void eraRxr(double a[3][3], double b[3][3], double atb[3][3])
/*
** - - - - - - -
** e r a R x r
** - - - - - - -
**
** Multiply two r-matrices.
**
** Given:
** a double[3][3] first r-matrix
** b double[3][3] second r-matrix
**
** Returned:
** atb double[3][3] a * b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** eraCr copy r-matrix
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int i, j, k;
double w, wm[3][3];
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
w = 0.0;
for (k = 0; k < 3; k++) {
w += a[i][k] * b[k][j];
}
wm[i][j] = w;
}
}
eraCr(wm, atb);
return;
}
void eraC2teqx(double rbpn[3][3], double gst, double rpom[3][3],
double rc2t[3][3])
/*
** - - - - - - - - - -
** e r a C 2 t e q x
** - - - - - - - - - -
**
** Assemble the celestial to terrestrial matrix from equinox-based
** components (the celestial-to-true matrix, the Greenwich Apparent
** Sidereal Time and the polar motion matrix).
**
** Given:
** rbpn double[3][3] celestial-to-true matrix
** gst double Greenwich (apparent) Sidereal Time
** rpom double[3][3] polar-motion matrix
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 2)
**
** Notes:
**
** 1) This function constructs the rotation matrix that transforms
** vectors in the celestial system into vectors in the terrestrial
** system. It does so starting from precomputed components, namely
** the matrix which rotates from celestial coordinates to the
** true equator and equinox of date, the Greenwich Apparent Sidereal
** Time and the polar motion matrix. One use of the present function
** is when generating a series of celestial-to-terrestrial matrices
** where only the Sidereal Time changes, avoiding the considerable
** overhead of recomputing the precession-nutation more often than
** necessary to achieve given accuracy objectives.
**
** 2) The relationship between the arguments is as follows:
**
** [TRS] = rpom * R_3(gst) * rbpn * [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).
**
** Called:
** eraCr copy r-matrix
** eraRz rotate around Z-axis
** eraRxr product of two r-matrices
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double r[3][3];
/* Construct the matrix. */
eraCr(rbpn, r);
eraRz(gst, r);
eraRxr(rpom, r, rc2t);
return;
}
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 eraPn06(double date1, double date2, double dpsi, double deps,
double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - -
** e r a P n 0 6
** - - - - - - - -
**
** Precession-nutation, IAU 2006 model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based use
** indirectly.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
**
** Returned:
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Note 8)
**
** 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 caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date. For high-accuracy
** applications, free core nutation should be included as well as
** any other relevant corrections to the position of the CIP.
**
** 3) The returned mean obliquity is consistent with the IAU 2006
** precession.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox
** of date to true equator and equinox of date by applying the
** nutation (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) The X,Y,Z coordinates of the Celestial Intermediate Pole are
** elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].
**
** 10) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the stated order.
**
** Called:
** eraPfw06 bias-precession F-W angles, IAU 2006
** eraFw2m F-W angles to r-matrix
** eraCr copy r-matrix
** eraTr transpose r-matrix
** eraRxr product of two r-matrices
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** Copyright (C) 2013-2017, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double gamb, phib, psib, eps, r1[3][3], r2[3][3], rt[3][3];
/* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
eraPfw06(ERFA_DJM0, ERFA_DJM00, &gamb, &phib, &psib, &eps);
/* B matrix. */
eraFw2m(gamb, phib, psib, eps, r1);
eraCr(r1, rb);
/* Bias-precession Fukushima-Williams angles of date. */
eraPfw06(date1, date2, &gamb, &phib, &psib, &eps);
/* Bias-precession matrix. */
eraFw2m(gamb, phib, psib, eps, r2);
eraCr(r2, rbp);
/* Solve for precession matrix. */
eraTr(r1, rt);
eraRxr(r2, rt, rp);
/* Equinox-based bias-precession-nutation matrix. */
eraFw2m(gamb, phib, psib + dpsi, eps + deps, r1);
eraCr(r1, rbpn);
/* Solve for nutation matrix. */
eraTr(r2, rt);
eraRxr(r1, rt, rn);
/* Obliquity, mean of date. */
*epsa = eps;
return;
}
void eraBp00(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** e r a B p 0 0
** - - - - - - - -
**
** Frame bias and precession, IAU 2000.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (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 matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** eraBi00 frame bias components, IAU 2000
** eraPr00 IAU 2000 precession adjustments
** eraIr initialize r-matrix to identity
** eraRx rotate around X-axis
** eraRy rotate around Y-axis
** eraRz rotate around Z-axis
** eraCr copy r-matrix
** eraRxr product of two r-matrices
**
** Reference:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** Copyright (C) 2013-2017, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* J2000.0 obliquity (Lieske et al. 1977) */
const double EPS0 = 84381.448 * ERFA_DAS2R;
double t, dpsibi, depsbi, dra0, psia77, oma77, chia,
dpsipr, depspr, psia, oma, rbw[3][3];
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* Frame bias. */
eraBi00(&dpsibi, &depsbi, &dra0);
/* Precession angles (Lieske et al. 1977) */
psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * ERFA_DAS2R;
oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * ERFA_DAS2R;
chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * ERFA_DAS2R;
/* Apply IAU 2000 precession corrections. */
eraPr00(date1, date2, &dpsipr, &depspr);
psia = psia77 + dpsipr;
oma = oma77 + depspr;
/* Frame bias matrix: GCRS to J2000.0. */
eraIr(rbw);
eraRz(dra0, rbw);
eraRy(dpsibi*sin(EPS0), rbw);
eraRx(-depsbi, rbw);
eraCr(rbw, rb);
/* Precession matrix: J2000.0 to mean of date. */
eraIr(rp);
eraRx(EPS0, rp);
eraRz(-psia, rp);
eraRx(-oma, rp);
eraRz(chia, rp);
/* Bias-precession matrix: GCRS to mean of date. */
eraRxr(rp, rbw, rbp);
return;
}
void eraC2tcio(double rc2i[3][3], double era, double rpom[3][3],
double rc2t[3][3])
/*
** - - - - - - - - - -
** e r a C 2 t c i o
** - - - - - - - - - -
**
** Assemble the celestial to terrestrial matrix from CIO-based
** components (the celestial-to-intermediate matrix, the Earth Rotation
** Angle and the polar motion matrix).
**
** Given:
** rc2i double[3][3] celestial-to-intermediate matrix
** era double Earth rotation angle (radians)
** rpom double[3][3] polar-motion matrix
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix
**
** Notes:
**
** 1) This function constructs the rotation matrix that transforms
** vectors in the celestial system into vectors in the terrestrial
** system. It does so starting from precomputed components, namely
** the matrix which rotates from celestial coordinates to the
** intermediate frame, the Earth rotation angle and the polar motion
** matrix. One use of the present function is when generating a
** series of celestial-to-terrestrial matrices where only the Earth
** Rotation Angle changes, avoiding the considerable overhead of
** recomputing the precession-nutation more often than necessary to
** achieve given accuracy objectives.
**
** 2) The relationship between the arguments is as follows:
**
** [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).
**
** Called:
** eraCr copy r-matrix
** eraRz rotate around Z-axis
** eraRxr product of two r-matrices
**
** Reference:
**
** 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 r[3][3];
/* Construct the matrix. */
eraCr(rc2i, r);
eraRz(era, r);
eraRxr(rpom, r, rc2t);
return;
}
