### SLA_FK45Z

FK4 to FK5, no P.M. or Parallax

ACTION:
Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero proper motion in the FK5 frame. This routine converts stars from the old, Bessel-Newcomb, FK4 system to the new, IAU 1976, FK5, Fricke system, in such a way that the FK5 proper motion is zero. Because such a star has, in general, a non-zero proper motion in the FK4 system, the routine requires the epoch at which the position in the FK4 system was determined. The method is from appendix 2 of reference 1, but using the constants of reference 4.
CALL:
CALL sla_FK45Z (R1950, D1950, BEPOCH, R2000, D2000)
##### GIVEN:
 R1950 D B1950.0 FK4 $\alpha$ at epoch BEPOCH (radians) D1950 D B1950.0 FK4 $\delta$ at epoch BEPOCH (radians) BEPOCH D Besselian epoch (e.g. 1979.3D0)

##### RETURNED:
 R2000 D J2000.0 FK5 $\alpha$ (radians) D2000 D J2000.0 FK5 $\delta$ (radians)

NOTES:
(1)
The epoch BEPOCH is strictly speaking Besselian, but if a Julian epoch is supplied the result will be affected only to a negligible extent.
(2)
Conversion from Besselian epoch 1950.0 to Julian epoch 2000.0 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 FK45Z 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)
REFERENCES:
(1)
Aoki, S., et al., 1983. Astr.Astrophys., 128, 263.
(2)
Smith, C.A. et al., 1989. Astr.J. 97, 265.
(3)
Yallop, B.D. et al., 1989. Astr.J. 97, 274.
(4)
Seidelmann, P.K. (ed), 1992. Explanatory Supplement to the Astronomical Almanac, ISBN 0-935702-68-7.