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SUBROUTINE sla_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)
*+
* - - - - - -
* M A P Q K
* - - - - - -
*
* Quick mean to apparent place: transform a star RA,Dec from
* mean place to geocentric apparent place, given the
* star-independent parameters.
*
* 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.
*
* If the parallax and proper motions are zero the sla_MAPQKZ
* routine can be used instead.
*
* The reference frames and timescales used are post IAU 1976.
*
* Given:
* RM,DM d mean RA,Dec (rad)
* PR,PD d proper motions: RA,Dec changes per Julian year
* PX d parallax (arcsec)
* RV d radial velocity (km/sec, +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) (grav rad Sun)*2/(Sun-Earth distance)
* (9-11) barycentric Earth velocity in units of c
* (12) sqrt(1-v**2) where v=modulus(ABV)
* (13-21) precession/nutation (3,3) matrix
*
* Returned:
* RA,DA d apparent RA,Dec (rad)
*
* References:
* 1984 Astronomical Almanac, pp B39-B41.
* (also Lederle & Schwan, Astron. Astrophys. 134,
* 1-6, 1984)
*
* Notes:
*
* 1) The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
* the mean equinox and equator of epoch EQ.
*
* 2) 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 arcsec of the
* centre of the Sun's disc. The term has a maximum value of
* about 1.85 arcsec at this radius, and decreases to zero as
* the centre of the disc is approached.
*
* Called:
* sla_DCS2C spherical to Cartesian
* sla_DVDV dot product
* sla_DMXV matrix x vector
* sla_DCC2S Cartesian to spherical
* sla_DRANRM normalize angle 0-2Pi
*
* P.T.Wallace Starlink 23 August 1996
*
* Copyright (C) 1996 Rutherford Appleton Laboratory
*-
IMPLICIT NONE
DOUBLE PRECISION RM,DM,PR,PD,PX,RV,AMPRMS(21),RA,DA
* Arc seconds to radians
DOUBLE PRECISION AS2R
PARAMETER (AS2R=0.484813681109535994D-5)
* Km/s to AU/year
DOUBLE PRECISION VF
PARAMETER (VF=0.21094502D0)
INTEGER I
DOUBLE PRECISION PMT,GR2E,AB1,EB(3),EHN(3),ABV(3),
: Q(3),PXR,W,EM(3),P(3),PN(3),PDE,PDEP1,
: P1(3),P1DV,P1DVP1,P2(3),P3(3)
DOUBLE PRECISION sla_DVDV,sla_DRANRM
* Unpack scalar and vector parameters
PMT = AMPRMS(1)
GR2E = AMPRMS(8)
AB1 = AMPRMS(12)
DO I=1,3
EB(I) = AMPRMS(I+1)
EHN(I) = AMPRMS(I+4)
ABV(I) = AMPRMS(I+8)
END DO
* Spherical to x,y,z
CALL sla_DCS2C(RM,DM,Q)
* Space motion (radians per year)
PXR = PX*AS2R
W = VF*RV*PXR
EM(1) = -PR*Q(2)-PD*COS(RM)*SIN(DM)+W*Q(1)
EM(2) = PR*Q(1)-PD*SIN(RM)*SIN(DM)+W*Q(2)
EM(3) = PD*COS(DM) +W*Q(3)
* Geocentric direction of star (normalized)
DO I=1,3
P(I) = Q(I)+PMT*EM(I)-PXR*EB(I)
END DO
CALL sla_DVN(P,PN,W)
* Light deflection (restrained within the Sun's disc)
PDE = sla_DVDV(PN,EHN)
PDEP1 = PDE+1D0
W = GR2E/MAX(PDEP1,1D-5)
DO I=1,3
P1(I) = PN(I)+W*(EHN(I)-PDE*PN(I))
END DO
* Aberration
P1DV = sla_DVDV(P1,ABV)
P1DVP1 = P1DV+1D0
W = 1D0+P1DV/(AB1+1D0)
DO I=1,3
P2(I) = (AB1*P1(I)+W*ABV(I))/P1DVP1
END DO
* Precession and nutation
CALL sla_DMXV(AMPRMS(13),P2,P3)
* Geocentric apparent RA,Dec
CALL sla_DCC2S(P3,RA,DA)
RA = sla_DRANRM(RA)
END
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