void eraHfk5z(double rh, double dh, double date1, double date2,
double *r5, double *d5, double *dr5, double *dd5)
/*
** - - - - - - - - -
** e r a H f k 5 z
** - - - - - - - - -
**
** Transform a Hipparcos star position into FK5 J2000.0, assuming
** zero Hipparcos proper motion.
**
** Given:
** rh double Hipparcos RA (radians)
** dh double Hipparcos Dec (radians)
** date1,date2 double TDB date (Note 1)
**
** Returned (all FK5, equinox J2000.0, date date1+date2):
** r5 double RA (radians)
** d5 double Dec (radians)
** dr5 double FK5 RA proper motion (rad/year, Note 4)
** dd5 double Dec proper motion (rad/year, Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 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) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
** 3) The FK5 to Hipparcos transformation is modeled as a pure rotation
** and spin; zonal errors in the FK5 catalogue are not taken into
** account.
**
** 4) It was the intention that Hipparcos should be a close
** approximation to an inertial frame, so that distant objects have
** zero proper motion; such objects have (in general) non-zero
** proper motion in FK5, and this function returns those fictitious
** proper motions.
**
** 5) The position returned by this function is in the FK5 J2000.0
** reference system but at date date1+date2.
**
** 6) See also eraFk52h, eraH2fk5, eraFk5zhz.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraFk5hip FK5 to Hipparcos rotation and spin
** eraRxp product of r-matrix and p-vector
** eraSxp multiply p-vector by scalar
** eraRxr product of two r-matrices
** eraTrxp product of transpose of r-matrix and p-vector
** eraPxp vector product of two p-vectors
** eraPv2s pv-vector to spherical
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3],
rst[3][3], r5ht[3][3], pv5e[2][3], vv[3],
w, r, v;
/* Time interval from fundamental epoch J2000.0 to given date (JY). */
t = ((date1 - DJ00) + date2) / DJY;
/* Hipparcos barycentric position vector (normalized). */
eraS2c(rh, dh, ph);
/* FK5 to Hipparcos orientation matrix and spin vector. */
eraFk5hip(r5h, s5h);
/* Rotate the spin into the Hipparcos system. */
eraRxp(r5h, s5h, sh);
/* Accumulated Hipparcos wrt FK5 spin over that interval. */
eraSxp(t, s5h, vst);
/* Express the accumulated spin as a rotation matrix. */
eraRv2m(vst, rst);
/* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
eraRxr(r5h, rst, r5ht);
/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
eraTrxp(r5ht, ph, pv5e[0]);
/* Apply spin to the position giving a space motion. */
eraPxp(sh, ph, vv);
/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
eraTrxp(r5ht, vv, pv5e[1]);
/* FK5 position/velocity pv-vector to spherical. */
eraPv2s(pv5e, &w, d5, &r, dr5, dd5, &v);
*r5 = eraAnp(w);
return;
}
int eraPvstar(double pv[2][3], double *ra, double *dec,
double *pmr, double *pmd, double *px, double *rv)
/*
** - - - - - - - - - -
** e r a P v s t a r
** - - - - - - - - - -
**
** Convert star position+velocity vector to catalog coordinates.
**
** 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 eraStarpv), 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 eraStarpv.
**
** Called:
** 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
** eraPm modulus of p-vector
** eraPpp p-vector plus p-vector
** eraPv2s pv-vector to spherical
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
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). */
eraPn(pv[0], &r, x);
vr = eraPdp(x, pv[1]);
eraSxp(vr, x, ur);
/* Isolate the transverse component of the velocity (AU/day, inertial). */
eraPmp(pv[1], ur, ut);
vt = eraPm(ut);
/* Special-relativity dimensionless parameters. */
bett = vt / ERFA_DC;
betr = vr / ERFA_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;
eraSxp(w, ur, usr);
/* Apply relativistic correction factor to tangential velocity */
/* component. */
eraSxp(1.0/d, ut, ust);
/* Combine the two to obtain the observed velocity vector (AU/day). */
eraPpp(usr, ust, pv[1]);
/* Cartesian to spherical. */
eraPv2s(pv, &a, dec, &r, &rad, &decd, &rd);
if (r == 0.0) return -2;
/* Return RA in range 0 to 2pi. */
*ra = eraAnp(a);
/* Return proper motions in radians per year. */
*pmr = rad * ERFA_DJY;
*pmd = decd * ERFA_DJY;
/* Return parallax in arcsec. */
*px = ERFA_DR2AS / r;
/* Return radial velocity in km/s. */
*rv = 1e-3 * rd * ERFA_DAU / ERFA_DAYSEC;
/* OK status. */
return 0;
}
