#include "sofam.h"
int iauStarpv(double ra, double dec,
double pmr, double pmd, double px, double rv,
double pv[2][3])
/*
** - - - - - - - - - -
** i a u S t a r p v
** - - - - - - - - - -
**
** Convert star catalog coordinates to position+velocity vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given (Note 1):
** ra double right ascension (radians)
** dec double declination (radians)
** pmr double RA proper motion (radians/year)
** pmd double Dec proper motion (radians/year)
** px double parallax (arcseconds)
** rv double radial velocity (km/s, positive = receding)
**
** Returned (Note 2):
** pv double[2][3] pv-vector (AU, AU/day)
**
** Returned (function value):
** int status:
** 0 = no warnings
** 1 = distance overridden (Note 6)
** 2 = excessive speed (Note 7)
** 4 = solution didn't converge (Note 8)
** else = binary logical OR of the above
**
** Notes:
**
** 1) The star data accepted by this function are "observables" for an
** imaginary observer at the solar-system barycenter. Proper motion
** and radial velocity are, strictly, in terms of barycentric
** coordinate time, TCB. For most practical applications, it is
** permissible to neglect the distinction between TCB and ordinary
** "proper" time on Earth (TT/TAI). The result will, as a rule, be
** limited by the intrinsic accuracy of the proper-motion and
** radial-velocity data; moreover, the pv-vector is likely to be
** merely an intermediate result, so that a change of time unit
** would cancel out overall.
**
** In accordance with normal star-catalog conventions, the object's
** right ascension and declination are freed from the effects of
** secular aberration. The frame, which is aligned to the catalog
** equator and equinox, is Lorentzian and centered on the SSB.
**
** 2) The resulting position and velocity pv-vector is with respect to
** the same frame and, like the catalog coordinates, is freed from
** the effects of secular aberration. Should the "coordinate
** direction", where the object was located at the catalog epoch, be
** required, it may be obtained by calculating the magnitude of the
** position vector pv[0][0-2] dividing by the speed of light in
** AU/day to give the light-time, and then multiplying the space
** velocity pv[1][0-2] by this light-time and adding the result to
** pv[0][0-2].
**
** Summarizing, the pv-vector returned is for most stars almost
** identical to the result of applying the standard geometrical
** "space motion" transformation. The differences, which are the
** subject of the Stumpff paper referenced below, are:
**
** (i) In stars with significant radial velocity and proper motion,
** the constantly changing light-time distorts the apparent proper
** motion. Note that this is a classical, not a relativistic,
** effect.
**
** (ii) The transformation complies with special relativity.
**
** 3) Care is needed with units. The star coordinates are in radians
** and the proper motions in radians per Julian year, but the
** parallax is in arcseconds; the radial velocity is in km/s, but
** the pv-vector result is in AU and AU/day.
**
** 4) The RA proper motion is in terms of coordinate angle, not true
** angle. If the catalog uses arcseconds for both RA and Dec proper
** motions, the RA proper motion will need to be divided by cos(Dec)
** before use.
**
** 5) Straight-line motion at constant speed, in the inertial frame,
** is assumed.
**
** 6) An extremely small (or zero or negative) parallax is interpreted
** to mean that the object is on the "celestial sphere", the radius
** of which is an arbitrary (large) value (see the constant PXMIN).
** When the distance is overridden in this way, the status,
** initially zero, has 1 added to it.
**
** 7) If the space velocity is a significant fraction of c (see the
** constant VMAX), it is arbitrarily set to zero. When this action
** occurs, 2 is added to the status.
**
** 8) The relativistic adjustment involves an iterative calculation.
** If the process fails to converge within a set number (IMAX) of
** iterations, 4 is added to the status.
**
** 9) The inverse transformation is performed by the function
** iauPvstar.
**
** Called:
** iauS2pv spherical coordinates to pv-vector
** iauPm modulus of p-vector
** iauZp zero p-vector
** iauPn decompose p-vector into modulus and direction
** iauPdp scalar product of two p-vectors
** iauSxp multiply p-vector by scalar
** iauPmp p-vector minus p-vector
** iauPpp p-vector plus p-vector
**
** Reference:
**
** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
**
** This revision: 2009 July 6
**
** SOFA release 2012-03-01
**
** Copyright (C) 2012 IAU SOFA Board. See notes at end.
*/
{
/* Smallest allowed parallax */
static const double PXMIN = 1e-7;
/* Largest allowed speed (fraction of c) */
static const double VMAX = 0.5;
/* Maximum number of iterations for relativistic solution */
static const int IMAX = 100;
int i, iwarn;
double w, r, rd, rad, decd, v, x[3], usr[3], ust[3],
vsr, vst, betst, betsr, bett, betr,
dd, ddel, ur[3], ut[3],
d = 0.0, del = 0.0, /* to prevent */
odd = 0.0, oddel = 0.0, /* compiler */
od = 0.0, odel = 0.0; /* warnings */
/* Distance (AU). */
if (px >= PXMIN) {
w = px;
iwarn = 0;
} else {
w = PXMIN;
iwarn = 1;
}
r = DR2AS / w;
/* Radial velocity (AU/day). */
rd = DAYSEC * rv * 1e3 / DAU;
/* Proper motion (radian/day). */
rad = pmr / DJY;
decd = pmd / DJY;
/* To pv-vector (AU,AU/day). */
iauS2pv(ra, dec, r, rad, decd, rd, pv);
/* If excessive velocity, arbitrarily set it to zero. */
v = iauPm(pv[1]);
if (v / DC > VMAX) {
iauZp(pv[1]);
iwarn += 2;
}
/* Isolate the radial component of the velocity (AU/day). */
iauPn(pv[0], &w, x);
vsr = iauPdp(x, pv[1]);
iauSxp(vsr, x, usr);
/* Isolate the transverse component of the velocity (AU/day). */
iauPmp(pv[1], usr, ust);
vst = iauPm(ust);
/* Special-relativity dimensionless parameters. */
betsr = vsr / DC;
betst = vst / DC;
/* Determine the inertial-to-observed relativistic correction terms. */
bett = betst;
betr = betsr;
for (i = 0; i < IMAX; i++) {
d = 1.0 + betr;
del = sqrt(1.0 - betr*betr - bett*bett) - 1.0;
betr = d * betsr + del;
bett = d * betst;
if (i > 0) {
dd = fabs(d - od);
ddel = fabs(del - odel);
if ((i > 1) && (dd >= odd) && (ddel >= oddel)) break;
odd = dd;
oddel = ddel;
}
od = d;
odel = del;
}
if (i >= IMAX) iwarn += 4;
/* Replace observed radial velocity with inertial value. */
w = (betsr != 0.0) ? d + del / betsr : 1.0;
iauSxp(w, usr, ur);
/* Replace observed tangential velocity with inertial value. */
iauSxp(d, ust, ut);
/* Combine the two to obtain the inertial space velocity. */
iauPpp(ur, ut, pv[1]);
/* Return the status. */
return iwarn;
/*----------------------------------------------------------------------
**
** Copyright (C) 2012
** 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
**
**--------------------------------------------------------------------*/
}