#include "sofa.h" void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]) /* ** - - - - - - ** i a u L d ** - - - - - - ** ** Apply light deflection by a solar-system body, as part of ** transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** bm double mass of the gravitating body (solar masses) ** p double[3] direction from observer to source (unit vector) ** q double[3] direction from body to source (unit vector) ** e double[3] direction from body to observer (unit vector) ** em double distance from body to observer (au) ** dlim double deflection limiter (Note 4) ** ** Returned: ** p1 double[3] observer to deflected source (unit vector) ** ** Notes: ** ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann ** 2013), with some rearrangement to minimize the effects of machine ** precision. ** ** 2) The mass parameter bm can, as required, be adjusted in order to ** allow for such effects as quadrupole field. ** ** 3) The barycentric position of the deflecting body should ideally ** correspond to the time of closest approach of the light ray to ** the body. ** ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is ** the angular separation (in radians) between source and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. ** ** 5) The returned vector p1 is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 6) The arguments p and p1 can be the same array. ** ** 7) To accumulate total light deflection taking into account the ** contributions from several bodies, call the present function for ** each body in succession, in decreasing order of distance from the ** observer. ** ** 8) For efficiency, validation is omitted. The supplied vectors must ** be of unit magnitude, and the deflection limiter non-zero and ** positive. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauPdp scalar product of two p-vectors ** iauPxp vector product of two p-vectors ** ** This revision: 2013 October 9 ** ** SOFA release 2020-07-21 ** ** Copyright (C) 2020 IAU SOFA Board. See notes at end. */ { int i; double qpe[3], qdqpe, w, eq[3], peq[3]; /* q . (q + e). */ for (i = 0; i < 3; i++) { qpe[i] = q[i] + e[i]; } qdqpe = iauPdp(q, qpe); /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */ w = bm * SRS / em / gmax(qdqpe,dlim); /* p x (e x q). */ iauPxp(e, q, eq); iauPxp(p, eq, peq); /* Apply the deflection. */ for (i = 0; i < 3; i++) { p1[i] = p[i] + w*peq[i]; } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2020 ** 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 ** **--------------------------------------------------------------------*/ }