void eraP2pv(double p[3], double pv[2][3])
/*
** - - - - - - - -
** e r a P 2 p v
** - - - - - - - -
**
** Extend a p-vector to a pv-vector by appending a zero velocity.
**
** Given:
** p double[3] p-vector
**
** Returned:
** pv double[2][3] pv-vector
**
** Called:
** eraCp copy p-vector
** eraZp zero p-vector
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
eraCp(p, pv[0]);
eraZp(pv[1]);
return;
}
void eraPn(double p[3], double *r, double u[3])
/*
** - - - - - -
** e r a P n
** - - - - - -
**
** Convert a p-vector into modulus and unit vector.
**
** Given:
** p double[3] p-vector
**
** Returned:
** r double modulus
** u double[3] unit vector
**
** Notes:
**
** 1) If p is null, the result is null. Otherwise the result is a unit
** vector.
**
** 2) It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** eraPm modulus of p-vector
** eraZp zero p-vector
** eraSxp multiply p-vector by scalar
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double w;
/* Obtain the modulus and test for zero. */
w = eraPm(p);
if (w == 0.0) {
/* Null vector. */
eraZp(u);
} else {
/* Unit vector. */
eraSxp(1.0/w, p, u);
}
/* Return the modulus. */
*r = w;
return;
}
void eraZpv(double pv[2][3])
/*
** - - - - - - -
** e r a Z p v
** - - - - - - -
**
** Zero a pv-vector.
**
** Returned:
** pv double[2][3] pv-vector
**
** Called:
** eraZp zero p-vector
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
eraZp(pv[0]);
eraZp(pv[1]);
return;
}
void eraAticq(double ri, double di, eraASTROM *astrom,
double *rc, double *dc)
/*
** - - - - - - - - -
** e r a A t i c q
** - - - - - - - - -
**
** Quick CIRS RA,Dec to ICRS astrometric place, given the star-
** independent astrometry parameters.
**
** Use of this function is appropriate when efficiency is important and
** where many star positions are all to be transformed for one date.
** The star-independent astrometry parameters can be obtained by
** calling one of the functions eraApci[13], eraApcg[13], eraApco[13]
** or eraApcs[13].
**
** Given:
** ri,di double CIRS RA,Dec (radians)
** astrom eraASTROM* star-independent astrometry parameters:
** pmt double PM time interval (SSB, Julian years)
** eb double[3] SSB to observer (vector, au)
** eh double[3] Sun to observer (unit vector)
** em double distance from Sun to observer (au)
** v double[3] barycentric observer velocity (vector, c)
** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
** bpn double[3][3] bias-precession-nutation matrix
** along double longitude + s' (radians)
** xpl double polar motion xp wrt local meridian (radians)
** ypl double polar motion yp wrt local meridian (radians)
** sphi double sine of geodetic latitude
** cphi double cosine of geodetic latitude
** diurab double magnitude of diurnal aberration vector
** eral double "local" Earth rotation angle (radians)
** refa double refraction constant A (radians)
** refb double refraction constant B (radians)
**
** Returned:
** rc,dc double ICRS astrometric RA,Dec (radians)
**
** Notes:
**
** 1) Only the Sun is taken into account in the light deflection
** correction.
**
** 2) Iterative techniques are used for the aberration and light
** deflection corrections so that the functions eraAtic13 (or
** eraAticq) and eraAtci13 (or eraAtciq) are accurate inverses;
** even at the edge of the Sun's disk the discrepancy is only about
** 1 nanoarcsecond.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraTrxp product of transpose of r-matrix and p-vector
** eraZp zero p-vector
** eraAb stellar aberration
** eraLdsun light deflection by the Sun
** eraC2s p-vector to spherical
** eraAnp normalize angle into range +/- pi
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int j, i;
double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r,
after[3];
/* CIRS RA,Dec to Cartesian. */
eraS2c(ri, di, pi);
/* Bias-precession-nutation, giving GCRS proper direction. */
eraTrxp(astrom->bpn, pi, ppr);
/* Aberration, giving GCRS natural direction. */
eraZp(d);
for (j = 0; j < 2; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = ppr[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraAb(before, astrom->v, astrom->em, astrom->bm1, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = ppr[i] - d[i];
pnat[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pnat[i] /= r;
}
}
/* Light deflection by the Sun, giving BCRS coordinate direction. */
eraZp(d);
for (j = 0; j < 5; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = pnat[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraLdsun(before, astrom->eh, astrom->em, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = pnat[i] - d[i];
pco[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pco[i] /= r;
}
}
/* ICRS astrometric RA,Dec. */
eraC2s(pco, &w, dc);
*rc = eraAnp(w);
/* Finished. */
}
int eraStarpv(double ra, double dec,
double pmr, double pmd, double px, double rv,
double pv[2][3])
/*
** - - - - - - - - - -
** e r a S t a r p v
** - - - - - - - - - -
**
** Convert star catalog coordinates to position+velocity vector.
**
** 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
** eraPvstar.
**
** Called:
** eraS2pv spherical coordinates to pv-vector
** eraPm modulus of p-vector
** eraZp zero p-vector
** eraPn decompose p-vector into modulus and direction
** eraPdp scalar product of two p-vectors
** eraSxp multiply p-vector by scalar
** eraPmp p-vector minus p-vector
** eraPpp p-vector plus p-vector
**
** Reference:
**
** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* 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 = ERFA_DR2AS / w;
/* Radial velocity (AU/day). */
rd = ERFA_DAYSEC * rv * 1e3 / ERFA_DAU;
/* Proper motion (radian/day). */
rad = pmr / ERFA_DJY;
decd = pmd / ERFA_DJY;
/* To pv-vector (AU,AU/day). */
eraS2pv(ra, dec, r, rad, decd, rd, pv);
/* If excessive velocity, arbitrarily set it to zero. */
v = eraPm(pv[1]);
if (v / ERFA_DC > VMAX) {
eraZp(pv[1]);
iwarn += 2;
}
/* Isolate the radial component of the velocity (AU/day). */
eraPn(pv[0], &w, x);
vsr = eraPdp(x, pv[1]);
eraSxp(vsr, x, usr);
/* Isolate the transverse component of the velocity (AU/day). */
eraPmp(pv[1], usr, ust);
vst = eraPm(ust);
/* Special-relativity dimensionless parameters. */
betsr = vsr / ERFA_DC;
betst = vst / ERFA_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;
eraSxp(w, usr, ur);
/* Replace observed tangential velocity with inertial value. */
eraSxp(d, ust, ut);
/* Combine the two to obtain the inertial space velocity. */
eraPpp(ur, ut, pv[1]);
/* Return the status. */
return iwarn;
}
