### SLA_MAPQK

Quick Mean to Apparent

ACTION:
Quick mean to apparent place: transform a star $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ from mean place to geocentric apparent place, given the star-independent parameters. The reference frames and time scales used are post IAU 1976.
CALL:
CALL sla_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)
##### GIVEN:
 RM,DM D mean $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ (radians) PR,PD D proper motions: $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ changes per Julian year PX D parallax (arcsec) RV D radial velocity (km s${}^{-1}$, +ve if receding) AMPRMS D(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)$×2/$(Sun-Earth distance) (9-11) v: barycentric Earth velocity in units of c (12) $\sqrt{1-{\left|\text{v}\right|}^{2}}$ (13-21) precession-nutation $3×3$ matrix

##### RETURNED:
 RA,DA D apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ (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 (in essence) referred to the mean equinox and equator of epoch EQ. For EQ=2000D0, they are referred to the ICRS.
(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\phantom{\rule{-0.54753pt}{0ex}}$${}^{\prime }{\phantom{\rule{-1.09506pt}{0ex}}}^{\prime }$ of the centre of the Sun’s disc. The term has a maximum value of about ′′185 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.