void iauLdsun(double p[3], double e[3], double em, double p1[3])
/*
** - - - - - - - - -
** i a u L d s u n
** - - - - - - - - -
**
** Deflection of starlight by the Sun.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** p double[3] direction from observer to star (unit vector)
** e double[3] direction from Sun to observer (unit vector)
** em double distance from Sun to observer (au)
**
** Returned:
** p1 double[3] observer to deflected star (unit vector)
**
** Notes:
**
** 1) The source is presumed to be sufficiently distant that its
** directions seen from the Sun and the observer are essentially
** the same.
**
** 2) The deflection is restrained when the angle between the star and
** the center of the Sun is less than a threshold value, falling to
** zero deflection for zero separation. The chosen threshold value
** is within the solar limb for all solar-system applications, and
** is about 5 arcminutes for the case of a terrestrial observer.
**
** 3) The arguments p and p1 can be the same array.
**
** Called:
** iauLd light deflection by a solar-system body
**
** This revision: 2016 June 16
**
** SOFA release 2016-05-03
**
** Copyright (C) 2016 IAU SOFA Board. See notes at end.
*/
{
double em2, dlim;
/* Deflection limiter (smaller for distant observers). */
em2 = em*em;
if ( em2 < 1.0 ) em2 = 1.0;
dlim = 1e-6 / (em2 > 1.0 ? em2 : 1.0);
/* Apply the deflection. */
iauLd(1.0, p, p, e, em, dlim, p1);
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2016
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
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: 2017 March 16
**
** SOFA release 2017-04-20
**
** Copyright (C) 2017 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) 2017
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}