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 2023-10-11 * * Copyright (C) 2023 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) 2023 * Standards of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA makes no warranties, express or implied, as * to non-infringement of third party rights, merchantability, or * fitness for any particular purpose. In no event will SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END