void eraXys00b(double date1, double date2,
double *x, double *y, double *s)
/*
** - - - - - - - - - -
** e r a X y s 0 0 b
** - - - - - - - - - -
**
** For a given TT date, compute the X,Y coordinates of the Celestial
** Intermediate Pole and the CIO locator s, using the IAU 2000B
** precession-nutation model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** x,y double Celestial Intermediate Pole (Note 2)
** s double the CIO locator s (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 Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 3) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 4) The present function is faster, but slightly less accurate (about
** 1 mas in X,Y), than the eraXys00a function.
**
** Called:
** eraPnm00b classical NPB matrix, IAU 2000B
** eraBpn2xy extract CIP X,Y coordinates from NPB matrix
** eraS00 the CIO locator s, given X,Y, IAU 2000A
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double rbpn[3][3];
/* Form the bias-precession-nutation matrix, IAU 2000A. */
eraPnm00b(date1, date2, rbpn);
/* Extract X,Y. */
eraBpn2xy(rbpn, x, y);
/* Obtain s. */
*s = eraS00(date1, date2, *x, *y);
return;
}
int eraApco13(double utc1, double utc2, double dut1,
double elong, double phi, double hm, double xp, double yp,
double phpa, double tc, double rh, double wl,
eraASTROM *astrom, double *eo)
/*
** - - - - - - - - - -
** e r a A p c o 1 3
** - - - - - - - - - -
**
** For a terrestrial observer, prepare star-independent astrometry
** parameters for transformations between ICRS and observed
** coordinates. The caller supplies UTC, site coordinates, ambient air
** conditions and observing wavelength, and ERFA models are used to
** obtain the Earth ephemeris, CIP/CIO and refraction constants.
**
** The parameters produced by this function are required in the
** parallax, light deflection, aberration, and bias-precession-nutation
** parts of the ICRS/CIRS transformations.
**
** Given:
** utc1 double UTC as a 2-part...
** utc2 double ...quasi Julian Date (Notes 1,2)
** dut1 double UT1-UTC (seconds, Note 3)
** elong double longitude (radians, east +ve, Note 4)
** phi double latitude (geodetic, radians, Note 4)
** hm double height above ellipsoid (m, geodetic, Notes 4,6)
** xp,yp double polar motion coordinates (radians, Note 5)
** phpa double pressure at the observer (hPa = mB, Note 6)
** tc double ambient temperature at the observer (deg C)
** rh double relative humidity at the observer (range 0-1)
** wl double wavelength (micrometers, Note 7)
**
** 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)
** eo double* equation of the origins (ERA-GST)
**
** Returned (function value):
** int status: +1 = dubious year (Note 2)
** 0 = OK
** -1 = unacceptable date
**
** Notes:
**
** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
** convenient way between the two arguments, for example where utc1
** is the Julian Day Number and utc2 is the fraction of a day.
**
** However, JD cannot unambiguously represent UTC during a leap
** second unless special measures are taken. The convention in the
** present function is that the JD day represents UTC days whether
** the length is 86399, 86400 or 86401 SI seconds.
**
** Applications should use the function eraDtf2d to convert from
** calendar date and time of day into 2-part quasi Julian Date, as
** it implements the leap-second-ambiguity convention just
** described.
**
** 2) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale or that are too far in the
** future to be trusted. See eraDat for further details.
**
** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly
** one second at the end of each positive UTC leap second,
** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
** practice is under review, and in the future UT1-UTC may grow
** essentially without limit.
**
** 4) The geographical coordinates are with respect to the ERFA_WGS84
** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
** longitude required by the present function is east-positive
** (i.e. right-handed), in accordance with geographical convention.
**
** 5) The polar motion xp,yp can be obtained from IERS bulletins. The
** values are the coordinates (in radians) of the Celestial
** Intermediate Pole with respect to the International Terrestrial
** Reference System (see IERS Conventions 2003), measured along the
** meridians 0 and 90 deg west respectively. For many
** applications, xp and yp can be set to zero.
**
** Internally, the polar motion is stored in a form rotated onto
** the local meridian.
**
** 6) If hm, the height above the ellipsoid of the observing station
** in meters, is not known but phpa, the pressure in hPa (=mB), is
** available, an adequate estimate of hm can be obtained from the
** expression
**
** hm = -29.3 * tsl * log ( phpa / 1013.25 );
**
** where tsl is the approximate sea-level air temperature in K
** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
** 52). Similarly, if the pressure phpa is not known, it can be
** estimated from the height of the observing station, hm, as
** follows:
**
** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
**
** Note, however, that the refraction is nearly proportional to
** the pressure and that an accurate phpa value is important for
** precise work.
**
** 7) The argument wl specifies the observing wavelength in
** micrometers. The transition from optical to radio is assumed to
** occur at 100 micrometers (about 3000 GHz).
**
** 8) 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.
**
** 9) In cases where the caller wishes to supply his own Earth
** ephemeris, Earth rotation information and refraction constants,
** the function eraApco can be used instead of the present function.
**
** 10) 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.
**
** 11) The context structure astrom produced by this function is used
** by eraAtioq, eraAtoiq, eraAtciq* and eraAticq*.
**
** Called:
** eraUtctai UTC to TAI
** eraTaitt TAI to TT
** eraUtcut1 UTC to UT1
** eraEpv00 Earth position and velocity
** 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
** eraEra00 Earth rotation angle, IAU 2000
** eraSp00 the TIO locator s', IERS 2000
** eraRefco refraction constants for given ambient conditions
** eraApco astrometry parameters, ICRS-observed
** eraEors equation of the origins, given NPB matrix and s
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int j;
double tai1, tai2, tt1, tt2, ut11, ut12, ehpv[2][3], ebpv[2][3],
r[3][3], x, y, s, theta, sp, refa, refb;
/* UTC to other time scales. */
j = eraUtctai(utc1, utc2, &tai1, &tai2);
if ( j < 0 ) return -1;
j = eraTaitt(tai1, tai2, &tt1, &tt2);
j = eraUtcut1(utc1, utc2, dut1, &ut11, &ut12);
if ( j < 0 ) return -1;
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
(void) eraEpv00(tt1, tt2, ehpv, ebpv);
/* Form the equinox based BPN matrix, IAU 2006/2000A. */
eraPnm06a(tt1, tt2, r);
/* Extract CIP X,Y. */
eraBpn2xy(r, &x, &y);
/* Obtain CIO locator s. */
s = eraS06(tt1, tt2, x, y);
/* Earth rotation angle. */
theta = eraEra00(ut11, ut12);
/* TIO locator s'. */
sp = eraSp00(tt1, tt2);
/* Refraction constants A and B. */
eraRefco(phpa, tc, rh, wl, &refa, &refb);
/* Compute the star-independent astrometry parameters. */
eraApco(tt1, tt2, ebpv, ehpv[0], x, y, s, theta,
elong, phi, hm, xp, yp, sp, refa, refb, astrom);
/* Equation of the origins. */
*eo = eraEors(r, s);
/* Return any warning status. */
return j;
/* Finished. */
}
double eraS06a(double date1, double date2)
/*
** - - - - - - - -
** e r a S 0 6 a
** - - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, using the IAU 2006
** precession and IAU 2000A nutation models.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double the CIO locator s in radians (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 CIO locator s is the difference between the right ascensions
** of the same point in two systems. The two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The CIO locator s remains a small fraction of
** 1 arcsecond throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series is
** more compact than a direct series for s would be. The present
** function uses the full IAU 2000A nutation model when predicting
** the CIP position.
**
** 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
**
** References:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "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.
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double rnpb[3][3], x, y, s;
/* Bias-precession-nutation-matrix, IAU 20006/2000A. */
eraPnm06a(date1, date2, rnpb);
/* Extract the CIP coordinates. */
eraBpn2xy(rnpb, &x, &y);
/* Compute the CIO locator s, given the CIP coordinates. */
s = eraS06(date1, date2, x, y);
return s;
}
void eraFw2xy(double gamb, double phib, double psi, double eps,
double *x, double *y)
/*
** - - - - - - - - -
** e r a F w 2 x y
** - - - - - - - - -
**
** CIP X,Y given Fukushima-Williams bias-precession-nutation angles.
**
** Given:
** gamb double F-W angle gamma_bar (radians)
** phib double F-W angle phi_bar (radians)
** psi double F-W angle psi (radians)
** eps double F-W angle epsilon (radians)
**
** Returned:
** x,y double CIP unit vector X,Y
**
** Notes:
**
** 1) Naming the following points:
**
** e = J2000.0 ecliptic pole,
** p = GCRS pole
** E = ecliptic pole of date,
** and P = CIP,
**
** the four Fukushima-Williams angles are as follows:
**
** gamb = gamma = epE
** phib = phi = pE
** psi = psi = pEP
** eps = epsilon = EP
**
** 2) The matrix representing the combined effects of frame bias,
** precession and nutation is:
**
** NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb)
**
** The returned values x,y are elements [2][0] and [2][1] of the
** matrix. Near J2000.0, they are essentially angles in radians.
**
** Called:
** eraFw2m F-W angles to r-matrix
** eraBpn2xy extract CIP X,Y coordinates from NPB matrix
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double r[3][3];
/* Form NxPxB matrix. */
eraFw2m(gamb, phib, psi, eps, r);
/* Extract CIP X,Y. */
eraBpn2xy(r, x, y);
return;
}
void eraXys06a(double date1, double date2,
double *x, double *y, double *s)
/*
** - - - - - - - - - -
** e r a X y s 0 6 a
** - - - - - - - - - -
**
** For a given TT date, compute the X,Y coordinates of the Celestial
** Intermediate Pole and the CIO locator s, using the IAU 2006
** precession and IAU 2000A nutation models.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** x,y double Celestial Intermediate Pole (Note 2)
** s double the CIO locator s (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 Celestial Intermediate Pole coordinates are the x,y components
** of the unit vector in the Geocentric Celestial Reference System.
**
** 3) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 4) Series-based solutions for generating X and Y are also available:
** see Capitaine & Wallace (2006) and eraXy06.
**
** 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
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double rbpn[3][3];
/* Form the bias-precession-nutation matrix, IAU 2006/2000A. */
eraPnm06a(date1, date2, rbpn);
/* Extract X,Y. */
eraBpn2xy(rbpn, x, y);
/* Obtain s. */
*s = eraS06(date1, date2, *x, *y);
return;
}
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;
}
void eraApci13(double date1, double date2,
eraASTROM *astrom, double *eo)
/*
** - - - - - - - - - -
** e r a A p c i 1 3
** - - - - - - - - - -
**
** For a terrestrial observer, prepare star-independent astrometry
** parameters for transformations between ICRS and geocentric CIRS
** coordinates. The caller supplies the date, and ERFA models are used
** to predict the Earth ephemeris and CIP/CIO.
**
** 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)
**
** 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
** eo double* equation of the origins (ERA-GST)
**
** 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 wishes to supply his own Earth
** ephemeris and CIP/CIO, the function eraApci can be used instead
** of the present function.
**
** 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:
** eraEpv00 Earth position and velocity
** 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
** eraApci astrometry parameters, ICRS-CIRS
** eraEors equation of the origins, given NPB matrix and s
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double ehpv[2][3], ebpv[2][3], r[3][3], x, y, s;
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
(void) eraEpv00(date1, date2, ehpv, ebpv);
/* Form the equinox based BPN matrix, IAU 2006/2000A. */
eraPnm06a(date1, date2, r);
/* Extract CIP X,Y. */
eraBpn2xy(r, &x, &y);
/* Obtain CIO locator s. */
s = eraS06(date1, date2, x, y);
/* Compute the star-independent astrometry parameters. */
eraApci(date1, date2, ebpv, ehpv[0], x, y, s, astrom);
/* Equation of the origins. */
*eo = eraEors(r, s);
/* Finished. */
}
double eraEo06a(double date1, double date2)
/*
** - - - - - - - - -
** e r a E o 0 6 a
** - - - - - - - - -
**
** Equation of the origins, IAU 2006 precession and IAU 2000A nutation.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double equation of the origins in radians
**
** 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 equation of the origins is the distance between the true
** equinox and the celestial intermediate origin and, equivalently,
** the difference between Earth rotation angle and Greenwich
** apparent sidereal time (ERA-GST). It comprises the precession
** (since J2000.0) in right ascension plus the equation of the
** equinoxes (including the small correction terms).
**
** 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
** eraEors equation of the origins, given NPB matrix and s
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double r[3][3], x, y, s, eo;
/* Classical nutation x precession x bias matrix. */
eraPnm06a(date1, date2, r);
/* Extract CIP coordinates. */
eraBpn2xy(r, &x, &y);
/* The CIO locator, s. */
s = eraS06(date1, date2, x, y);
/* Solve for the EO. */
eo = eraEors(r, s);
return eo;
}
void eraC2ibpn(double date1, double date2, double rbpn[3][3],
double rc2i[3][3])
/*
** - - - - - - - - - -
** e r a C 2 i b p n
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date given
** the bias-precession-nutation matrix. IAU 2000.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** rbpn double[3][3] celestial-to-true matrix (Note 2)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 3)
**
** 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 rbpn transforms vectors from GCRS to true equator (and
** CIO or equinox) of date. Only the CIP (bottom row) is used.
**
** 3) 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.
**
** 4) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** eraBpn2xy extract CIP X,Y coordinates from NPB matrix
** eraC2ixy celestial-to-intermediate matrix, given X,Y
**
** References:
** "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.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double x, y;
/* Extract the X,Y coordinates. */
eraBpn2xy(rbpn, &x, &y);
/* Form the celestial-to-intermediate matrix (n.b. IAU 2000 specific). */
eraC2ixy(date1, date2, x, y, rc2i);
return;
}
