double iauEe00b(double date1, double date2)
/*
** - - - - - - - - -
** i a u E e 0 0 b
** - - - - - - - - -
**
** Equation of the equinoxes, compatible with IAU 2000 resolutions but
** using the truncated nutation model IAU 2000B.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double equation of the equinoxes (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 result, which is in radians, operates in the following sense:
**
** Greenwich apparent ST = GMST + equation of the equinoxes
**
** 3) The result is compatible with the IAU 2000 resolutions except
** that accuracy has been compromised for the sake of speed. For
** further details, see McCarthy & Luzum (2001), IERS Conventions
** 2003 and Capitaine et al. (2003).
**
** Called:
** iauPr00 IAU 2000 precession adjustments
** iauObl80 mean obliquity, IAU 1980
** iauNut00b nutation, IAU 2000B
** iauEe00 equation of the equinoxes, IAU 2000
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
** precession-nutation of the celestial pole", Celestial Mechanics &
** Dynamical Astronomy, 85, 37-49 (2003)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** This revision: 2008 May 18
**
** SOFA release 2010-12-01
**
** Copyright (C) 2010 IAU SOFA Board. See notes at end.
*/
{
double dpsipr, depspr, epsa, dpsi, deps, ee;
/* IAU 2000 precession-rate adjustments. */
iauPr00(date1, date2, &dpsipr, &depspr);
/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
epsa = iauObl80(date1, date2) + depspr;
/* Nutation in longitude. */
iauNut00b(date1, date2, &dpsi, &deps);
/* Equation of the equinoxes. */
ee = iauEe00(date1, date2, epsa, dpsi);
return ee;
/*----------------------------------------------------------------------
**
** Copyright (C) 2010
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
** WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The name(s) of all routine(s) in your derived work shall not
** include the prefix "iau".
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. In any published work or commercial products which includes
** results achieved by using the SOFA software, you shall
** acknowledge that the SOFA software was used in obtaining those
** results.
**
** 5. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 6. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 7. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauC2tpe(double tta, double ttb, double uta, double utb,
double dpsi, double deps, double xp, double yp,
double rc2t[3][3])
/*
** - - - - - - - - -
** i a u C 2 t p e
** - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1,
** the nutation and the polar motion. IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
** xp,yp double coordinates of the pole (radians, Note 3)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any of
** these ways, among others:
**
** uta utb
**
** 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 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 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 arguments xp and yp 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 to 0 and 90 deg west respectively.
**
** 4) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [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), RBPN is the
** bias-precession-nutation matrix, GST is the Greenwich (apparent)
** Sidereal Time and RPOM is the polar motion matrix.
**
** 5) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** iauPn00 bias/precession/nutation results, IAU 2000
** iauGmst00 Greenwich mean sidereal time, IAU 2000
** iauSp00 the TIO locator s', IERS 2000
** iauEe00 equation of the equinoxes, IAU 2000
** iauPom00 polar motion matrix
** iauC2teqx form equinox-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** This revision: 2013 June 18
**
** SOFA release 2017-04-20
**
** Copyright (C) 2017 IAU SOFA Board. See notes at end.
*/
{
double epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3],
rbpn[3][3], gmst, ee, sp, rpom[3][3];
/* Form the celestial-to-true matrix for this TT. */
iauPn00(tta, ttb, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn);
/* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */
gmst = iauGmst00(uta, utb, tta, ttb);
/* Predict the equation of the equinoxes given TT and nutation. */
ee = iauEe00(tta, ttb, epsa, dpsi);
/* Estimate s'. */
sp = iauSp00(tta, ttb);
/* Form the polar motion matrix. */
iauPom00(xp, yp, sp, rpom);
/* Combine to form the celestial-to-terrestrial matrix. */
iauC2teqx(rbpn, gmst + ee, rpom, rc2t);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2017
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
