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SUBROUTINE slFK45 (R1950,D1950,DR1950,DD1950,P1950,V1950,
: R2000,D2000,DR2000,DD2000,P2000,V2000)
*+
* - - - - - -
* F K 4 5
* - - - - - -
*
* Convert B1950.0 FK4 star data to J2000.0 FK5 (double precision)
*
* This routine converts stars from the old, Bessel-Newcomb, FK4
* system to the new, IAU 1976, FK5, Fricke 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 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)
*
* Returned: (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)
*
* 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) 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 FK425 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., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301 USA
*
* Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
*-
IMPLICIT NONE
DOUBLE PRECISION R1950,D1950,DR1950,DD1950,P1950,V1950,
: R2000,D2000,DR2000,DD2000,P2000,V2000
* Miscellaneous
DOUBLE PRECISION R,D,UR,UD,PX,RV,SR,CR,SD,CD,W,WD
DOUBLE PRECISION X,Y,Z,XD,YD,ZD
DOUBLE PRECISION RXYSQ,RXYZSQ,RXY,RXYZ,SPXY,SPXYZ
INTEGER I,J
* Star position and velocity vectors
DOUBLE PRECISION R0(3),RD0(3)
* Combined position and velocity vectors
DOUBLE PRECISION V1(6),V2(6)
* 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(3),AD(3),EM(6,6)
DATA A,AD/ -1.62557D-6, -0.31919D-6, -0.13843D-6,
: +1.245D-3, -1.580D-3, -0.659D-3/
DATA (EM(I,1),I=1,6) / +0.9999256782D0,
: +0.0111820610D0,
: +0.0048579479D0,
: -0.000551D0,
: +0.238514D0,
: -0.435623D0 /
DATA (EM(I,2),I=1,6) / -0.0111820611D0,
: +0.9999374784D0,
: -0.0000271474D0,
: -0.238565D0,
: -0.002667D0,
: +0.012254D0 /
DATA (EM(I,3),I=1,6) / -0.0048579477D0,
: -0.0000271765D0,
: +0.9999881997D0,
: +0.435739D0,
: -0.008541D0,
: +0.002117D0 /
DATA (EM(I,4),I=1,6) / +0.00000242395018D0,
: +0.00000002710663D0,
: +0.00000001177656D0,
: +0.99994704D0,
: +0.01118251D0,
: +0.00485767D0 /
DATA (EM(I,5),I=1,6) / -0.00000002710663D0,
: +0.00000242397878D0,
: -0.00000000006582D0,
: -0.01118251D0,
: +0.99995883D0,
: -0.00002714D0 /
DATA (EM(I,6),I=1,6) / -0.00000001177656D0,
: -0.00000000006587D0,
: +0.00000242410173D0,
: -0.00485767D0,
: -0.00002718D0,
: +1.00000956D0 /
* Pick up B1950 data (units radians and arcsec/TC)
R=R1950
D=D1950
UR=DR1950*PMF
UD=DD1950*PMF
PX=P1950
RV=V1950
* Spherical to Cartesian
SR=SIN(R)
CR=COS(R)
SD=SIN(D)
CD=COS(D)
R0(1)=CR*CD
R0(2)=SR*CD
R0(3)= SD
W=VF*RV*PX
RD0(1)=-SR*CD*UR-CR*SD*UD+W*R0(1)
RD0(2)= CR*CD*UR-SR*SD*UD+W*R0(2)
RD0(3)= CD*UD+W*R0(3)
* Allow for e-terms and express as position+velocity 6-vector
W=R0(1)*A(1)+R0(2)*A(2)+R0(3)*A(3)
WD=R0(1)*AD(1)+R0(2)*AD(2)+R0(3)*AD(3)
DO I=1,3
V1(I)=R0(I)-A(I)+W*R0(I)
V1(I+3)=RD0(I)-AD(I)+WD*R0(I)
END DO
* Convert position+velocity vector to Fricke system
DO I=1,6
W=0D0
DO J=1,6
W=W+EM(I,J)*V1(J)
END DO
V2(I)=W
END DO
* Revert to spherical coordinates
X=V2(1)
Y=V2(2)
Z=V2(3)
XD=V2(4)
YD=V2(5)
ZD=V2(6)
RXYSQ=X*X+Y*Y
RXYZSQ=RXYSQ+Z*Z
RXY=SQRT(RXYSQ)
RXYZ=SQRT(RXYZSQ)
SPXY=X*XD+Y*YD
SPXYZ=SPXY+Z*ZD
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*SPXY)/(RXYZSQ*RXY)
END IF
IF (PX.GT.TINY) THEN
RV=SPXYZ/(PX*RXYZ*VF)
PX=PX/RXYZ
END IF
* Return results
R2000=R
D2000=D
DR2000=UR/PMF
DD2000=UD/PMF
V2000=RV
P2000=PX
END
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