SUBROUTINE iau_PVSTAR ( PV, RA, DEC, PMR, PMD, PX, RV, J )
*+
* - - - - - - - - - - -
* i a u _ P V S T A R
* - - - - - - - - - - -
*
* Convert star position+velocity vector to catalog coordinates.
*
* This routine is part of the International Astronomical Union's
* SOFA (Standards of Fundamental Astronomy) software collection.
*
* Status: support routine.
*
* Given (Note 1):
* PV d(3,2) pv-vector (au, au/day)
*
* Returned (Note 2):
* RA d right ascension (radians)
* DEC d declination (radians)
* PMR d RA proper motion (radians/year)
* PMD d Dec proper motion (radians/year)
* PX d parallax (arcsec)
* RV d radial velocity (km/s, positive = receding)
* J i status:
* 0 = OK
* -1 = superluminal speed (Note 5)
* -2 = null position vector
*
* Notes:
*
* 1) The specified pv-vector is the coordinate direction (and its rate
* of change) for the epoch at which the light leaving the star
* reached the solar-system barycenter.
*
* 2) The star data returned by this routine are "observables" for an
* imaginary observer at the solar-system barycenter. Proper motion
* and radial velocity are, strictly, in terms of barycentric
* coordinate time, TCB. For most practical applications, it is
* permissible to neglect the distinction between TCB and ordinary
* "proper" time on Earth (TT/TAI). The result will, as a rule, be
* limited by the intrinsic accuracy of the proper-motion and radial-
* velocity data; moreover, the supplied pv-vector is likely to be
* merely an intermediate result (for example generated by the
* routine iau_STARPV), so that a change of time unit will cancel
* out overall.
*
* In accordance with normal star-catalog conventions, the object's
* right ascension and declination are freed from the effects of
* secular aberration. The frame, which is aligned to the catalog
* equator and equinox, is Lorentzian and centered on the SSB.
*
* Summarizing, the specified pv-vector is for most stars almost
* identical to the result of applying the standard geometrical
* "space motion" transformation to the catalog data. The
* differences, which are the subject of the Stumpff paper cited
* below, are:
*
* (i) In stars with significant radial velocity and proper motion,
* the constantly changing light-time distorts the apparent proper
* motion. Note that this is a classical, not a relativistic,
* effect.
*
* (ii) The transformation complies with special relativity.
*
* 3) Care is needed with units. The star coordinates are in radians
* and the proper motions in radians per Julian year, but the
* parallax is in arcseconds; the radial velocity is in km/s, but
* the pv-vector result is in au and au/day.
*
* 4) The proper motions are the rate of change of the right ascension
* and declination at the catalog epoch and are in radians per Julian
* year. The RA proper motion is in terms of coordinate angle, not
* true angle, and will thus be numerically larger at high
* declinations.
*
* 5) Straight-line motion at constant speed in the inertial frame is
* assumed. If the speed is greater than or equal to the speed of
* light, the routine aborts with an error status.
*
* 6) The inverse transformation is performed by the routine iau_STARPV.
*
* Called:
* iau_PN decompose p-vector into modulus and direction
* iau_PDP scalar product of two p-vectors
* iau_SXP multiply p-vector by scalar
* iau_PMP p-vector minus p-vector
* iau_PM modulus of p-vector
* iau_PPP p-vector plus p-vector
* iau_PV2S pv-vector to spherical
* iau_ANP normalize angle into range 0 to 2pi
*
* Reference:
*
* Stumpff, P., Astron.Astrophys. 144, 232-240 (1985).
*
* This revision: 2017 March 16
*
* SOFA release 2021-05-12
*
* Copyright (C) 2021 IAU SOFA Board. See notes at end.
*
*-----------------------------------------------------------------------
IMPLICIT NONE
DOUBLE PRECISION PV(3,2), RA, DEC, PMR, PMD, PX, RV
INTEGER J
* Julian years to days
DOUBLE PRECISION Y2D
PARAMETER ( Y2D = 365.25D0 )
* Radians to arcseconds
DOUBLE PRECISION DR2AS
PARAMETER ( DR2AS = 206264.8062470963551564734D0 )
* Days to seconds
DOUBLE PRECISION D2S
PARAMETER ( D2S = 86400D0 )
* Speed of light (m/s)
DOUBLE PRECISION CMPS
PARAMETER ( CMPS = 299792458D0 )
* Astronomical unit (m, IAU 2012)
DOUBLE PRECISION AUM
PARAMETER ( AUM = 149597870.7D3 )
* Speed of light (au per day)
DOUBLE PRECISION C
PARAMETER ( C = D2S*CMPS/AUM )
DOUBLE PRECISION R, X(3), VR, UR(3), VT, UT(3), BETT, BETR, D, W,
: DEL, USR(3), UST(3), A, RAD, DECD, RD
DOUBLE PRECISION iau_ANP
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* Isolate the radial component of the velocity (au/day, inertial).
CALL iau_PN ( PV(1,1), R, X )
CALL iau_PDP ( X, PV(1,2), VR )
CALL iau_SXP ( VR, X, UR )
* Isolate the transverse component of the velocity (au/day, inertial).
CALL iau_PMP ( PV(1,2), UR, UT )
CALL iau_PM ( UT, VT )
* Special-relativity dimensionless parameters.
BETT = VT / C
BETR = VR / C
* The inertial-to-observed correction terms.
D = 1D0 + BETR
W = BETR*BETR + BETT*BETT
IF ( D.EQ.0D0 .OR. W.GE.1D0 ) THEN
J = -1
GO TO 9
END IF
DEL = - W / ( SQRT(1D0-W) + 1D0 )
* Apply relativistic correction factor to radial velocity component.
IF ( BETR.NE.0D0 ) THEN
W = ( BETR-DEL ) / ( BETR*D )
ELSE
W = 1D0
END IF
CALL iau_SXP ( W, UR, USR )
* Apply relativistic correction factor to tangential velocity component.
CALL iau_SXP ( 1D0/D, UT, UST )
* Combine the two to obtain the observed velocity vector (au/day).
CALL iau_PPP ( USR, UST, PV(1,2) )
* Cartesian to spherical.
CALL iau_PV2S ( PV, A, DEC, R, RAD, DECD, RD )
IF ( R .EQ. 0D0 ) THEN
J = -2
GO TO 9
END IF
* Return RA in range 0 to 2pi.
RA = iau_ANP ( A )
* Return proper motions in radians per year.
PMR = RAD * Y2D
PMD = DECD * Y2D
* Return parallax in arcsec.
PX = DR2AS / R
* Return radial velocity in km/s.
RV = 1D-3 * RD * AUM / D2S
* OK status.
J = 0
* Exit.
9 CONTINUE
* Finished.
*+----------------------------------------------------------------------
*
* Copyright (C) 2021
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
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* =====================
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*-----------------------------------------------------------------------
END