#include "sofa.h" void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]) /*+ ** - - - - - - - ** i a u L d n ** - - - - - - - ** ** For a star, apply light deflection by multiple solar-system bodies, ** 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: ** n int number of bodies (note 1) ** b iauLDBODY[n] data for each of the n bodies (Notes 1,2): ** bm double mass of the body (solar masses, Note 3) ** dl double deflection limiter (Note 4) ** pv [2][3] barycentric PV of the body (au, au/day) ** ob double[3] barycentric position of the observer (au) ** sc double[3] observer to star coord direction (unit vector) ** ** Returned: ** sn double[3] observer to deflected star (unit vector) ** ** 1) The array b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 2) The array b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 3) In the entry in the b array for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 4) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 5) For cases where the starlight passes the body before reaching the ** observer, the body is placed back along its barycentric track by ** the light time from that point to the observer. For cases where ** the body is "behind" the observer no such shift is applied. If ** a different treatment is preferred, the user has the option of ** instead using the iauLd function. Similarly, iauLd can be used ** for cases where the source is nearby, not a star. ** ** 6) The returned vector sn is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 7) The arguments sc and sn can be the same array. ** ** 8) For efficiency, validation is omitted. The supplied masses must ** be greater than zero, the position and velocity vectors must be ** right, and the deflection limiter greater than zero. ** ** Reference: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.2.4. ** ** Called: ** iauCp copy p-vector ** iauPdp scalar product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPpsp p-vector plus scaled p-vector ** iauPn decompose p-vector into modulus and direction ** iauLd light deflection by a solar-system body ** ** This revision: 2013 October 9 ** ** SOFA release 2015-02-09 ** ** Copyright (C) 2015 IAU SOFA Board. See notes at end. */ { /* Light time for 1 AU (days) */ const double CR = AULT/DAYSEC; int i; double v[3], dt, ev[3], em, e[3]; /* Star direction prior to deflection. */ iauCp(sc, sn); /* Body by body. */ for ( i = 0; i < n; i++ ) { /* Body to observer vector at epoch of observation (au). */ iauPmp ( ob, b[i].pv[0], v ); /* Minus the time since the light passed the body (days). */ dt = iauPdp(sn,v) * CR; /* Neutralize if the star is "behind" the observer. */ dt = gmin(dt, 0.0); /* Backtrack the body to the time the light was passing the body. */ iauPpsp(v, -dt, b[i].pv[1], ev); /* Body to observer vector as magnitude and direction. */ iauPn(ev, &em, e); /* Apply light deflection for this body. */ iauLd ( b[i].bm, sn, sn, e, em, b[i].dl, sn ); /* Next body. */ } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2015 ** 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 ** **--------------------------------------------------------------------*/ }