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: 2023 May 4 * * SOFA release 2023-10-11 * * Copyright (C) 2023 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, PU(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, PU ) CALL iau_PDP ( PU, PV(1,2), VR ) CALL iau_SXP ( VR, PU, 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 observed-to-inertial 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 ) * Scale inertial tangential velocity vector into observed (au/d). CALL iau_SXP ( 1D0/D, UT, UST ) * Compute observed radial velocity vector (au/d). CALL iau_SXP ( C*(BETR-DEL)/D, PU, USR ) * Combine the two to obtain the observed velocity vector. 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) 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