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| author | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
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| committer | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
| commit | d54fe7c1f704a63824c5bfa0ece65245572e9b27 (patch) | |
| tree | afc52015ffc2c74e0266653eecef1c8ef8ba5d91 /src/slalib/sun67.htx/node211.html | |
| download | calfuse-d54fe7c1f704a63824c5bfa0ece65245572e9b27.tar.gz | |
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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 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) + by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds +* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan +* with significant contributions from: + Jens Lippman, Marek Rouchal, Martin Wilck and others --> +<HTML> +<HEAD> +<TITLE>Mean Place Transformations</TITLE> +<META NAME="description" CONTENT="Mean Place Transformations"> +<META NAME="keywords" CONTENT="sun67"> +<META NAME="resource-type" CONTENT="document"> +<META NAME="distribution" CONTENT="global"> +<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"> +<LINK REL="STYLESHEET" HREF="sun67.css"> +<LINK REL="next" HREF="node212.html"> +<LINK REL="previous" HREF="node210.html"> +<LINK REL="up" HREF="node197.html"> +<LINK REL="next" HREF="node212.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html2561" HREF="node212.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2559" HREF="node197.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2553" HREF="node210.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2562" HREF="node212.html">Mean Place to Apparent Place</A> +<BR> +<B>Up:</B> <A NAME="tex2html2560" HREF="node197.html">EXPLANATION AND EXAMPLES</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2554" HREF="node210.html">Different Sorts of Mean Place</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<H2><A NAME="SECTION000511000000000000000"> +Mean Place Transformations</A> +</H2> +Figure 1 is based upon three varieties of mean <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> all of which are +of practical significance to observing astronomers in the present era: +<UL> +<LI> Old style (FK4) with known proper motion in the FK4 + system, and with parallax and radial velocity either + known or assumed zero. +<LI> Old style (FK4) with zero proper motion in FK5, + and with parallax and radial velocity assumed zero. +<LI> New style (FK5) with proper motion, parallax and + radial velocity either known or assumed zero. +</UL> +The figure outlines the steps required to convert positions in +any of these systems to a J2000 <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> 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 <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$">.Only in the (common) cases of FK4, equinox and epoch B1950, +to FK5, equinox and epoch J2000, and <I>vice versa</I> are +proper motion, parallax and radial velocity transformed +along with the star position itself, the +focus of SLALIB support. +<P> +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 <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> of arbitrary equinox and epoch and with +known proper motion and +parallax is transformed into an FK5 J2000 <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> for the current +epoch. As a test star we will use <IMG WIDTH="30" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img285.gif" + ALT="$\alpha=$"><IMG WIDTH="104" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" + SRC="img286.gif" + ALT="$16^{h}\,09^{m}\,55^{s}.13$">,<IMG WIDTH="28" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img287.gif" + ALT="$\delta=$"><IMG WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0" + SRC="img288.gif" + ALT="$-75^{\circ}\,59^{'}\,27^{''}.2$">, equinox 1900, epoch 1963.087, +<IMG WIDTH="38" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img289.gif" + ALT="$\mu_\alpha=$"><IMG WIDTH="61" HEIGHT="26" ALIGN="MIDDLE" BORDER="0" + SRC="img290.gif" + ALT="$-0^{\rm s}\hspace{-0.3em}.0312$">/<I>y</I>, <IMG WIDTH="36" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img291.gif" + ALT="$\mu_\delta=$"> <IMG WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0" + SRC="img292.gif" + ALT="$+0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.103$"> /<I>y</I>, +parallax = + <IMG WIDTH="39" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img293.gif" + ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.062$"> , radial velocity = -34.22 km/s. The +epoch of observation is 1994.35. +<P><PRE> + 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) + : +</PRE> +<P> +It is interesting to look at how the <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> changes during the +course of the calculation: +<PRE><TT> + <TT>16 09 55.130 -75 59 27.20</TT> <I>original equinox and epoch</I> + <TT>16 09 54.155 -75 59 23.98</TT> <I>with space motion</I> + <TT>16 09 54.229 -75 59 24.18</TT> <I>with old E-terms removed</I> + <TT>16 16 28.213 -76 06 54.57</TT> <I>precessed to 1950.0</I> + <TT>16 16 28.138 -76 06 54.37</TT> <I>with new E-terms</I> + <TT>16 23 07.901 -76 13 58.87</TT> <I>J2000, current epoch</I> + <TT>16 23 07.907 -76 13 58.92</TT> <I>including parallax</I> +</TT></PRE> +<P> +Other remarks about the above (unusually complicated) example: +<UL> +<LI> If the original equinox and epoch were B1950, as is quite + likely, then it would be unnecessary to treat space motions + and E-terms explicitly. Transformation to FK5 J2000 could + be accomplished simply by calling +sla_FK425, after which + a call to +sla_PM and the parallax code would complete the + work. +<LI> The rigorous treatment of the E-terms + has only a small effect on the result. Such refinements + are, nevertheless, worthwhile in order to facilitate comparisons and + to increase the chances that star positions from different + suppliers are compatible. +<LI> The FK4 to FK5 transformations, +sla_FK425 + and +sla_FK45Z, + are not as is sometimes assumed simply 50 years of precession, + though this indeed accounts for most of the change. The + transformations also include adjustments + to the equinox, a revised precession model, elimination of the + E-terms, a change to the proper-motion time unit and so on. + The reason there are two routines rather than just one + is that the FK4 frame rotates relative to the background, whereas + the FK5 frame is a much better approximation to an + inertial frame, and zero proper + motion in FK4 does not, therefore, mean zero proper motion in FK5. + SLALIB also provides two routines, +sla_FK524 + and +sla_FK54Z, + to perform the inverse transformations. +<LI> Some star catalogues (FK4 itself is one) were constructed using slightly + different procedures for the polar regions compared with + elsewhere. SLALIB ignores this inhomogeneity and always + applies the standard + transformations irrespective of location on the celestial sphere. +</UL> +<BR> <HR> +<A NAME="tex2html2561" HREF="node212.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2559" HREF="node197.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2553" HREF="node210.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2562" HREF="node212.html">Mean Place to Apparent Place</A> +<BR> +<B>Up:</B> <A NAME="tex2html2560" HREF="node197.html">EXPLANATION AND EXAMPLES</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2554" HREF="node210.html">Different Sorts of Mean Place</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<ADDRESS> +<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I> +</ADDRESS> +</BODY> +</HTML> |