SUBROUTINE iau_LD ( BM, P, Q, E, EM, DLIM, P1 ) *+ * - - - - - - - * i a u _ L D * - - - - - - - * * Apply light deflection by a solar-system body, 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: * BM d mass of the gravitating body (solar masses) * P d(3) direction from observer to source (unit vector) * Q d(3) direction from body to source (unit vector) * E d(3) direction from body to observer (unit vector) * EM d distance from body to observer (au) * DLIM d deflection limiter (Note 4) * * Returned: * P1 d(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) To accumulate total light deflection taking into account the * contributions from several bodies, call the present routine for * each body in succession, in decreasing order of distance from the * observer. * * 7) 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: * iau_PDP scalar product of two p-vectors * iau_PXP vector product of two p-vectors * * This revision: 2013 September 3 * * SOFA release 2021-05-12 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION BM, P(3), Q(3), E(3), EM, DLIM, P1(3) * Schwarzschild radius of the Sun (au) * = 2 * 1.32712440041 D20 / (2.99792458 D8)^2 / 1.49597870700 D11 DOUBLE PRECISION SRS PARAMETER ( SRS = 1.97412574336D-08 ) INTEGER I DOUBLE PRECISION QPE(3), QDQPE, W, EQ(3), PEQ(3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Q . (Q + E). DO 1 I=1,3 QPE(I) = Q(I) + E(I) 1 CONTINUE CALL iau_PDP ( Q, QPE, QDQPE ) * 2 x G x BM / ( EM x c^2 x ( Q . (Q + E) ) ). W = BM * SRS / EM / MAX ( QDQPE, DLIM ) * P x (E x Q). CALL iau_PXP ( E, Q, EQ ) CALL iau_PXP ( P, EQ, PEQ ) * Apply the deflection. DO 2 I = 1,3 P1(I) = P(I) + W*PEQ(I) 2 CONTINUE * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2021 * 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