +
Also near the poles, cases can arise where there are two useful + solutions. The argument N indicates whether the second of the + two solutions returned is useful. N=1 + indicates only one useful solution, the usual case; under + these circumstances, the second solution corresponds to the + ``over-the-pole'' case, and this is reflected in the values + of RAZ2 and DECZ2 which are returned. +
4. +
The DECZ1 and DECZ2 values returned are in the range $\pm \pi$, but in the ordinary, non-pole-crossing, case, the range is + $\pm\pi/2$.
5. +
RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians. +
6. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
7. +
When working in $[\,x,y,z\,]$ rather than spherical coordinates, the + equivalent Cartesian routine sla_DTPV2C is available. +
+
+ +next + +up + +previous +
+ Next: SLA_DTPV2C - Plate centre from and x,y,z +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTP2V - Tangent Plane to Direction Cosines +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node79.html b/src/slalib/sun67.htx/node79.html new file mode 100644 index 0000000..de0194d --- /dev/null +++ b/src/slalib/sun67.htx/node79.html @@ -0,0 +1,144 @@ + + + + +SLA_DTPV2C - Plate centre from and x,y,z + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DTT - TT minus UTC +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTPS2C - Plate centre from and +

+

+

    +
+SLA_DTPV2C - Plate centre from $\xi,\eta$ and x,y,z +

+
+
ACTION: +
From the tangent plane coordinates of a star of known +direction cosines, determine the direction cosines + of the tangent point (double precision) +

CALL: +
CALL sla_DTPV2C (XI, ETA, V, V01, V02, N) +

+

+
GIVEN: +
+
+ + + + + + + + + +
XI,ETADtangent plane coordinates of star (radians)
VD(3)direction cosines of star
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
V01D(3)direction cosines of tangent point, solution 1
V01D(3)direction cosines of tangent point, solution 2
NInumber of solutions:
0 = no solutions returned (note 2)
1 = only the first solution is useful (note 3)
2 = there are two useful solutions (note 3)
+

+
NOTES: +
+
1. +
The vector V must be of unit length or the result will be wrong. +
2. +
Cases where there is no solution can only arise near the poles. +For example, it is clearly impossible for a star at the pole + itself to have a non-zero XI value. +
3. +
Also near the poles, cases can arise where there are two useful + solutions. The argument N indicates whether the second of the + two solutions returned is useful. + N=1 + indicates only one useful solution, the usual case; under these + circumstances, the second solution can be regarded as valid if + the vector V02 is interpreted as the ``over-the-pole'' case. +
4. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
5. +
This routine is the Cartesian equivalent of the routine sla_DTPS2C. +
+
+ +next + +up + +previous +
+ Next: SLA_DTT - TT minus UTC +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTPS2C - Plate centre from and +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node8.html b/src/slalib/sun67.htx/node8.html new file mode 100644 index 0000000..81261d2 --- /dev/null +++ b/src/slalib/sun67.htx/node8.html @@ -0,0 +1,85 @@ + + + + +C Version + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Future Versions +
+Up: INTRODUCTION +
+ Previous: Fortran Version +

+

+

+C Version +

+An ANSI C version of SLALIB is available from the author +but is not part of the Starlink release. +The functionality of this (proprietary) C version closely matches +that of the Starlink Fortran SLALIB, partly for the convenience of +existing users of the Fortran version, some of whom have in the past +implemented C ``wrappers''. The function names +cannot be the same as the Fortran versions because of potential +linking problems when +both forms of the library are present; the C routine which +is the equivalent of (for example) SLA_REFRO is slaRefro. +The types of arguments follow the Fortran version, except +that integers are int rather than long. +Argument passing is by value +(except for arrays and strings of course) +for given arguments and by pointer for returned arguments. +All the C functions are re-entrant. +

+The Fortran routines sla_GRESID, sla_RANDOM and +sla_WAIT have no C counterparts. +

+Further details of the C version of SLALIB are available +from the author. The definitive guide to +the calling sequences is the file slalib.h. +

+

+ +next + +up + +previous +
+ Next: Future Versions +
+Up: INTRODUCTION +
+ Previous: Fortran Version +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node80.html b/src/slalib/sun67.htx/node80.html new file mode 100644 index 0000000..e7704f5 --- /dev/null +++ b/src/slalib/sun67.htx/node80.html @@ -0,0 +1,111 @@ + + + + +SLA_DTT - TT minus UTC + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DV2TP - Direction Cosines to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTPV2C - Plate centre from and x,y,z +

+

+

SLA_DTT - TT minus UTC +   +

+
+
ACTION: +
Compute $\Delta$TT, the increment to be applied to +Coordinated Universal Time UTC to give + Terrestrial Time TT. +

CALL: +
D = sla_DTT (DJU) +

+

+
GIVEN: +
+
+ + + + + +
DJUDUTC date as a modified JD (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
sla_DTTDTT-UTC in seconds
+

+
NOTES: +
+
1. +
The UTC is specified to be a date rather than a time to indicate +that care needs to be taken not to specify an instant which lies +within a leap second. Though in most cases UTC can include the + fractional part, correct behaviour on the day of a leap second + can be guaranteed only up to the end of the second + $23^{\rm h}\,59^{\rm m}\,59^{\rm s}$.
2. +
Pre 1972 January 1 a fixed value of 10 + ET-TAI is returned. +
3. +
TT is one interpretation of the defunct timescale + Ephemeris Time, ET. +
4. +
See also the routine sla_DT, which roughly estimates ET-UT for + historical epochs. +
+
+ +next + +up + +previous +
+ Next: SLA_DV2TP - Direction Cosines to Tangent Plane +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTPV2C - Plate centre from and x,y,z +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node81.html b/src/slalib/sun67.htx/node81.html new file mode 100644 index 0000000..eba8ed9 --- /dev/null +++ b/src/slalib/sun67.htx/node81.html @@ -0,0 +1,137 @@ + + + + +SLA_DV2TP - Direction Cosines to Tangent Plane + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DVDV - Scalar Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTT - TT minus UTC +

+

+

SLA_DV2TP - Direction Cosines to Tangent Plane +   +

+
+
ACTION: +
Given the direction cosines of a star and of the tangent point, +determine the star's tangent-plane coordinates + (double precision). +

CALL: +
CALL sla_DV2TP (V, V0, XI, ETA, J) +

+

+
GIVEN: +
+
+ + + + + + + + + +
VD(3)direction cosines of star
V0D(3)direction cosines of tangent point
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
XI,ETADtangent plane coordinates (radians)
JIstatus:
0 = OK, star on tangent plane
1 = error, star too far from axis
2 = error, antistar on tangent plane
3 = error, antistar too far from axis
+

+
NOTES: +
+
1. +
If vector V0 is not of unit length, or if vector V is of zero +length, the results will be wrong. +
2. +
If V0 points at a pole, the returned $\xi,\eta$ will be based on the + arbitrary assumption that $\alpha=0$ at the tangent point. +
3. +
The projection is called the gnomonic projection; the + Cartesian coordinates $[\,\xi,\eta\,]$ are called + standard coordinates. The latter + are in units of the distance from the tangent plane to the projection + point, i.e. radians near the origin. +
4. +
This routine is the Cartesian equivalent of the routine sla_DS2TP. +
+
+ +next + +up + +previous +
+ Next: SLA_DVDV - Scalar Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DTT - TT minus UTC +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node82.html b/src/slalib/sun67.htx/node82.html new file mode 100644 index 0000000..024100b --- /dev/null +++ b/src/slalib/sun67.htx/node82.html @@ -0,0 +1,91 @@ + + + + +SLA_DVDV - Scalar Product + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DVN - Normalize Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DV2TP - Direction Cosines to Tangent Plane +

+

+

SLA_DVDV - Scalar Product +   +

+
+
ACTION: +
Scalar product of two 3-vectors (double precision). +
CALL: +
D = sla_DVDV (VA, VB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
VAD(3)first vector
VBD(3)second vector
+

+
RETURNED: +
+
+ + + + + +
sla_DVDVDscalar product VA.VB
+
+ +next + +up + +previous +
+ Next: SLA_DVN - Normalize Vector +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DV2TP - Direction Cosines to Tangent Plane +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node83.html b/src/slalib/sun67.htx/node83.html new file mode 100644 index 0000000..073d4ef --- /dev/null +++ b/src/slalib/sun67.htx/node83.html @@ -0,0 +1,95 @@ + + + + +SLA_DVN - Normalize Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_DVXV - Vector Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DVDV - Scalar Product +

+

+

SLA_DVN - Normalize Vector +   +

+
+
ACTION: +
Normalize a 3-vector, also giving the modulus (double precision). +
CALL: +
CALL sla_DVN (V, UV, VM) +

+

+
GIVEN: +
+
+ + + + + +
VD(3)vector
+

+
RETURNED: +
+
+ + + + + + + + + +
UVD(3)unit vector in direction of V
VMDmodulus of V
+

+
NOTE: +
If the modulus of V is zero, UV is set to zero as well. +
+
+ +next + +up + +previous +
+ Next: SLA_DVXV - Vector Product +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DVDV - Scalar Product +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node84.html b/src/slalib/sun67.htx/node84.html new file mode 100644 index 0000000..745d1f0 --- /dev/null +++ b/src/slalib/sun67.htx/node84.html @@ -0,0 +1,93 @@ + + + + +SLA_DVXV - Vector Product + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_E2H - to Az,El +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DVN - Normalize Vector +

+

+

SLA_DVXV - Vector Product +   +

+
+
ACTION: +
Vector product of two 3-vectors (double precision). +
CALL: +
CALL sla_DVXV (VA, VB, VC) +

+

+
GIVEN: +
+
+ + + + + + + + + +
VAD(3)first vector
VBD(3)second vector
+

+
RETURNED: +
+
+ + + + + +
VCD(3)vector product VA$\times$VB
+
+ +next + +up + +previous +
+ Next: SLA_E2H - to Az,El +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DVN - Normalize Vector +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node85.html b/src/slalib/sun67.htx/node85.html new file mode 100644 index 0000000..3c589df --- /dev/null +++ b/src/slalib/sun67.htx/node85.html @@ -0,0 +1,145 @@ + + + + +SLA_E2H - to Az,El + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EARTH - Approx Earth Pos/Vel +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DVXV - Vector Product +

+

+

    +
+SLA_E2H - $h,\delta$ to Az,El +

+
+
ACTION: +
Equatorial to horizon coordinates +(single precision). +

CALL: +
CALL sla_DE2H (HA, DEC, PHI, AZ, EL) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
HARhour angle (radians)
DECRdeclination (radians)
PHIRlatitude (radians)
+

+
RETURNED: +
+
+ + + + + + + + + +
AZRazimuth (radians)
ELRelevation (radians)
+

+
NOTES: +
+
1. +
Azimuth is returned in the range $0\!-\!2\pi$; north is zero, +and east is $+\pi/2$. Elevation is returned in the range +$\pm \pi$.
2. +
The latitude must be geodetic. In critical applications, + corrections for polar motion should be applied. +
3. +
In some applications it will be important to specify the + correct type of hour angle and declination in order to + produce the required type of azimuth and elevation. In + particular, it may be important to distinguish between + elevation as affected by refraction, which would + require the observed $[\,h,\delta\,]$, and the elevation + in vacuo, which would require the topocentric + $[\,h,\delta\,]$. If the effects of diurnal aberration can be neglected, the + apparent $[\,h,\delta\,]$ may be used instead of the topocentric + $[\,h,\delta\,]$.
4. +
No range checking of arguments is carried out. +
5. +
In applications which involve many such calculations, rather + than calling the present routine it will be more efficient to + use inline code, having previously computed fixed terms such + as sine and cosine of latitude, and (for tracking a star) + sine and cosine of declination. +
+
+ +next + +up + +previous +
+ Next: SLA_EARTH - Approx Earth Pos/Vel +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_DVXV - Vector Product +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node86.html b/src/slalib/sun67.htx/node86.html new file mode 100644 index 0000000..6507524 --- /dev/null +++ b/src/slalib/sun67.htx/node86.html @@ -0,0 +1,124 @@ + + + + +SLA_EARTH - Approx Earth Pos/Vel + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ECLEQ - Ecliptic to Equatorial +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_E2H - to Az,El +

+

+

SLA_EARTH - Approx Earth Pos/Vel +   +

+
+
ACTION: +
Approximate heliocentric position and velocity of the Earth +(single precision). +

CALL: +
CALL sla_EARTH (IY, ID, FD, PV) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
IYIyear
IDIday in year (1 = Jan 1st)
FDRfraction of day
+

+
RETURNED: +
+
+ + + + + +
PVR(6)Earth $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ (AU, AU s-1)
+

+
NOTES: +
+
1. +
The date and time is TDB (loosely ET) in a Julian calendar +which has been aligned to the ordinary Gregorian +calendar for the interval 1900 March 1 to 2100 February 28. + The year and day can be obtained by calling sla_CALYD or + sla_CLYD. +
2. +
The Earth heliocentric 6-vector is referred to the + FK4 mean equator and equinox of date. +
3. +
Maximum/RMS errors 1950-2050: +
    +
  • 13/5 $\times10^{-5}$ AU = 19200/7600 km in position +
  • 47/26 $\times10^{-10}$ AU s-1 = + 0.0070/0.0039 km s-1 in speed +
+
4. +
More accurate results are obtainable with the routine sla_EVP. +
+
+ +next + +up + +previous +
+ Next: SLA_ECLEQ - Ecliptic to Equatorial +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_E2H - to Az,El +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node87.html b/src/slalib/sun67.htx/node87.html new file mode 100644 index 0000000..5935487 --- /dev/null +++ b/src/slalib/sun67.htx/node87.html @@ -0,0 +1,97 @@ + + + + +SLA_ECLEQ - Ecliptic to Equatorial + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ECMAT - Form Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EARTH - Approx Earth Pos/Vel +

+

+

SLA_ECLEQ - Ecliptic to Equatorial +   +

+
+
ACTION: +
Transformation from ecliptic longitude and latitude to +J2000.0 $[\,\alpha,\delta\,]$.

CALL: +
CALL sla_ECLEQ (DL, DB, DATE, DR, DD) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DL,DBDecliptic longitude and latitude +(mean of date, IAU 1980 theory, radians)
DATEDTDB (formerly ET) as Modified Julian Date +(JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
DR,DDDJ2000.0 mean $[\,\alpha,\delta\,]$ (radians)
+
+ +next + +up + +previous +
+ Next: SLA_ECMAT - Form Matrix +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EARTH - Approx Earth Pos/Vel +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node88.html b/src/slalib/sun67.htx/node88.html new file mode 100644 index 0000000..895c629 --- /dev/null +++ b/src/slalib/sun67.htx/node88.html @@ -0,0 +1,106 @@ + + + + +SLA_ECMAT - Form Matrix + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ECOR - RV & Time Corrns to Sun +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ECLEQ - Ecliptic to Equatorial +

+

+

    +
+SLA_ECMAT - Form $\alpha,\delta\rightarrow\lambda,\beta$ Matrix +

+
+
ACTION: +
Form the equatorial to ecliptic rotation matrix (IAU 1980 theory). +
CALL: +
CALL sla_ECMAT (DATE, RMAT) +

+

+
GIVEN: +
+
+ + + + + +
DATEDTDB (formerly ET) as Modified Julian Date +(JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
RMATD(3,3)rotation matrix
+

+
NOTES: +
+
1. +
RMAT is matrix M in the expression +vecl = M$\cdot$vequ. +
2. +
The equator, equinox and ecliptic are mean of date. +
+

+
REFERENCE: +
Murray, C.A., Vectorial Astrometry, section 4.3. +
+
+ +next + +up + +previous +
+ Next: SLA_ECOR - RV & Time Corrns to Sun +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ECLEQ - Ecliptic to Equatorial +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node89.html b/src/slalib/sun67.htx/node89.html new file mode 100644 index 0000000..990df2a --- /dev/null +++ b/src/slalib/sun67.htx/node89.html @@ -0,0 +1,140 @@ + + + + +SLA_ECOR - RV & Time Corrns to Sun + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EG50 - B1950 to Galactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ECMAT - Form Matrix +

+

+

SLA_ECOR - RV & Time Corrns to Sun +   +

+
+
ACTION: +
Component of Earth orbit velocity and heliocentric +light time in a given direction. +

CALL: +
CALL sla_ECOR (RM, DM, IY, ID, FD, RV, TL) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
RM,DMRmean $[\,\alpha,\delta\,]$ of date (radians)
IYIyear
IDIday in year (1 = Jan 1st)
FDRfraction of day
+

+
RETURNED: +
+
+ + + + + + + + + +
RVRcomponent of Earth orbital velocity (km s-1)
TLRcomponent of heliocentric light time (s)
+

+
NOTES: +
+
1. +
The date and time is TDB (loosely ET) in a Julian calendar +which has been aligned to the ordinary Gregorian +calendar for the interval 1900 March 1 to 2100 February 28. + The year and day can be obtained by calling sla_CALYD or + sla_CLYD. +
2. +
Sign convention: +
    +
  • The velocity component is +ve when the + Earth is receding from + the given point on the sky. +
  • The light time component is +ve + when the Earth lies between the Sun and + the given point on the sky. +
+
3. +
Accuracy: +
    +
  • The velocity component is usually within 0.004 km s-1 + of the correct value and is never in error by more than + 0.007 km s-1. +
  • The error in light time correction is about + $0^{\rm s}\hspace{-0.3em}.03$ at worst, + but is usually better than $0^{\rm s}\hspace{-0.3em}.01$.
+ For applications requiring higher accuracy, see the sla_EVP routine. +
+
+ +next + +up + +previous +
+ Next: SLA_EG50 - B1950 to Galactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ECMAT - Form Matrix +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node9.html b/src/slalib/sun67.htx/node9.html new file mode 100644 index 0000000..a9d8058 --- /dev/null +++ b/src/slalib/sun67.htx/node9.html @@ -0,0 +1,75 @@ + + + + +Future Versions + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: New Functions +
+Up: INTRODUCTION +
+ Previous: C Version +

+

+

+Future Versions +

+The homogeneity and ease of use of SLALIB could perhaps be improved +in the future +by turning to C++ and object-oriented techniques. For example ``celestial +position'' could be a class and many of the transformations +could happen automatically. This requires further study and +would almost certainly result in a complete redesign. +Similarly, +the impact of Fortran 90 has yet to be assessed. Once compilers +become widely available, some internal recoding may be worthwhile +in order to simplify parts of the code. However, as with C++, +a redesign of the +application interfaces will be needed if the capabilities of the +new language are to be exploited to the full. +

+

+ +next + +up + +previous +
+ Next: New Functions +
+Up: INTRODUCTION +
+ Previous: C Version +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node90.html b/src/slalib/sun67.htx/node90.html new file mode 100644 index 0000000..1deba43 --- /dev/null +++ b/src/slalib/sun67.htx/node90.html @@ -0,0 +1,106 @@ + + + + +SLA_EG50 - B1950 to Galactic + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EL2UE - Conventional to Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ECOR - RV & Time Corrns to Sun +

+

+

    +
+SLA_EG50 - B1950 $\alpha,\delta$ to Galactic +

+
+
ACTION: +
Transformation from B1950.0 FK4 equatorial coordinates to +IAU 1958 galactic coordinates. +

CALL: +
CALL sla_EG50 (DR, DD, DL, DB) +

+

+
GIVEN: +
+
+ + + + + +
DR,DDDB1950.0 $[\,\alpha,\delta\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
DL,DBDgalactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$ (radians)
+

+
NOTE: +
The equatorial coordinates are B1950.0 FK4. Use the +routine sla_EQGAL if conversion from J2000.0 FK5 coordinates + is required. +
+

+
REFERENCE: +
Blaauw et al., 1960, Mon.Not.R.astr.Soc., +121, 123. +
+
+ +next + +up + +previous +
+ Next: SLA_EL2UE - Conventional to Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_ECOR - RV & Time Corrns to Sun +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node91.html b/src/slalib/sun67.htx/node91.html new file mode 100644 index 0000000..2beedff --- /dev/null +++ b/src/slalib/sun67.htx/node91.html @@ -0,0 +1,330 @@ + + + + +SLA_EL2UE - Conventional to Universal Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EPB - MJD to Besselian Epoch +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EG50 - B1950 to Galactic +

+

+

SLA_EL2UE - Conventional to Universal Elements +   +

+
+
ACTION: +
Transform conventional osculating orbital elements +into ``universal'' form. +

CALL: +
CALL sla_EL2UE ( + DATE, JFORM, EPOCH, ORBINC, ANODE, + PERIH, AORQ, E, AORL, DM, + U, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDepoch (TT MJD) of osculation (Note 3)
JFORMIchoice of element set (1-3; Note 6)
EPOCHDepoch of elements (t0 or T, TT MJD)
ORBINCDinclination (i, radians)
ANODEDlongitude of the ascending node ($\Omega$, radians)
PERIHDlongitude or argument of perihelion +($\varpi$ or $\omega$,
radians)
AORQDmean distance or perihelion distance (a or q, AU)
EDeccentricity (e)
AORLDmean anomaly or longitude +(M or L, radians,
JFORM=1,2 only)
DMDdaily motion (n, radians, JFORM=1 only)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal orbital elements (Note 1)
(1)combined mass (M+m)
(2)total energy of the orbit ($\alpha$)
(3)reference (osculating) epoch (t0)
(4-6)position at reference epoch (${\rm \bf r}_0$)
(7-9)velocity at reference epoch (${\rm \bf v}_0$)
(10)heliocentric distance at reference epoch
(11)${\rm \bf r}_0.{\rm \bf v}_0$
(12)date (t)
(13)universal eccentric anomaly ($\psi$) of date, +approx
   
JSTATIstatus:
0 = OK
-1 = illegal JFORM
-2 = illegal E
-3 = illegal AORQ
-4 = illegal DM
-5 = numerical error
+

+
NOTES: +
+
1. +
The ``universal'' elements are those which define the orbit for +the purposes of the method of universal variables (see reference). +They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) $\alpha$, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, + (iii) the outwards component of the velocity at the given epoch, + (iv) an estimate of $\psi$, the ``universal eccentric anomaly'' at a + given date and (v) that date. +
2. +
The companion routine is sla_UE2PV. This takes the set of numbers + that the present routine outputs and uses them to derive the + object's position and velocity. A single prediction requires one + call to the present routine followed by one call to sla_UE2PV; + for convenience, the two calls are packaged as the routine + sla_PLANEL. Multiple predictions may be made by again calling the + present routine once, but then calling sla_UE2PV multiple times, + which is faster than multiple calls to sla_PLANEL. +
3. +
DATE is the epoch of osculation. It is in the TT timescale + (formerly Ephemeris Time, ET) and is a Modified Julian Date + (JD-2400000.5). +
4. +
The supplied orbital elements are with respect to the J2000 + ecliptic and equinox. The position and velocity parameters + returned in the array U are with respect to the mean equator and + equinox of epoch J2000, and are for the perihelion prior to the + specified epoch. +
5. +
The universal elements returned in the array U are in canonical + units (solar masses, AU and canonical days). +
6. +
Three different element-format options are supported, as + follows.
+

+JFORM=1, suitable for the major planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 longitude of perihelion $\varpi$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean longitude L (radians)
+		 DM 		 = 		 daily motion n (radians)        
+
+

+JFORM=2, suitable for minor planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e \leq 10 )$
+
7. +
Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are + not accessed. +
8. +
The algorithm was originally adapted from the EPHSLA program of + D.H.P.Jones (private communication, 1996). The method + is based on Stumpff's Universal Variables. +
+

+
REFERENCE: +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_EPB - MJD to Besselian Epoch +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EG50 - B1950 to Galactic +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node92.html b/src/slalib/sun67.htx/node92.html new file mode 100644 index 0000000..854488f --- /dev/null +++ b/src/slalib/sun67.htx/node92.html @@ -0,0 +1,91 @@ + + + + +SLA_EPB - MJD to Besselian Epoch + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EPB2D - Besselian Epoch to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EL2UE - Conventional to Universal Elements +

+

+

SLA_EPB - MJD to Besselian Epoch +   +

+
+
ACTION: +
Conversion of Modified Julian Date to Besselian Epoch. +
CALL: +
D = sla_EPB (DATE) +

+

+
GIVEN: +
+
+ + + + + +
DATEDModified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
sla_EPBDBesselian Epoch
+

+
REFERENCE: +
Lieske, J.H., 1979, Astr.Astrophys. 73, 282. +
+
+ +next + +up + +previous +
+ Next: SLA_EPB2D - Besselian Epoch to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EL2UE - Conventional to Universal Elements +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node93.html b/src/slalib/sun67.htx/node93.html new file mode 100644 index 0000000..c142fe7 --- /dev/null +++ b/src/slalib/sun67.htx/node93.html @@ -0,0 +1,91 @@ + + + + +SLA_EPB2D - Besselian Epoch to MJD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EPCO - Convert Epoch to B or J +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPB - MJD to Besselian Epoch +

+

+

SLA_EPB2D - Besselian Epoch to MJD +   +

+
+
ACTION: +
Conversion of Besselian Epoch to Modified Julian Date. +
CALL: +
D = sla_EPB2D (EPB) +

+

+
GIVEN: +
+
+ + + + + +
EPBDBesselian Epoch
+

+
RETURNED: +
+
+ + + + + +
sla_EPB2DDModified Julian Date (JD-2400000.5)
+

+
REFERENCE: +
Lieske, J.H., 1979. Astr.Astrophys. 73, 282. +
+
+ +next + +up + +previous +
+ Next: SLA_EPCO - Convert Epoch to B or J +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPB - MJD to Besselian Epoch +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node94.html b/src/slalib/sun67.htx/node94.html new file mode 100644 index 0000000..e71fda8 --- /dev/null +++ b/src/slalib/sun67.htx/node94.html @@ -0,0 +1,110 @@ + + + + +SLA_EPCO - Convert Epoch to B or J + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EPJ - MJD to Julian Epoch +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPB2D - Besselian Epoch to MJD +

+

+

SLA_EPCO - Convert Epoch to B or J +   +

+
+
ACTION: +
Convert an epoch to Besselian or Julian to match another one. +
CALL: +
D = sla_EPCO (K0, K, E) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
K0Cform of result: `B'=Besselian, `J'=Julian
KCform of given epoch: `B' or `J'
EDepoch
+

+
RETURNED: +
+
+ + + + + +
sla_EPCODthe given epoch converted as necessary
+

+
NOTES: +
+
1. +
The result is always either equal to or very close to +the given epoch E. The routine is required only in +applications where punctilious treatment of heterogeneous + mixtures of star positions is necessary. +
2. +
K0 and K are not validated. They are interpreted as follows: +
    +
  • If K0 and K are the same, the result is E. +
  • If K0 is `B' and K isn't, the conversion is J to B. +
  • In all other cases, the conversion is B to J. +
+
+ +next + +up + +previous +
+ Next: SLA_EPJ - MJD to Julian Epoch +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPB2D - Besselian Epoch to MJD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node95.html b/src/slalib/sun67.htx/node95.html new file mode 100644 index 0000000..aefb9d6 --- /dev/null +++ b/src/slalib/sun67.htx/node95.html @@ -0,0 +1,91 @@ + + + + +SLA_EPJ - MJD to Julian Epoch + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EPJ2D - Julian Epoch to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPCO - Convert Epoch to B or J +

+

+

SLA_EPJ - MJD to Julian Epoch +   +

+
+
ACTION: +
Convert Modified Julian Date to Julian Epoch. +
CALL: +
D = sla_EPJ (DATE) +

+

+
GIVEN: +
+
+ + + + + +
DATEDModified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
sla_EPJDJulian Epoch
+

+
REFERENCE: +
Lieske, J.H., 1979. Astr.Astrophys., 73, 282. +
+
+ +next + +up + +previous +
+ Next: SLA_EPJ2D - Julian Epoch to MJD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPCO - Convert Epoch to B or J +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node96.html b/src/slalib/sun67.htx/node96.html new file mode 100644 index 0000000..c0f38a9 --- /dev/null +++ b/src/slalib/sun67.htx/node96.html @@ -0,0 +1,91 @@ + + + + +SLA_EPJ2D - Julian Epoch to MJD + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EQECL - J2000 to Ecliptic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPJ - MJD to Julian Epoch +

+

+

SLA_EPJ2D - Julian Epoch to MJD +   +

+
+
ACTION: +
Convert Julian Epoch to Modified Julian Date. +
CALL: +
D = sla_EPJ2D (EPJ) +

+

+
GIVEN: +
+
+ + + + + +
EPJDJulian Epoch
+

+
RETURNED: +
+
+ + + + + +
sla_EPJ2DDModified Julian Date (JD-2400000.5)
+

+
REFERENCE: +
Lieske, J.H., 1979. Astr.Astrophys., 73, 282. +
+
+ +next + +up + +previous +
+ Next: SLA_EQECL - J2000 to Ecliptic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPJ - MJD to Julian Epoch +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node97.html b/src/slalib/sun67.htx/node97.html new file mode 100644 index 0000000..a386ad5 --- /dev/null +++ b/src/slalib/sun67.htx/node97.html @@ -0,0 +1,98 @@ + + + + +SLA_EQECL - J2000 to Ecliptic + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EQEQX - Equation of the Equinoxes +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPJ2D - Julian Epoch to MJD +

+

+

    +
+SLA_EQECL - J2000 $\alpha,\delta$ to Ecliptic +

+
+
ACTION: +
Transformation from J2000.0 equatorial coordinates to +ecliptic longitude and latitude. +

CALL: +
CALL sla_EQECL (DR, DD, DATE, DL, DB) +

+

+
GIVEN: +
+
+ + + + + + + + + +
DR,DDDJ2000.0 mean $[\,\alpha,\delta\,]$ (radians)
DATEDTDB (formerly ET) as Modified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
DL,DBDecliptic longitude and latitude +(mean of date, IAU 1980 theory, radians)
+
+ +next + +up + +previous +
+ Next: SLA_EQEQX - Equation of the Equinoxes +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EPJ2D - Julian Epoch to MJD +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node98.html b/src/slalib/sun67.htx/node98.html new file mode 100644 index 0000000..e5a2cc7 --- /dev/null +++ b/src/slalib/sun67.htx/node98.html @@ -0,0 +1,111 @@ + + + + +SLA_EQEQX - Equation of the Equinoxes + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EQGAL - J2000 to Galactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EQECL - J2000 to Ecliptic +

+

+

SLA_EQEQX - Equation of the Equinoxes +   +

+
+
ACTION: +
Equation of the equinoxes (IAU 1994). +
CALL: +
D = sla_EQEQX (DATE) +

+

+
GIVEN: +
+
+ + + + + +
DATEDTDB (formerly ET) as Modified Julian Date (JD-2400000.5)
+

+
RETURNED: +
+
+ + + + + +
sla_EQEQXDThe equation of the equinoxes (radians)
+

+
NOTES: +
+
1. +
The equation of the equinoxes is defined here as GAST - GMST: +it is added to a mean sidereal time to give the +apparent sidereal time. +
2. +
The change from the classic ``textbook'' expression + $\Delta\psi\,cos\,\epsilon$ occurred with IAU Resolution C7, + Recommendation 3 (1994). The new formulation takes into + account cross-terms between the various precession and + nutation quantities, amounting to about 3 milliarcsec. + The transition from the old to the new model officially + takes place on 1997 February 27. +
+

+
REFERENCE: +
Capitaine, N. & Gontier, A.-M. (1993), +Astron. Astrophys., + 275, 645-650. +
+
+ +next + +up + +previous +
+ Next: SLA_EQGAL - J2000 to Galactic +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EQECL - J2000 to Ecliptic +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/node99.html b/src/slalib/sun67.htx/node99.html new file mode 100644 index 0000000..1e4582a --- /dev/null +++ b/src/slalib/sun67.htx/node99.html @@ -0,0 +1,105 @@ + + + + +SLA_EQGAL - J2000 to Galactic + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_ETRMS - E-terms of Aberration +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EQEQX - Equation of the Equinoxes +

+

+

    +
+SLA_EQGAL - J2000 $\alpha,\delta$ to Galactic +

+
+
ACTION: +
Transformation from J2000.0 FK5 equatorial coordinates to +IAU 1958 galactic coordinates. +

CALL: +
CALL sla_EQGAL (DR, DD, DL, DB) +

+

+
GIVEN: +
+
+ + + + + +
DR,DDDJ2000.0 $[\,\alpha,\delta\,]$ (radians)
+

+
RETURNED: +
+
+ + + + + +
DL,DBDgalactic longitude and latitude $[\,l^{I\!I},b^{I\!I}\,]$ (radians)
+

+
NOTE: +
The equatorial coordinates are J2000.0 FK5. Use the routine +sla_EG50 if conversion from B1950.0 FK4 coordinates is required. +
+

+
REFERENCE: +
Blaauw et al., 1960, Mon.Not.R.astr.Soc., +121, 123. +
+
+ +next + +up + +previous +
+ Next: SLA_ETRMS - E-terms of Aberration +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EQEQX - Equation of the Equinoxes +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/orangeball.gif b/src/slalib/sun67.htx/orangeball.gif new file mode 100644 index 0000000..e757cd0 Binary files /dev/null and b/src/slalib/sun67.htx/orangeball.gif differ diff --git a/src/slalib/sun67.htx/pinkball.gif b/src/slalib/sun67.htx/pinkball.gif new file mode 100644 index 0000000..43e843b Binary files /dev/null and b/src/slalib/sun67.htx/pinkball.gif differ diff --git a/src/slalib/sun67.htx/previous_group_motif.gif b/src/slalib/sun67.htx/previous_group_motif.gif new file mode 100644 index 0000000..03ea0dc Binary files /dev/null and b/src/slalib/sun67.htx/previous_group_motif.gif differ diff --git a/src/slalib/sun67.htx/previous_group_motif_gr.gif b/src/slalib/sun67.htx/previous_group_motif_gr.gif new file mode 100644 index 0000000..c7a1e2b Binary files /dev/null and b/src/slalib/sun67.htx/previous_group_motif_gr.gif differ diff --git a/src/slalib/sun67.htx/previous_motif.gif b/src/slalib/sun67.htx/previous_motif.gif new file mode 100644 index 0000000..aef90f1 Binary files /dev/null and b/src/slalib/sun67.htx/previous_motif.gif differ diff --git a/src/slalib/sun67.htx/previous_motif_gr.gif b/src/slalib/sun67.htx/previous_motif_gr.gif new file mode 100644 index 0000000..c6acaab Binary files /dev/null and b/src/slalib/sun67.htx/previous_motif_gr.gif differ diff --git a/src/slalib/sun67.htx/purpleball.gif b/src/slalib/sun67.htx/purpleball.gif new file mode 100644 index 0000000..4836265 Binary files /dev/null and b/src/slalib/sun67.htx/purpleball.gif differ diff --git a/src/slalib/sun67.htx/redball.gif b/src/slalib/sun67.htx/redball.gif new file mode 100644 index 0000000..b1a9580 Binary files /dev/null and b/src/slalib/sun67.htx/redball.gif differ diff --git a/src/slalib/sun67.htx/source.gif b/src/slalib/sun67.htx/source.gif new file mode 100755 index 0000000..c8dea79 Binary files /dev/null and b/src/slalib/sun67.htx/source.gif differ diff --git a/src/slalib/sun67.htx/sun67.css b/src/slalib/sun67.htx/sun67.css new file mode 100644 index 0000000..3970428 --- /dev/null +++ b/src/slalib/sun67.htx/sun67.css @@ -0,0 +1,10 @@ + +SMALL.TINY { font-size : xx-small } +SMALL.SCRIPTSIZE { font-size : xx-small } +SMALL.FOOTNOTESIZE { font-size : x-small } +SMALL.SMALL { font-size : small } +BIG.LARGE { font-size : large } +BIG.XLARGE { font-size : x-large } +BIG.XXLARGE { font-size : xx-large } +BIG.HUGE { font-size : xx-large } +BIG.XHUGE { font-size : xx-large } diff --git a/src/slalib/sun67.htx/sun67.html b/src/slalib/sun67.htx/sun67.html new file mode 100644 index 0000000..1836213 --- /dev/null +++ b/src/slalib/sun67.htx/sun67.html @@ -0,0 +1,610 @@ + + + + +SLALIB -- Positional Astronomy Library + + + + + + + + + +
+ +next +up +previous +
+ Next: Abstract +
+

+

+

  +

+ SLALIB -- Positional Astronomy Library +
+2.4-0 +
+Programmer's Manual +

+

+ Starlink User Note67.45 +
+P.T.Wallace +
+12 October 1999 +

+ CCLRC +/ + Rutherford Appleton Laboratory +
+ Particle Physics & Astronomy Research Council +
+

+ Starlink Project +

+ Retrieve hardcopy +
+ 
+

Contents

+


+ +  + + +
+ +next +up +previous +
+ Next: Abstract +
+

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + diff --git a/src/slalib/sun67.htx/up_motif.gif b/src/slalib/sun67.htx/up_motif.gif new file mode 100644 index 0000000..3d1aebf Binary files /dev/null and b/src/slalib/sun67.htx/up_motif.gif differ diff --git a/src/slalib/sun67.htx/up_motif_gr.gif b/src/slalib/sun67.htx/up_motif_gr.gif new file mode 100644 index 0000000..a8b463a Binary files /dev/null and b/src/slalib/sun67.htx/up_motif_gr.gif differ diff --git a/src/slalib/sun67.htx/whiteball.gif b/src/slalib/sun67.htx/whiteball.gif new file mode 100644 index 0000000..4a90ea1 Binary files /dev/null and b/src/slalib/sun67.htx/whiteball.gif differ diff --git a/src/slalib/sun67.htx/yellowball.gif b/src/slalib/sun67.htx/yellowball.gif new file mode 100644 index 0000000..c6ba6b1 Binary files /dev/null and b/src/slalib/sun67.htx/yellowball.gif differ -- cgit