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author: Joseph Hunkeler <jhunkeler@gmail.com> 2015-03-04 21:21:30 -0500
committer: Joseph Hunkeler <jhunkeler@gmail.com> 2015-03-04 21:21:30 -0500
commit: d54fe7c1f704a63824c5bfa0ece65245572e9b27 (patch)
tree: afc52015ffc2c74e0266653eecef1c8ef8ba5d91 /src/slalib/sun67.htx/node212.html
download: calfuse-d54fe7c1f704a63824c5bfa0ece65245572e9b27.tar.gz
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+<!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 -->
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+<TITLE>Mean Place to Apparent Place</TITLE>
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+<BR> <HR> <P>
+<P><!--End of Navigation Panel-->
+<H2><A NAME="SECTION000512000000000000000">
+Mean Place to Apparent Place</A>
+</H2>
+The <I>geocentric apparent place</I> of a source, or <I>apparent place</I>
+for short,
+is the <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> if viewed from the centre of the Earth,
+with respect to the true equator and equinox of date.
+Transformation of an FK5 mean <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$">, equinox J2000,
+current epoch, to apparent place involves the following effects:
+<P><UL>
+<LI> Light deflection - the gravitational lens effect of
+         the sun.
+<LI> Annual aberration.
+<LI> Precession/nutation.
+</UL>
+The <I>light deflection</I> is seldom significant.  Its value
+at the limb of the Sun is about
+<P>      <IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img294.gif"
+ ALT="$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.74$">   ;  it falls off rapidly with distance from the
+Sun and has shrunk to about
+<P>      <IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img295.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.02$">    at an elongation of <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img296.gif"
+ ALT="$20^\circ$">.<P>
+As already described, the <I>annual aberration</I>
+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 
+      <IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img265.gif"
+ ALT="$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$">   .
+<P>
+The <I>precession/nutation</I>, from J2000 to the current epoch, is
+expressed by a rotation matrix which is available through the
+SLALIB routine
+sla_PRENUT.
+<P>
+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
+<I>North Polar Distance</I> (<IMG WIDTH="54" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
+ SRC="img297.gif"
+ ALT="$90^\circ-\delta$">) of Polaris for
+the decade of closest approach to the Pole:
+<P><PRE>
+            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
+</PRE>
+<P>
+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 <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> 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.
+<P>
+The routines
+sla_AMP
+and
+sla_AMPQK
+allow the reverse transformation, from apparent to mean place.
+<P>
+<BR> <HR>
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+<BR>
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+<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>
author	Joseph Hunkeler <jhunkeler@gmail.com>	2015-03-04 21:21:30 -0500
committer	Joseph Hunkeler <jhunkeler@gmail.com>	2015-03-04 21:21:30 -0500
commit	d54fe7c1f704a63824c5bfa0ece65245572e9b27 (patch)
tree	afc52015ffc2c74e0266653eecef1c8ef8ba5d91 /src/slalib/sun67.htx/node212.html
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