void eraApci(double date1, double date2,
double ebpv[2][3], double ehp[3],
double x, double y, double s,
eraASTROM *astrom)
/*
** - - - - - - - -
** e r a A p c i
** - - - - - - - -
**
** For a terrestrial observer, prepare star-independent astrometry
** parameters for transformations between ICRS and geocentric CIRS
** coordinates. The Earth ephemeris and CIP/CIO are supplied by the
** caller.
**
** The parameters produced by this function are required in the
** parallax, light deflection, aberration, and bias-precession-nutation
** parts of the astrometric transformation chain.
**
** Given:
** date1 double TDB as a 2-part...
** date2 double ...Julian Date (Note 1)
** ebpv double[2][3] Earth barycentric position/velocity (au, au/day)
** ehp double[3] Earth heliocentric position (au)
** x,y double CIP X,Y (components of unit vector)
** s double the CIO locator s (radians)
**
** Returned:
** 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 unchanged
** xpl double unchanged
** ypl double unchanged
** sphi double unchanged
** cphi double unchanged
** diurab double unchanged
** eral double unchanged
** refa double unchanged
** refb double unchanged
**
** Notes:
**
** 1) The TDB date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TDB)=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. For most
** applications of this function the choice will not be at all
** critical.
**
** TT can be used instead of TDB without any significant impact on
** accuracy.
**
** 2) All the vectors are with respect to BCRS axes.
**
** 3) In cases where the caller does not wish to provide the Earth
** ephemeris and CIP/CIO, the function eraApci13 can be used instead
** of the present function. This computes the required quantities
** using other ERFA functions.
**
** 4) This is one of several functions that inserts into the astrom
** structure star-independent parameters needed for the chain of
** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
**
** The various functions support different classes of observer and
** portions of the transformation chain:
**
** functions observer transformation
**
** eraApcg eraApcg13 geocentric ICRS <-> GCRS
** eraApci eraApci13 terrestrial ICRS <-> CIRS
** eraApco eraApco13 terrestrial ICRS <-> observed
** eraApcs eraApcs13 space ICRS <-> GCRS
** eraAper eraAper13 terrestrial update Earth rotation
** eraApio eraApio13 terrestrial CIRS <-> observed
**
** Those with names ending in "13" use contemporary ERFA models to
** compute the various ephemerides. The others accept ephemerides
** supplied by the caller.
**
** The transformation from ICRS to GCRS covers space motion,
** parallax, light deflection, and aberration. From GCRS to CIRS
** comprises frame bias and precession-nutation. From CIRS to
** observed takes account of Earth rotation, polar motion, diurnal
** aberration and parallax (unless subsumed into the ICRS <-> GCRS
** transformation), and atmospheric refraction.
**
** 5) The context structure astrom produced by this function is used by
** eraAtciq* and eraAticq*.
**
** Called:
** eraApcg astrometry parameters, ICRS-GCRS, geocenter
** eraC2ixys celestial-to-intermediate matrix, given X,Y and s
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Star-independent astrometry parameters for geocenter. */
eraApcg(date1, date2, ebpv, ehp, astrom);
/* CIO based BPN matrix. */
eraC2ixys(x, y, s, astrom->bpn);
/* Finished. */
}
void eraApco(double date1, double date2,
double ebpv[2][3], double ehp[3],
double x, double y, double s, double theta,
double elong, double phi, double hm,
double xp, double yp, double sp,
double refa, double refb,
eraASTROM *astrom)
/*
** - - - - - - - -
** e r a A p c o
** - - - - - - - -
**
** For a terrestrial observer, prepare star-independent astrometry
** parameters for transformations between ICRS and observed
** coordinates. The caller supplies the Earth ephemeris, the Earth
** rotation information and the refraction constants as well as the
** site coordinates.
**
** Given:
** date1 double TDB as a 2-part...
** date2 double ...Julian Date (Note 1)
** ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2)
** ehp double[3] Earth heliocentric P (au, Note 2)
** x,y double CIP X,Y (components of unit vector)
** s double the CIO locator s (radians)
** theta double Earth rotation angle (radians)
** elong double longitude (radians, east +ve, Note 3)
** phi double latitude (geodetic, radians, Note 3)
** hm double height above ellipsoid (m, geodetic, Note 3)
** xp,yp double polar motion coordinates (radians, Note 4)
** sp double the TIO locator s' (radians, Note 4)
** refa double refraction constant A (radians, Note 5)
** refb double refraction constant B (radians, Note 5)
**
** Returned:
** 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)
**
** Notes:
**
** 1) The TDB date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TDB)=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. For most
** applications of this function the choice will not be at all
** critical.
**
** TT can be used instead of TDB without any significant impact on
** accuracy.
**
** 2) The vectors eb, eh, and all the astrom vectors, are with respect
** to BCRS axes.
**
** 3) The geographical coordinates are with respect to the ERFA_WGS84
** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN
** CONVENTION: the longitude required by the present function is
** right-handed, i.e. east-positive, in accordance with geographical
** convention.
**
** 4) xp and yp are the coordinates (in radians) of the Celestial
** Intermediate Pole with respect to the International Terrestrial
** Reference System (see IERS Conventions), measured along the
** meridians 0 and 90 deg west respectively. sp is the TIO locator
** s', in radians, which positions the Terrestrial Intermediate
** Origin on the equator. For many applications, xp, yp and
** (especially) sp can be set to zero.
**
** Internally, the polar motion is stored in a form rotated onto the
** local meridian.
**
** 5) The refraction constants refa and refb are for use in a
** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed
** (i.e. refracted) zenith distance and dZ is the amount of
** refraction.
**
** 6) It is advisable to take great care with units, as even unlikely
** values of the input parameters are accepted and processed in
** accordance with the models used.
**
** 7) In cases where the caller does not wish to provide the Earth
** Ephemeris, the Earth rotation information and refraction
** constants, the function eraApco13 can be used instead of the
** present function. This starts from UTC and weather readings etc.
** and computes suitable values using other ERFA functions.
**
** 8) This is one of several functions that inserts into the astrom
** structure star-independent parameters needed for the chain of
** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
**
** The various functions support different classes of observer and
** portions of the transformation chain:
**
** functions observer transformation
**
** eraApcg eraApcg13 geocentric ICRS <-> GCRS
** eraApci eraApci13 terrestrial ICRS <-> CIRS
** eraApco eraApco13 terrestrial ICRS <-> observed
** eraApcs eraApcs13 space ICRS <-> GCRS
** eraAper eraAper13 terrestrial update Earth rotation
** eraApio eraApio13 terrestrial CIRS <-> observed
**
** Those with names ending in "13" use contemporary ERFA models to
** compute the various ephemerides. The others accept ephemerides
** supplied by the caller.
**
** The transformation from ICRS to GCRS covers space motion,
** parallax, light deflection, and aberration. From GCRS to CIRS
** comprises frame bias and precession-nutation. From CIRS to
** observed takes account of Earth rotation, polar motion, diurnal
** aberration and parallax (unless subsumed into the ICRS <-> GCRS
** transformation), and atmospheric refraction.
**
** 9) The context structure astrom produced by this function is used by
** eraAtioq, eraAtoiq, eraAtciq* and eraAticq*.
**
** Called:
** eraAper astrometry parameters: update ERA
** eraC2ixys celestial-to-intermediate matrix, given X,Y and s
** eraPvtob position/velocity of terrestrial station
** eraTrxpv product of transpose of r-matrix and pv-vector
** eraApcs astrometry parameters, ICRS-GCRS, space observer
** eraCr copy r-matrix
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double sl, cl, r[3][3], pvc[2][3], pv[2][3];
/* Longitude with adjustment for TIO locator s'. */
astrom->along = elong + sp;
/* Polar motion, rotated onto the local meridian. */
sl = sin(astrom->along);
cl = cos(astrom->along);
astrom->xpl = xp*cl - yp*sl;
astrom->ypl = xp*sl + yp*cl;
/* Functions of latitude. */
astrom->sphi = sin(phi);
astrom->cphi = cos(phi);
/* Refraction constants. */
astrom->refa = refa;
astrom->refb = refb;
/* Local Earth rotation angle. */
eraAper(theta, astrom);
/* Disable the (redundant) diurnal aberration step. */
astrom->diurab = 0.0;
/* CIO based BPN matrix. */
eraC2ixys(x, y, s, r);
/* Observer's geocentric position and velocity (m, m/s, CIRS). */
eraPvtob(elong, phi, hm, xp, yp, sp, theta, pvc);
/* Rotate into GCRS. */
eraTrxpv(r, pvc, pv);
/* ICRS <-> GCRS parameters. */
eraApcs(date1, date2, pv, ebpv, ehp, astrom);
/* Store the CIO based BPN matrix. */
eraCr(r, astrom->bpn );
/* Finished. */
}
void eraC2i06a(double date1, double date2, double rc2i[3][3])
/*
** - - - - - - - - - -
** e r a C 2 i 0 6 a
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date using the
** IAU 2006 precession and IAU 2000A nutation models.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 2)
**
** 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 matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = RC2T * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** Called:
** eraPnm06a classical NPB matrix, IAU 2006/2000A
** eraBpn2xy extract CIP X,Y coordinates from NPB matrix
** eraS06 the CIO locator s, given X,Y, IAU 2006
** eraC2ixys celestial-to-intermediate matrix, given X,Y and s
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double rbpn[3][3], x, y, s;
/* Obtain the celestial-to-true matrix (IAU 2006/2000A). */
eraPnm06a(date1, date2, rbpn);
/* Extract the X,Y coordinates. */
eraBpn2xy(rbpn, &x, &y);
/* Obtain the CIO locator. */
s = eraS06(date1, date2, x, y);
/* Form the celestial-to-intermediate matrix. */
eraC2ixys(x, y, s, rc2i);
return;
}
