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267 lines
8.3 KiB
Fortran
267 lines
8.3 KiB
Fortran
SUBROUTINE sla_FK425 (R1950,D1950,DR1950,DD1950,P1950,V1950,
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: R2000,D2000,DR2000,DD2000,P2000,V2000)
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*+
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* - - - - - -
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* F K 4 2 5
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* - - - - - -
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*
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* Convert B1950.0 FK4 star data to J2000.0 FK5 (double precision)
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*
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* This routine converts stars from the old, Bessel-Newcomb, FK4
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* system to the new, IAU 1976, FK5, Fricke system. The precepts
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* of Smith et al (Ref 1) are followed, using the implementation
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* by Yallop et al (Ref 2) of a matrix method due to Standish.
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* Kinoshita's development of Andoyer's post-Newcomb precession is
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* used. The numerical constants from Seidelmann et al (Ref 3) are
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* used canonically.
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*
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* Given: (all B1950.0,FK4)
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* R1950,D1950 dp B1950.0 RA,Dec (rad)
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* DR1950,DD1950 dp B1950.0 proper motions (rad/trop.yr)
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* P1950 dp parallax (arcsec)
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* V1950 dp radial velocity (km/s, +ve = moving away)
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*
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* Returned: (all J2000.0,FK5)
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* R2000,D2000 dp J2000.0 RA,Dec (rad)
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* DR2000,DD2000 dp J2000.0 proper motions (rad/Jul.yr)
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* P2000 dp parallax (arcsec)
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* V2000 dp radial velocity (km/s, +ve = moving away)
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*
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* Notes:
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*
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* 1) The proper motions in RA are dRA/dt rather than
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* cos(Dec)*dRA/dt, and are per year rather than per century.
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*
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* 2) Conversion from Besselian epoch 1950.0 to Julian epoch
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* 2000.0 only is provided for. Conversions involving other
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* epochs will require use of the appropriate precession,
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* proper motion, and E-terms routines before and/or
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* after FK425 is called.
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*
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* 3) In the FK4 catalogue the proper motions of stars within
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* 10 degrees of the poles do not embody the differential
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* E-term effect and should, strictly speaking, be handled
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* in a different manner from stars outside these regions.
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* However, given the general lack of homogeneity of the star
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* data available for routine astrometry, the difficulties of
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* handling positions that may have been determined from
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* astrometric fields spanning the polar and non-polar regions,
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* the likelihood that the differential E-terms effect was not
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* taken into account when allowing for proper motion in past
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* astrometry, and the undesirability of a discontinuity in
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* the algorithm, the decision has been made in this routine to
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* include the effect of differential E-terms on the proper
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* motions for all stars, whether polar or not. At epoch 2000,
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* and measuring on the sky rather than in terms of dRA, the
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* errors resulting from this simplification are less than
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* 1 milliarcsecond in position and 1 milliarcsecond per
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* century in proper motion.
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*
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* References:
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*
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* 1 Smith, C.A. et al, 1989. "The transformation of astrometric
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* catalog systems to the equinox J2000.0". Astron.J. 97, 265.
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*
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* 2 Yallop, B.D. et al, 1989. "Transformation of mean star places
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* from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
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* Astron.J. 97, 274.
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*
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* 3 Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to
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* the Astronomical Almanac", ISBN 0-935702-68-7.
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*
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* P.T.Wallace Starlink 19 December 1993
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*
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* Copyright (C) 1995 Rutherford Appleton Laboratory
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*
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* License:
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program (see SLA_CONDITIONS); if not, write to the
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* Free Software Foundation, Inc., 59 Temple Place, Suite 330,
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* Boston, MA 02111-1307 USA
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*
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*-
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IMPLICIT NONE
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DOUBLE PRECISION R1950,D1950,DR1950,DD1950,P1950,V1950,
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: R2000,D2000,DR2000,DD2000,P2000,V2000
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* Miscellaneous
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DOUBLE PRECISION R,D,UR,UD,PX,RV,SR,CR,SD,CD,W,WD
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DOUBLE PRECISION X,Y,Z,XD,YD,ZD
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DOUBLE PRECISION RXYSQ,RXYZSQ,RXY,RXYZ,SPXY,SPXYZ
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INTEGER I,J
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* Star position and velocity vectors
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DOUBLE PRECISION R0(3),RD0(3)
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* Combined position and velocity vectors
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DOUBLE PRECISION V1(6),V2(6)
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* 2Pi
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DOUBLE PRECISION D2PI
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PARAMETER (D2PI=6.283185307179586476925287D0)
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* Radians per year to arcsec per century
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DOUBLE PRECISION PMF
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PARAMETER (PMF=100D0*60D0*60D0*360D0/D2PI)
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* Small number to avoid arithmetic problems
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DOUBLE PRECISION TINY
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PARAMETER (TINY=1D-30)
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*
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* CANONICAL CONSTANTS (see references)
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*
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* Km per sec to AU per tropical century
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* = 86400 * 36524.2198782 / 149597870
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DOUBLE PRECISION VF
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PARAMETER (VF=21.095D0)
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* Constant vector and matrix (by columns)
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DOUBLE PRECISION A(3),AD(3),EM(6,6)
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DATA A,AD/ -1.62557D-6, -0.31919D-6, -0.13843D-6,
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: +1.245D-3, -1.580D-3, -0.659D-3/
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DATA (EM(I,1),I=1,6) / +0.9999256782D0,
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: +0.0111820610D0,
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: +0.0048579479D0,
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: -0.000551D0,
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: +0.238514D0,
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: -0.435623D0 /
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DATA (EM(I,2),I=1,6) / -0.0111820611D0,
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: +0.9999374784D0,
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: -0.0000271474D0,
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: -0.238565D0,
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: -0.002667D0,
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: +0.012254D0 /
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DATA (EM(I,3),I=1,6) / -0.0048579477D0,
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: -0.0000271765D0,
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: +0.9999881997D0,
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: +0.435739D0,
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: -0.008541D0,
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: +0.002117D0 /
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DATA (EM(I,4),I=1,6) / +0.00000242395018D0,
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: +0.00000002710663D0,
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: +0.00000001177656D0,
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: +0.99994704D0,
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: +0.01118251D0,
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: +0.00485767D0 /
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DATA (EM(I,5),I=1,6) / -0.00000002710663D0,
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: +0.00000242397878D0,
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: -0.00000000006582D0,
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: -0.01118251D0,
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: +0.99995883D0,
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: -0.00002714D0 /
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DATA (EM(I,6),I=1,6) / -0.00000001177656D0,
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: -0.00000000006587D0,
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: +0.00000242410173D0,
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: -0.00485767D0,
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: -0.00002718D0,
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: +1.00000956D0 /
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* Pick up B1950 data (units radians and arcsec/TC)
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R=R1950
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D=D1950
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UR=DR1950*PMF
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UD=DD1950*PMF
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PX=P1950
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RV=V1950
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* Spherical to Cartesian
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SR=SIN(R)
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CR=COS(R)
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SD=SIN(D)
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CD=COS(D)
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R0(1)=CR*CD
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R0(2)=SR*CD
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R0(3)= SD
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W=VF*RV*PX
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RD0(1)=-SR*CD*UR-CR*SD*UD+W*R0(1)
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RD0(2)= CR*CD*UR-SR*SD*UD+W*R0(2)
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RD0(3)= CD*UD+W*R0(3)
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* Allow for e-terms and express as position+velocity 6-vector
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W=R0(1)*A(1)+R0(2)*A(2)+R0(3)*A(3)
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WD=R0(1)*AD(1)+R0(2)*AD(2)+R0(3)*AD(3)
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DO I=1,3
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V1(I)=R0(I)-A(I)+W*R0(I)
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V1(I+3)=RD0(I)-AD(I)+WD*R0(I)
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END DO
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* Convert position+velocity vector to Fricke system
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DO I=1,6
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W=0D0
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DO J=1,6
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W=W+EM(I,J)*V1(J)
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END DO
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V2(I)=W
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END DO
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* Revert to spherical coordinates
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X=V2(1)
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Y=V2(2)
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Z=V2(3)
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XD=V2(4)
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YD=V2(5)
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ZD=V2(6)
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RXYSQ=X*X+Y*Y
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RXYZSQ=RXYSQ+Z*Z
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RXY=SQRT(RXYSQ)
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RXYZ=SQRT(RXYZSQ)
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SPXY=X*XD+Y*YD
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SPXYZ=SPXY+Z*ZD
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IF (X.EQ.0D0.AND.Y.EQ.0D0) THEN
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R=0D0
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ELSE
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R=ATAN2(Y,X)
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IF (R.LT.0.0D0) R=R+D2PI
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END IF
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D=ATAN2(Z,RXY)
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IF (RXY.GT.TINY) THEN
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UR=(X*YD-Y*XD)/RXYSQ
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UD=(ZD*RXYSQ-Z*SPXY)/(RXYZSQ*RXY)
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END IF
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IF (PX.GT.TINY) THEN
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RV=SPXYZ/(PX*RXYZ*VF)
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PX=PX/RXYZ
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END IF
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* Return results
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R2000=R
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D2000=D
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DR2000=UR/PMF
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DD2000=UD/PMF
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V2000=RV
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P2000=PX
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END
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