### SLA_MAPPA

Mean to Apparent Parameters

ACTION:
Compute star-independent parameters in preparation for conversions between mean place and geocentric apparent place. The parameters produced by this routine are required in the parallax, light deflection, aberration, and precession-nutation parts of the mean/apparent transformations. The reference frames and time scales used are post IAU 1976.
CALL:
CALL sla_MAPPA (EQ, DATE, AMPRMS)
##### GIVEN:
 EQ D epoch of mean equinox to be used (Julian) DATE D TDB (JD$-$2400000.5)

##### RETURNED:
 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

NOTES:
(1)
For DATE, the distinction between the required TDB and TT is always negligible. Moreover, for all but the most critical applications UTC is adequate.
(2)
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.
(3)
The parameters produced by this routine are used by sla_MAPQK, sla_MAPQKZ and sla_AMPQK.
(4)
The accuracy, starting from ICRS star data, is limited to about 1 mas by the precession-nutation model used, SF2001. A different precession-nutation model can be introduced by first calling the present routine and then replacing the precession-nutation matrix in AMPRMS(13-21) directly.
(5)
A further limit to the accuracy of routines using the parameter array AMPRMS is imposed by the routine sla_EVP, used here to compute the Earth position and velocity by the methods of Stumpff. The maximum error in the resulting aberration corrections is about 0.3 milliarcsecond.
REFERENCES:
(1)
1984 Astronomical Almanac, pp B39-B41.
(2)
Lederle & Schwan, 1984. Astr.Astrophys. 134, 1-6.