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, +ve = 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 a p-vector * iau_PN normalize p-vector returning modulus * iau_PDP dot 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: 2003 January 14 * * Copyright (C) 2003 IAU SOFA Review 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 arc seconds DOUBLE PRECISION DR2AS PARAMETER ( DR2AS = 206264.8062470963551564733D0 ) * Days to seconds DOUBLE PRECISION D2S PARAMETER ( D2S = 86400D0 ) * AU (meters) DOUBLE PRECISION AUM PARAMETER ( AUM = 149597870D3 ) * Speed of light (AU per day) DOUBLE PRECISION C PARAMETER ( C = D2S/499.004782D0 ) * Maximum number of iterations for relativistic solution INTEGER I,IMAX PARAMETER ( IMAX = 100 ) INTEGER IWARN DOUBLE PRECISION W, R, RD, RAD, DECD, V, X(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 velocity (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, X ) CALL iau_PDP ( X, PV(1,2), VSR ) CALL iau_SXP ( VSR, X, 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 inertial-to-observed relativistic correction terms. BETT = BETST BETR = BETSR DO 1 I=1,IMAX D = 1D0 + BETR DEL = SQRT(1D0 - BETR*BETR - BETT*BETT) - 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.EQ.ODD .AND. : DDEL.EQ.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 * Replace observed radial velocity with inertial value. IF ( BETSR .NE. 0D0 ) THEN W = D + DEL/BETSR ELSE W = 1D0 END IF CALL iau_SXP ( W, USR, UR ) * Replace observed tangential velocity with inertial value. CALL iau_SXP ( D, UST, UT ) * Combine the two to obtain the inertial space velocity. CALL iau_PPP ( UR, UT, PV(1,2) ) * Return the status. J = IWARN * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2003 * Standards Of Fundamental Astronomy Review Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS * WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Review Board ("the Board"). * * 2. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the 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. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "as is" and the Board makes * no warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may * obtain by using the Software. The Board 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 the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * * *----------------------------------------------------------------------- END