void eraC2i00b(double date1, double date2, double rc2i[3][3])
/*
** - - - - - - - - - -
** e r a C 2 i 0 0 b
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date using the
** IAU 2000B precession-nutation model.
**
** 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.
**
** 3) The present function is faster, but slightly less accurate (about
** 1 mas), than the eraC2i00a function.
**
** Called:
** eraPnm00b classical NPB matrix, IAU 2000B
** eraC2ibpn celestial-to-intermediate matrix, given NPB matrix
**
** 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, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double rbpn[3][3];
/* Obtain the celestial-to-true matrix (IAU 2000B). */
eraPnm00b(date1, date2, rbpn);
/* Form the celestial-to-intermediate matrix. */
eraC2ibpn(date1, date2, rbpn, rc2i);
return;
}
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;
}
double eraS00b(double date1, double date2)
/*
** - - - - - - - -
** e r a S 0 0 b
** - - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, using the IAU 2000B
** precession-nutation model.
**
** 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 IAU 2000B truncated nutation model when
** predicting the CIP position. The function eraS00a uses instead
** the full IAU 2000A model, but with no significant increase in
** accuracy and at some cost in speed.
**
** Called:
** eraPnm00b classical NPB matrix, IAU 2000B
** eraBnp2xy extract CIP X,Y from the BPN matrix
** eraS00 the CIO locator s, given X,Y, IAU 2000A
**
** 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.
**
** 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 rbpn[3][3], x, y, s;
/* Bias-precession-nutation-matrix, IAU 2000B. */
eraPnm00b(date1, date2, rbpn);
/* Extract the CIP coordinates. */
eraBpn2xy(rbpn, &x, &y);
/* Compute the CIO locator s, given the CIP coordinates. */
s = eraS00(date1, date2, x, y);
return s;
}
