#include "erfa.h"
void eraLdn(int n, eraLDBODY b[], double ob[3], double sc[3],
double sn[3])
/*+
** - - - - - - -
** e r a L d n
** - - - - - - -
**
** For a star, apply light deflection by multiple solar-system bodies,
** as part of transforming coordinate direction into natural direction.
**
** Given:
** n int number of bodies (note 1)
** b eraLDBODY[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 eraLd function. Similarly, eraLd 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:
** eraCp copy p-vector
** eraPdp scalar product of two p-vectors
** eraPmp p-vector minus p-vector
** eraPpsp p-vector plus scaled p-vector
** eraPn decompose p-vector into modulus and direction
** eraLd light deflection by a solar-system body
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Light time for 1 AU (days) */
const double CR = ERFA_AULT/ERFA_DAYSEC;
int i;
double v[3], dt, ev[3], em, e[3];
/* Star direction prior to deflection. */
eraCp(sc, sn);
/* Body by body. */
for ( i = 0; i < n; i++ ) {
/* Body to observer vector at epoch of observation (au). */
eraPmp ( ob, b[i].pv[0], v );
/* Minus the time since the light passed the body (days). */
dt = eraPdp(sn,v) * CR;
/* Neutralize if the star is "behind" the observer. */
dt = ERFA_GMIN(dt, 0.0);
/* Backtrack the body to the time the light was passing the body. */
eraPpsp(v, -dt, b[i].pv[1], ev);
/* Body to observer vector as magnitude and direction. */
eraPn(ev, &em, e);
/* Apply light deflection for this body. */
eraLd ( b[i].bm, sn, sn, e, em, b[i].dl, sn );
/* Next body. */
}
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2016, 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.
**
*/