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SUBROUTINE sla_FK524 (R2000,D2000,DR2000,DD2000,P2000,V2000,
: R1950,D1950,DR1950,DD1950,P1950,V1950)
*+
* - - - - - -
* F K 5 2 4
* - - - - - -
*
* Convert J2000.0 FK5 star data to B1950.0 FK4 (double precision)
*
* 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 (Ref 1) are followed, using the implementation
* by Yallop et al (Ref 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 (Ref 3) are
* used canonically.
*
* Given: (all J2000.0,FK5)
* R2000,D2000 dp J2000.0 RA,Dec (rad)
* DR2000,DD2000 dp J2000.0 proper motions (rad/Jul.yr)
* P2000 dp parallax (arcsec)
* V2000 dp radial velocity (km/s, +ve = moving away)
*
* Returned: (all B1950.0,FK4)
* R1950,D1950 dp B1950.0 RA,Dec (rad)
* DR1950,DD1950 dp B1950.0 proper motions (rad/trop.yr)
* P1950 dp parallax (arcsec)
* V1950 dp radial velocity (km/s, +ve = moving away)
*
* Notes:
*
* 1) The proper motions in RA are dRA/dt rather than
* cos(Dec)*dRA/dt, 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
* 10 degrees of the poles do not embody the differential
* E-term 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 dRA, the
* errors resulting from this simplification are less than
* 1 milliarcsecond in position and 1 milliarcsecond per
* century in proper motion.
*
* References:
*
* 1 Smith, C.A. et al, 1989. "The transformation of astrometric
* catalog systems to the equinox J2000.0". Astron.J. 97, 265.
*
* 2 Yallop, B.D. et al, 1989. "Transformation of mean star places
* from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
* Astron.J. 97, 274.
*
* 3 Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to
* the Astronomical Almanac", ISBN 0-935702-68-7.
*
* P.T.Wallace Starlink 19 December 1993
*
* Copyright (C) 1995 Rutherford Appleton Laboratory
*
* License:
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program (see SLA_CONDITIONS); if not, write to the
* Free Software Foundation, Inc., 59 Temple Place, Suite 330,
* Boston, MA 02111-1307 USA
*
*-
IMPLICIT NONE
DOUBLE PRECISION R2000,D2000,DR2000,DD2000,P2000,V2000,
: R1950,D1950,DR1950,DD1950,P1950,V1950
* Miscellaneous
DOUBLE PRECISION R,D,UR,UD,PX,RV
DOUBLE PRECISION SR,CR,SD,CD,X,Y,Z,W
DOUBLE PRECISION V1(6),V2(6)
DOUBLE PRECISION XD,YD,ZD
DOUBLE PRECISION RXYZ,WD,RXYSQ,RXY
INTEGER I,J
* 2Pi
DOUBLE PRECISION D2PI
PARAMETER (D2PI=6.283185307179586476925287D0)
* Radians per year to arcsec per century
DOUBLE PRECISION PMF
PARAMETER (PMF=100D0*60D0*60D0*360D0/D2PI)
* Small number to avoid arithmetic problems
DOUBLE PRECISION TINY
PARAMETER (TINY=1D-30)
*
* CANONICAL CONSTANTS (see references)
*
* Km per sec to AU per tropical century
* = 86400 * 36524.2198782 / 149597870
DOUBLE PRECISION VF
PARAMETER (VF=21.095D0)
* Constant vector and matrix (by columns)
DOUBLE PRECISION A(6),EMI(6,6)
DATA A/ -1.62557D-6, -0.31919D-6, -0.13843D-6,
: +1.245D-3, -1.580D-3, -0.659D-3/
DATA (EMI(I,1),I=1,6) / +0.9999256795D0,
: -0.0111814828D0,
: -0.0048590040D0,
: -0.000551D0,
: -0.238560D0,
: +0.435730D0 /
DATA (EMI(I,2),I=1,6) / +0.0111814828D0,
: +0.9999374849D0,
: -0.0000271557D0,
: +0.238509D0,
: -0.002667D0,
: -0.008541D0 /
DATA (EMI(I,3),I=1,6) / +0.0048590039D0,
: -0.0000271771D0,
: +0.9999881946D0,
: -0.435614D0,
: +0.012254D0,
: +0.002117D0 /
DATA (EMI(I,4),I=1,6) / -0.00000242389840D0,
: +0.00000002710544D0,
: +0.00000001177742D0,
: +0.99990432D0,
: -0.01118145D0,
: -0.00485852D0 /
DATA (EMI(I,5),I=1,6) / -0.00000002710544D0,
: -0.00000242392702D0,
: +0.00000000006585D0,
: +0.01118145D0,
: +0.99991613D0,
: -0.00002716D0 /
DATA (EMI(I,6),I=1,6) / -0.00000001177742D0,
: +0.00000000006585D0,
: -0.00000242404995D0,
: +0.00485852D0,
: -0.00002717D0,
: +0.99996684D0 /
* Pick up J2000 data (units radians and arcsec/JC)
R=R2000
D=D2000
UR=DR2000*PMF
UD=DD2000*PMF
PX=P2000
RV=V2000
* Spherical to Cartesian
SR=SIN(R)
CR=COS(R)
SD=SIN(D)
CD=COS(D)
X=CR*CD
Y=SR*CD
Z= SD
W=VF*RV*PX
V1(1)=X
V1(2)=Y
V1(3)=Z
V1(4)=-UR*Y-CR*SD*UD+W*X
V1(5)= UR*X-SR*SD*UD+W*Y
V1(6)= CD*UD+W*Z
* Convert position+velocity vector to BN system
DO I=1,6
W=0D0
DO J=1,6
W=W+EMI(I,J)*V1(J)
END DO
V2(I)=W
END DO
* Position vector components and magnitude
X=V2(1)
Y=V2(2)
Z=V2(3)
RXYZ=SQRT(X*X+Y*Y+Z*Z)
* Apply E-terms to position
W=X*A(1)+Y*A(2)+Z*A(3)
X=X+A(1)*RXYZ-W*X
Y=Y+A(2)*RXYZ-W*Y
Z=Z+A(3)*RXYZ-W*Z
* Recompute magnitude
RXYZ=SQRT(X*X+Y*Y+Z*Z)
* Apply E-terms to both position and velocity
X=V2(1)
Y=V2(2)
Z=V2(3)
W=X*A(1)+Y*A(2)+Z*A(3)
WD=X*A(4)+Y*A(5)+Z*A(6)
X=X+A(1)*RXYZ-W*X
Y=Y+A(2)*RXYZ-W*Y
Z=Z+A(3)*RXYZ-W*Z
XD=V2(4)+A(4)*RXYZ-WD*X
YD=V2(5)+A(5)*RXYZ-WD*Y
ZD=V2(6)+A(6)*RXYZ-WD*Z
* Convert to spherical
RXYSQ=X*X+Y*Y
RXY=SQRT(RXYSQ)
IF (X.EQ.0D0.AND.Y.EQ.0D0) THEN
R=0D0
ELSE
R=ATAN2(Y,X)
IF (R.LT.0.0D0) R=R+D2PI
END IF
D=ATAN2(Z,RXY)
IF (RXY.GT.TINY) THEN
UR=(X*YD-Y*XD)/RXYSQ
UD=(ZD*RXYSQ-Z*(X*XD+Y*YD))/((RXYSQ+Z*Z)*RXY)
END IF
* Radial velocity and parallax
IF (PX.GT.TINY) THEN
RV=(X*XD+Y*YD+Z*ZD)/(PX*VF*RXYZ)
PX=PX/RXYZ
END IF
* Return results
R1950=R
D1950=D
DR1950=UR/PMF
DD1950=UD/PMF
P1950=PX
V1950=RV
END