#include "erfa.h"
void eraLd(double bm, double p[3], double q[3], double e[3],
double em, double dlim, double p1[3])
/*
** - - - - - -
** e r a L d
** - - - - - -
**
** Apply light deflection by a solar-system body, as part of
** transforming coordinate direction into natural direction.
**
** 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:
** eraPdp scalar product of two p-vectors
** eraPxp vector product of two p-vectors
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
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 = eraPdp(q, qpe);
/* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
w = bm * ERFA_SRS / em / ERFA_GMAX(qdqpe,dlim);
/* p x (e x q). */
eraPxp(e, q, eq);
eraPxp(p, eq, peq);
/* Apply the deflection. */
for (i = 0; i < 3; i++) {
p1[i] = p[i] + w*peq[i];
}
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/