; it falls off rapidly with distance from the Sun and has shrunk to about
at an elongation of .
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 .
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 () 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 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.
SLALIB --- Positional Astronomy Library