void palSubet ( double rc, double dc, double eq, double *rm, double *dm ) {
double a[3]; /* The E-terms */
double v[3];
double f;
int i;
/* Note the preference for IAU routines */
/* Retrieve the E-terms */
palEtrms( eq, a );
/* Spherical to Cartesian */
iauS2c( rc, dc, v );
/* Include the E-terms */
f = 1.0 + iauPdp( v, a );
for (i=0; i<3; i++) {
v[i] = f*v[i] - a[i];
}
/* Cartesian to spherical */
iauC2s( v, rm, dm );
/* Bring RA into conventional range */
*rm = iauAnp( *rm );
}
int iauPvstar(double pv[2][3], double *ra, double *dec,
double *pmr, double *pmd, double *px, double *rv)
/*
** - - - - - - - - - -
** i a u P v s t a r
** - - - - - - - - - -
**
** Convert star position+velocity vector to catalog coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given (Note 1):
** pv double[2][3] pv-vector (AU, AU/day)
**
** Returned (Note 2):
** 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 (arcsec)
** rv double radial velocity (km/s, positive = receding)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = superluminal speed (Note 5)
** -2 = null position vector
**
** Notes:
**
** 1) The specified pv-vector is the coordinate direction (and its rate
** of change) for the date at which the light leaving the star
** reached the solar-system barycenter.
**
** 2) The star data returned 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 supplied pv-vector is likely
** to be merely an intermediate result (for example generated by the
** function iauStarpv), so that a change of time unit will 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.
**
** Summarizing, the specified pv-vector is for most stars almost
** identical to the result of applying the standard geometrical
** "space motion" transformation to the catalog data. The
** differences, which are the subject of the Stumpff paper cited
** 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 proper motions are the rate of change of the right ascension
** and declination at the catalog epoch and are in radians per Julian
** year. The RA proper motion is in terms of coordinate angle, not
** true angle, and will thus be numerically larger at high
** declinations.
**
** 5) Straight-line motion at constant speed in the inertial frame is
** assumed. If the speed is greater than or equal to the speed of
** light, the function aborts with an error status.
**
** 6) The inverse transformation is performed by the function iauStarpv.
**
** Called:
** 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
** iauPm modulus of p-vector
** iauPpp p-vector plus p-vector
** iauPv2s pv-vector to spherical
** iauAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
**
** This revision: 2013 June 18
**
** SOFA release 2015-02-09
**
** Copyright (C) 2015 IAU SOFA Board. See notes at end.
*/
{
double r, x[3], vr, ur[3], vt, ut[3], bett, betr, d, w, del,
usr[3], ust[3], a, rad, decd, rd;
/* Isolate the radial component of the velocity (AU/day, inertial). */
iauPn(pv[0], &r, x);
vr = iauPdp(x, pv[1]);
iauSxp(vr, x, ur);
/* Isolate the transverse component of the velocity (AU/day, inertial). */
iauPmp(pv[1], ur, ut);
vt = iauPm(ut);
/* Special-relativity dimensionless parameters. */
bett = vt / DC;
betr = vr / DC;
/* The inertial-to-observed correction terms. */
d = 1.0 + betr;
w = 1.0 - betr*betr - bett*bett;
if (d == 0.0 || w < 0) return -1;
del = sqrt(w) - 1.0;
/* Apply relativistic correction factor to radial velocity component. */
w = (betr != 0) ? (betr - del) / (betr * d) : 1.0;
iauSxp(w, ur, usr);
/* Apply relativistic correction factor to tangential velocity */
/* component. */
iauSxp(1.0/d, ut, ust);
/* Combine the two to obtain the observed velocity vector (AU/day). */
iauPpp(usr, ust, pv[1]);
/* Cartesian to spherical. */
iauPv2s(pv, &a, dec, &r, &rad, &decd, &rd);
if (r == 0.0) return -2;
/* Return RA in range 0 to 2pi. */
*ra = iauAnp(a);
/* Return proper motions in radians per year. */
*pmr = rad * DJY;
*pmd = decd * DJY;
/* Return parallax in arcsec. */
*px = DR2AS / r;
/* Return radial velocity in km/s. */
*rv = 1e-3 * rd * DAU / DAYSEC;
/* OK status. */
return 0;
/*----------------------------------------------------------------------
**
** Copyright (C) 2015
** 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 iauLd(double bm, double p[3], double q[3], double e[3],
double em, double dlim, double p1[3])
/*
** - - - - - -
** i a u L d
** - - - - - -
**
** Apply light deflection by a solar-system body, 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:
** 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:
** iauPdp scalar product of two p-vectors
** iauPxp vector product of two p-vectors
**
** This revision: 2013 October 9
**
** SOFA release 2015-02-09
**
** Copyright (C) 2015 IAU SOFA Board. See notes at end.
*/
{
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 = iauPdp(q, qpe);
/* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
w = bm * SRS / em / gmax(qdqpe,dlim);
/* p x (e x q). */
iauPxp(e, q, eq);
iauPxp(p, eq, peq);
/* Apply the deflection. */
for (i = 0; i < 3; i++) {
p1[i] = p[i] + w*peq[i];
}
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2015
** 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
**
**--------------------------------------------------------------------*/
}
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.
**
** 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
**
** Original version 2012-03-01
**
** Copyright (C) 2013 Naoki Arita. 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;
/*----------------------------------------------------------------------
**
** Celes is a wrapper of the SOFA Library for Ruby.
**
** This file is redistributed and relicensed in accordance with
** the SOFA Software License (http://www.iausofa.org/tandc.html).
**
** The original library is available from IAU Standards of
** Fundamental Astronomy (http://www.iausofa.org/).
**
**
**
**
**
** Copyright (C) 2013, Naoki Arita
** All rights reserved.
**
** 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.
**
**--------------------------------------------------------------------*/
}
double iauSepp(double a[3], double b[3])
/*
** - - - - - - - -
** i a u S e p p
** - - - - - - - -
**
** Angular separation between two p-vectors.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector (not necessarily unit length)
** b double[3] second p-vector (not necessarily unit length)
**
** Returned (function value):
** double angular separation (radians, always positive)
**
** Notes:
**
** 1) If either vector is null, a zero result is returned.
**
** 2) The angular separation is most simply formulated in terms of
** scalar product. However, this gives poor accuracy for angles
** near zero and pi. The present algorithm uses both cross product
** and dot product, to deliver full accuracy whatever the size of
** the angle.
**
** Called:
** iauPxp vector product of two p-vectors
** iauPm modulus of p-vector
** iauPdp scalar product of two p-vectors
**
** This revision: 2008 May 22
**
** SOFA release 2012-03-01
**
** Copyright (C) 2012 IAU SOFA Board. See notes at end.
*/
{
double axb[3], ss, cs, s;
/* Sine of angle between the vectors, multiplied by the two moduli. */
iauPxp(a, b, axb);
ss = iauPm(axb);
/* Cosine of the angle, multiplied by the two moduli. */
cs = iauPdp(a, b);
/* The angle. */
s = ((ss != 0.0) || (cs != 0.0)) ? atan2(ss, cs) : 0.0;
return s;
/*----------------------------------------------------------------------
**
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
double iauPap(double a[3], double b[3])
/*
** - - - - - - -
** i a u P a p
** - - - - - - -
**
** Position-angle from two p-vectors.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] direction of reference point
** b double[3] direction of point whose PA is required
**
** Returned (function value):
** double position angle of b with respect to a (radians)
**
** Notes:
**
** 1) The result is the position angle, in radians, of direction b with
** respect to direction a. It is in the range -pi to +pi. The
** sense is such that if b is a small distance "north" of a the
** position angle is approximately zero, and if b is a small
** distance "east" of a the position angle is approximately +pi/2.
**
** 2) The vectors a and b need not be of unit length.
**
** 3) Zero is returned if the two directions are the same or if either
** vector is null.
**
** 4) If vector a is at a pole, the result is ill-defined.
**
** Called:
** iauPn decompose p-vector into modulus and direction
** iauPm modulus of p-vector
** iauPxp vector product of two p-vectors
** iauPmp p-vector minus p-vector
** iauPdp scalar product of two p-vectors
**
** This revision: 2008 May 25
**
** SOFA release 2012-03-01
**
** Copyright (C) 2012 IAU SOFA Board. See notes at end.
*/
{
double am, au[3], bm, st, ct, xa, ya, za, eta[3], xi[3], a2b[3], pa;
/* Modulus and direction of the a vector. */
iauPn(a, &am, au);
/* Modulus of the b vector. */
bm = iauPm(b);
/* Deal with the case of a null vector. */
if ((am == 0.0) || (bm == 0.0)) {
st = 0.0;
ct = 1.0;
} else {
/* The "north" axis tangential from a (arbitrary length). */
xa = a[0];
ya = a[1];
za = a[2];
eta[0] = -xa * za;
eta[1] = -ya * za;
eta[2] = xa*xa + ya*ya;
/* The "east" axis tangential from a (same length). */
iauPxp(eta, au, xi);
/* The vector from a to b. */
iauPmp(b, a, a2b);
/* Resolve into components along the north and east axes. */
st = iauPdp(a2b, xi);
ct = iauPdp(a2b, eta);
/* Deal with degenerate cases. */
if ((st == 0.0) && (ct == 0.0)) ct = 1.0;
}
/* Position angle. */
pa = atan2(st, ct);
return pa;
/*----------------------------------------------------------------------
**
** 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: [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
**
**--------------------------------------------------------------------*/
}
int iauStarpm(double ra1, double dec1,
double pmr1, double pmd1, double px1, double rv1,
double ep1a, double ep1b, double ep2a, double ep2b,
double *ra2, double *dec2,
double *pmr2, double *pmd2, double *px2, double *rv2)
/*
** - - - - - - - - - -
** i a u S t a r p m
** - - - - - - - - - -
**
** Star proper motion: update star catalog data for space motion.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** ra1 double right ascension (radians), before
** dec1 double declination (radians), before
** pmr1 double RA proper motion (radians/year), before
** pmd1 double Dec proper motion (radians/year), before
** px1 double parallax (arcseconds), before
** rv1 double radial velocity (km/s, +ve = receding), before
** ep1a double "before" epoch, part A (Note 1)
** ep1b double "before" epoch, part B (Note 1)
** ep2a double "after" epoch, part A (Note 1)
** ep2b double "after" epoch, part B (Note 1)
**
** Returned:
** ra2 double right ascension (radians), after
** dec2 double declination (radians), after
** pmr2 double RA proper motion (radians/year), after
** pmd2 double Dec proper motion (radians/year), after
** px2 double parallax (arcseconds), after
** rv2 double radial velocity (km/s, +ve = receding), after
**
** Returned (function value):
** int status:
** -1 = system error (should not occur)
** 0 = no warnings or errors
** 1 = distance overridden (Note 6)
** 2 = excessive velocity (Note 7)
** 4 = solution didn't converge (Note 8)
** else = binary logical OR of the above warnings
**
** Notes:
**
** 1) The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are
** Julian Dates, apportioned in any convenient way between the two
** parts (A and B). For example, JD(TDB)=2450123.7 could be
** expressed in any of these ways, among others:
**
** epna epnb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) 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.
**
** The proper motions are the rate of change of the right ascension
** and declination at the catalog epoch and are in radians per TDB
** Julian year.
**
** The parallax and radial velocity are in the same frame.
**
** 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.
**
** 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 iauStarpv
** function for the value used). 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 in the function iauStarpv), it is arbitrarily set
** to zero. When this action occurs, 2 is added to the status.
**
** 8) The relativistic adjustment carried out in the iauStarpv function
** involves an iterative calculation. If the process fails to
** converge within a set number of iterations, 4 is added to the
** status.
**
** Called:
** iauStarpv star catalog data to space motion pv-vector
** iauPvu update a pv-vector
** iauPdp scalar product of two p-vectors
** iauPvstar space motion pv-vector to star catalog data
**
** This revision: 2008 May 16
**
** SOFA release 2012-03-01
**
** Copyright (C) 2012 IAU SOFA Board. See notes at end.
*/
{
double pv1[2][3], tl1, dt, pv[2][3], r2, rdv, v2, c2mv2, tl2,
pv2[2][3];
int j1, j2, j;
/* RA,Dec etc. at the "before" epoch to space motion pv-vector. */
j1 = iauStarpv(ra1, dec1, pmr1, pmd1, px1, rv1, pv1);
/* Light time when observed (days). */
tl1 = iauPm(pv1[0]) / DC;
/* Time interval, "before" to "after" (days). */
dt = (ep2a - ep1a) + (ep2b - ep1b);
/* Move star along track from the "before" observed position to the */
/* "after" geometric position. */
iauPvu(dt + tl1, pv1, pv);
/* From this geometric position, deduce the observed light time (days) */
/* at the "after" epoch (with theoretically unneccessary error check). */
r2 = iauPdp(pv[0], pv[0]);
rdv = iauPdp(pv[0], pv[1]);
v2 = iauPdp(pv[1], pv[1]);
c2mv2 = DC*DC - v2;
if (c2mv2 <= 0) return -1;
tl2 = (-rdv + sqrt(rdv*rdv + c2mv2*r2)) / c2mv2;
/* Move the position along track from the observed place at the */
/* "before" epoch to the observed place at the "after" epoch. */
iauPvu(dt + (tl1 - tl2), pv1, pv2);
/* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */
j2 = iauPvstar(pv2, ra2, dec2, pmr2, pmd2, px2, rv2);
/* Final status. */
j = (j2 == 0) ? j1 : -1;
return j;
/*----------------------------------------------------------------------
**
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
