SUBROUTINE iau_LDN ( N, B, OB, SC, SN ) *+ * - - - - - - - - * 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 routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * N i number of bodies (Note 1) * B d(8,N) data for each of the N bodies (Notes 1,2): * (1,I) mass of the body (solar masses, Note 3) * (2,I) deflection limiter (Note 4) * (3-5,I) barycentric position of the body (au) * (6-8,I) barycentric velocity of the body (au/day) * OB d(3) barycentric position of the observer (au) * SC d(3) observer to star coordinate direction (unit vector) * * Returned: * SN d(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(1,I) * can, as required, be adjusted in order to allow for such effects * as quadrupole field. * * 4) The deflection limiter parameter B(2,I) 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(1,I) B(2,I) * * Sun 1D0 6D-6 * Jupiter 0.00095435D0 3D-9 * Saturn 0.00028574D0 3D-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 iau_LD routine. Similarly, iau_LD 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) 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: * iau_CP copy p-vector * iau_PDP scalar product of two p-vectors * iau_PMP p-vector minus p-vector * iau_PPSP p-vector plus scaled p-vector * iau_PN decompose p-vector into modulus and direction * iau_LD light deflection by a solar-system body * * This revision: 2017 March 16 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE INTEGER N DOUBLE PRECISION B(8,N), OB(3), SC(3), SN(3) * Seconds per day. DOUBLE PRECISION DAYSEC PARAMETER ( DAYSEC = 86400D0 ) * Speed of light (m/s) DOUBLE PRECISION CMPS PARAMETER ( CMPS = 299792458D0 ) * Astronomical unit (m, IAU 2012) DOUBLE PRECISION AUM PARAMETER ( AUM = 149597870.7D3 ) * Light time for 1 au (day) DOUBLE PRECISION CR PARAMETER ( CR = AUM/CMPS/DAYSEC ) INTEGER I DOUBLE PRECISION S(3), V(3), D , DT, EV(3), EM, E(3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Star direction prior to deflection. CALL iau_CP ( SC, S ) * Body by body. DO 1 I=1,N * Body to observer vector at epoch of observation (au). CALL iau_PMP ( OB, B(3,I), V ) * Minus the time since the light passed the body (days). CALL iau_PDP ( S, V, D ) DT = D * CR * Neutralize if the star is "behind" the observer. DT = MIN ( DT, 0D0 ) * Backtrack the body to the time the light was passing the body. CALL iau_PPSP ( V, -DT, B(6,I), EV ) * Separate the body to observer vector into magnitude and direction. CALL iau_PN ( EV, EM, E ) * Apply light deflection for this body. CALL iau_LD ( B(1,I), S, S, E, EM, B(2,I), V ) * Update the star direction. CALL iau_CP ( V, S ) * Next body. 1 CONTINUE * Return the deflected star direction. CALL iau_CP ( S, SN ) * 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