#include "sofa.h" int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv) /* ** - - - - - - - - - - ** i a u P v s t a r ** - - - - - - - - - - ** ** Convert star position+velocity vector to catalog coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (Note 1): ** pv double[2][3] pv-vector (au, au/day) ** ** Returned (Note 2): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (function value): ** int 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 date at which the light leaving the star ** reached the solar-system barycenter. ** ** 2) The star data returned by this function 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 ** function iauStarpv), 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 function aborts with an error status. ** ** 6) The inverse transformation is performed by the function iauStarpv. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPm modulus of p-vector ** iauPpp p-vector plus p-vector ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** ** This revision: 2017 March 16 ** ** SOFA release 2018-01-30 ** ** Copyright (C) 2018 IAU SOFA Board. See notes at end. */ { double r, x[3], vr, ur[3], vt, ut[3], bett, betr, d, w, del, usr[3], ust[3], a, rad, decd, rd; /* Isolate the radial component of the velocity (au/day, inertial). */ iauPn(pv[0], &r, x); vr = iauPdp(x, pv[1]); iauSxp(vr, x, ur); /* Isolate the transverse component of the velocity (au/day, inertial). */ iauPmp(pv[1], ur, ut); vt = iauPm(ut); /* Special-relativity dimensionless parameters. */ bett = vt / DC; betr = vr / DC; /* The inertial-to-observed correction terms. */ d = 1.0 + betr; w = betr*betr + bett*bett; if (d == 0.0 || w > 1.0) return -1; del = - w / (sqrt(1.0-w) + 1.0); /* Apply relativistic correction factor to radial velocity component. */ w = (betr != 0) ? (betr - del) / (betr * d) : 1.0; iauSxp(w, ur, usr); /* Apply relativistic correction factor to tangential velocity */ /* component. */ iauSxp(1.0/d, ut, ust); /* Combine the two to obtain the observed velocity vector (au/day). */ iauPpp(usr, ust, pv[1]); /* Cartesian to spherical. */ iauPv2s(pv, &a, dec, &r, &rad, &decd, &rd); if (r == 0.0) return -2; /* Return RA in range 0 to 2pi. */ *ra = iauAnp(a); /* Return proper motions in radians per year. */ *pmr = rad * DJY; *pmd = decd * DJY; /* Return parallax in arcsec. */ *px = DR2AS / r; /* Return radial velocity in km/s. */ *rv = 1e-3 * rd * DAU / DAYSEC; /* OK status. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2018 ** 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 ** **--------------------------------------------------------------------*/ }