SUBROUTINE iau_PMPX ( RC, DC, PR, PD, PX, RV, PMT, POB, PCO )
*+
* - - - - - - - - -
* i a u _ P M P X
* - - - - - - - - -
*
* Proper motion and parallax.
*
* This routine is part of the International Astronomical Union's
* SOFA (Standards of Fundamental Astronomy) software collection.
*
* Status: support routine.
*
* Given:
* RC,DC d ICRS RA,Dec at catalog epoch (radians)
* PR d RA proper motion (radians/year, Note 1)
* PD d Dec proper motion (radians/year)
* PX d parallax (arcsec)
* RV d radial velocity (km/s, +ve if receding)
* PMT d proper motion time interval (SSB, Julian years)
* POB d(3) SSB to observer vector (au)
*
* Returned:
* PCO d(3) coordinate direction (BCRS unit vector)
*
* Notes:
*
* 1) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
*
* 2) The proper motion time interval is for when the starlight
* reaches the solar system barycenter.
*
* 3) To avoid the need for iteration, the Roemer effect (i.e. the
* small annual modulation of the proper motion coming from the
* changing light time) is applied approximately, using the
* direction of the star at the catalog epoch.
*
* References:
*
* 1984 Astronomical Almanac, pp B39-B41.
*
* Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
* the Astronomical Almanac, 3rd ed., University Science Books
* (2013), Section 7.2.
*
* Called:
* iau_PDP scalar product of two p-vectors
* iau_PN decompose p-vector into modulus and direction
*
* This revision: 2021 April 3
*
* SOFA release 2021-05-12
*
* Copyright (C) 2021 IAU SOFA Board. See notes at end.
*
*-----------------------------------------------------------------------
IMPLICIT NONE
DOUBLE PRECISION RC, DC, PR, PD, PX, RV, PMT, POB(3), PCO(3)
* Days to seconds
DOUBLE PRECISION D2S
PARAMETER ( D2S = 86400D0 )
* Days per Julian year
DOUBLE PRECISION DJY
PARAMETER ( DJY = 365.25D0 )
* Days per Julian millennium
DOUBLE PRECISION DJM
PARAMETER ( DJM = 365250D0 )
* Speed of light (m/s)
DOUBLE PRECISION CMPS
PARAMETER ( CMPS = 299792458D0 )
* Astronomical unit (m, IAU 2012)
DOUBLE PRECISION AUM
PARAMETER ( AUM = 149597870.7D3 )
* Light time for 1 au, Julian years
DOUBLE PRECISION AULTY
PARAMETER ( AULTY = AUM/CMPS/D2S/DJY )
* Km/s to au/year
DOUBLE PRECISION VF
PARAMETER ( VF = D2S*DJM/AUM )
* Arcseconds to radians
DOUBLE PRECISION DAS2R
PARAMETER ( DAS2R = 4.848136811095359935899141D-6 )
INTEGER I
DOUBLE PRECISION SR, CR, SD, CD, X, Y, Z, P(3), PDB,
: DT, PXR, W, PDZ, PM(3)
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* Catalog spherical coordinates to unit vector (and useful functions).
SR = SIN(RC)
CR = COS(RC)
SD = SIN(DC)
CD = COS(DC)
X = CR*CD
Y = SR*CD
Z = SD
P(1) = X
P(2) = Y
P(3) = Z
* Component of observer vector in star direction.
CALL iau_PDP ( P, POB, PDB )
* Proper motion time interval (y), including Roemer effect.
DT = PMT + PDB*AULTY
* Space motion (radians per year).
PXR = PX*DAS2R
W = VF*RV*PXR
PDZ = PD*Z
PM(1) = - PR*Y - PDZ*CR + W*X
PM(2) = PR*X - PDZ*SR + W*Y
PM(3) = PD*CD + W*Z
* Coordinate direction of star (unit vector, BCRS).
DO 1 I=1,3
P(I) = P(I) + DT*PM(I) - PXR*POB(I)
1 CONTINUE
CALL iau_PN ( P, W, PCO )
* Finished.
*+----------------------------------------------------------------------
*
* Copyright (C) 2021
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
* =====================
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* =====================
*
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*
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*
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*
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*-----------------------------------------------------------------------
END