### SLA_FK524

FK5 to FK4

ACTION:
Convert J2000.0 FK5 star data to B1950.0 FK4. This routine converts stars from the new, IAU 1976, FK5, Fricke system, to the old, Bessel-Newcomb, FK4 system. The precepts of Smith et al. (reference 1) are followed, using the implementation by Yallop et al. (reference 2) of a matrix method due to Standish. Kinoshita’s development of Andoyer’s post-Newcomb precession is used. The numerical constants from Seidelmann et al. (reference 3) are used canonically.
CALL:
CALL sla_FK524 (R2000, D2000, DR2000, DD2000, P2000, V2000, R1950, D1950, DR1950, DD1950, P1950, V1950)
##### GIVEN:
 R2000 D J2000.0 $\alpha$ (radians) D2000 D J2000.0 $\delta$ (radians) DR2000 D J2000.0 proper motion in $\alpha$ (radians per Julian year) DD2000 D J2000.0 proper motion in $\delta$ (radians per Julian year) P2000 D J2000.0 parallax (arcsec) V2000 D J2000 radial velocity (km s${}^{-1}$, +ve = moving away)

##### RETURNED:
 R1950 D B1950.0 $\alpha$ (radians) D1950 D B1950.0 $\delta$ (radians) DR1950 D B1950.0 proper motion in $\alpha$ (radians per tropical year) DD1950 D B1950.0 proper motion in $\delta$ (radians per tropical year) P1950 D B1950.0 parallax (arcsec) V1950 D radial velocity (km s${}^{-1}$, +ve = moving away)

NOTES:
(1)
The $\alpha$ proper motions are $\stackrel{̇}{\alpha }$ rather than $\stackrel{̇}{\alpha }cos\delta$, and are per year rather than per century.
(2)
Note that conversion from Julian epoch 2000.0 to Besselian epoch 1950.0 only is provided for. Conversions involving other epochs will require use of the appropriate precession, proper motion, and E-terms routines before and/or after FK524 is called.
(3)
In the FK4 catalogue the proper motions of stars within $1{0}^{\circ }$ of the poles do not include the differential E-terms effect and should, strictly speaking, be handled in a different manner from stars outside these regions. However, given the general lack of homogeneity of the star data available for routine astrometry, the difficulties of handling positions that may have been determined from astrometric fields spanning the polar and non-polar regions, the likelihood that the differential E-terms effect was not taken into account when allowing for proper motion in past astrometry, and the undesirability of a discontinuity in the algorithm, the decision has been made in this routine to include the effect of differential E-terms on the proper motions for all stars, whether polar or not. At epoch 2000, and measuring on the sky rather than in terms of $\Delta \alpha$, the errors resulting from this simplification are less than 1 milliarcsecond in position and 1 milliarcsecond per century in proper motion.
(4)