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/node212.html | 171 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 171 insertions(+) create mode 100644 src/slalib/sun67.htx/node212.html (limited to 'src/slalib/sun67.htx/node212.html') 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 +
+ + -- cgit