SUBROUTINE iau_STARPV ( RA, DEC, PMR, PMD, PX, RV, PV, J ) *+ * - - - - - - - - - - - * i a u _ S T A R P V * - - - - - - - - - - - * * Convert star catalog coordinates to position+velocity vector. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given (Note 1): * 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 (arcseconds) * RV d radial velocity (km/s, positive = receding) * * Returned (Note 2): * PV d(3,2) pv-vector (au, au/day) * J i status: * 0 = no warnings * 1 = distance overridden (Note 6) * 2 = excessive velocity (Note 7) * 4 = solution didn't converge (Note 8) * else = binary logical OR of the above * * Notes: * * 1) The star data accepted 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 pv-vector is likely to be merely an * intermediate result, so that a change of time unit would 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. * * 2) The resulting position and velocity pv-vector is with respect to * the same frame and, like the catalog coordinates, is freed from * the effects of secular aberration. Should the "coordinate * direction", where the object was located at the catalog epoch, be * required, it may be obtained by calculating the magnitude of the * position vector PV(1-3,1) dividing by the speed of light in au/day * to give the light-time, and then multiplying the space velocity * PV(1-3,2) by this light-time and adding the result to PV(1-3,1). * * Summarizing, the pv-vector returned is for most stars almost * identical to the result of applying the standard geometrical * "space motion" transformation. The differences, which are the * subject of the Stumpff paper referenced 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 RA proper motion is in terms of coordinate angle, not true * angle. If the catalog uses arcseconds for both RA and Dec proper * motions, the RA proper motion will need to be divided by cos(Dec) * before use. * * 5) Straight-line motion at constant speed, in the inertial frame, * is assumed. * * 6) An extremely small (or zero or negative) parallax is interpreted * to mean that the object is on the "celestial sphere", the radius * of which is an arbitrary (large) value (see the constant PXMIN). * When the distance is overridden in this way, the status, initially * zero, has 1 added to it. * * 7) If the space velocity is a significant fraction of c (see the * constant VMAX), it is arbitrarily set to zero. When this action * occurs, 2 is added to the status. * * 8) The relativistic adjustment involves an iterative calculation. * If the process fails to converge within a set number (IMAX) of * iterations, 4 is added to the status. * * 9) The inverse transformation is performed by the routine iau_PVSTAR. * * Called: * iau_S2PV spherical coordinates to pv-vector * iau_PM modulus of p-vector * iau_ZP zero p-vector * 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_PPP p-vector plus p-vector * * 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 RA, DEC, PMR, PMD, PX, RV, PV(3,2) INTEGER J * Smallest allowed parallax DOUBLE PRECISION PXMIN PARAMETER ( PXMIN = 1D-7 ) * Largest allowed speed (fraction of c) DOUBLE PRECISION VMAX PARAMETER ( VMAX = 0.5D0 ) * 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 ) * Maximum number of iterations for relativistic solution INTEGER I,IMAX PARAMETER ( IMAX = 100 ) INTEGER IWARN DOUBLE PRECISION W, R, RD, RAD, DECD, V, PU(3), USR(3), UST(3), : VSR, VST, BETST, BETSR, BETT, BETR, OD, ODEL, : DD, DDEL, ODD, ODDEL, D, DEL, UR(3), UT(3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Distance (au). IF ( PX.GE.PXMIN ) THEN W = PX IWARN = 0 ELSE W = PXMIN IWARN = 1 END IF R = DR2AS / W * Radial speed (au/day). RD = D2S * RV * 1D3 / AUM * Proper motion (radian/day). RAD = PMR / Y2D DECD = PMD / Y2D * To pv-vector (au,au/day). CALL iau_S2PV ( RA, DEC, R, RAD, DECD, RD, PV ) * If excessive velocity, arbitrarily set it to zero. CALL iau_PM ( PV(1,2), V ) IF ( V/C .GT. VMAX ) THEN CALL iau_ZP ( PV(1,2) ) IWARN = IWARN + 2 END IF * Isolate the radial component of the velocity (au/day). CALL iau_PN ( PV(1,1), W, PU ) CALL iau_PDP ( PU, PV(1,2), VSR ) CALL iau_SXP ( VSR, PU, USR ) * Isolate the transverse component of the velocity (au/day). CALL iau_PMP ( PV(1,2), USR, UST ) CALL iau_PM ( UST, VST ) * Special-relativity dimensionless parameters. BETSR = VSR / C BETST = VST / C * Determine the observed-to-inertial correction terms. OD = 0D0 ODEL = 0D0 ODD = 0D0 ODDEL = 0D0 BETT = BETST BETR = BETSR DO 1 I=1,IMAX D = 1D0 + BETR W = BETR*BETR + BETT*BETT DEL = - W / ( SQRT(1D0-W) + 1D0 ) BETR = D*BETSR + DEL BETT = D*BETST IF ( I .GT. 1 ) THEN DD = ABS(D-OD) DDEL = ABS(DEL-ODEL) IF ( I.GT.2 .AND. : DD.GE.ODD .AND. : DDEL.GE.ODDEL ) GO TO 2 IF ( I .GE. IMAX ) IWARN = IWARN + 4 ODD = DD ODDEL = DDEL END IF OD = D ODEL = DEL 1 CONTINUE 2 CONTINUE * Scale observed tangential velocity vector into inertial (au/d). */ CALL iau_SXP ( D, UST, UT ) * Compute inertial radial velocity vector (au/d). CALL iau_SXP ( C*(D*BETSR+DEL), PU, UR ) * Combine the two to obtain the inertial space velocity vector. CALL iau_PPP ( UR, UT, PV(1,2) ) * Return the status. J = IWARN * 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