void palEqgal ( double dr, double dd, double *dl, double *db ) {
double v1[3];
double v2[3];
/*
* L2,B2 system of galactic coordinates
*
* P = 192.25 RA of galactic north pole (mean B1950.0)
* Q = 62.6 inclination of galactic to mean B1950.0 equator
* R = 33 longitude of ascending node
*
* P,Q,R are degrees
*
* Equatorial to galactic rotation matrix (J2000.0), obtained by
* applying the standard FK4 to FK5 transformation, for zero proper
* motion in FK5, to the columns of the B1950 equatorial to
* galactic rotation matrix:
*/
double rmat[3][3] = {
{ -0.054875539726,-0.873437108010,-0.483834985808 },
{ +0.494109453312,-0.444829589425,+0.746982251810 },
{ -0.867666135858,-0.198076386122,+0.455983795705 }
};
/* Spherical to Cartesian */
iauS2c( dr, dd, v1 );
/* Equatorial to Galactic */
iauRxp( rmat, v1, v2 );
/* Cartesian to spherical */
iauC2s( v2, dl, db );
/* Express in conventional ranges */
*dl = iauAnp( *dl );
*db = iauAnpm( *db );
}
void iauNut80(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - -
** i a u N u t 8 0
** - - - - - - - - -
**
** Nutation, IAU 1980 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi double nutation in longitude (radians)
** deps double nutation in obliquity (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 nutation components are with respect to the ecliptic of
** date.
**
** Called:
** iauAnpm normalize angle into range +/- pi
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222 (p111).
**
** This revision: 2008 September 30
**
** SOFA release 2010-12-01
**
** Copyright (C) 2010 IAU SOFA Board. See notes at end.
*/
{
double t, el, elp, f, d, om, dp, de, arg, s, c;
int j;
/* Units of 0.1 milliarcsecond to radians */
const double U2R = DAS2R / 1e4;
/* ------------------------------------------------ */
/* Table of multiples of arguments and coefficients */
/* ------------------------------------------------ */
/* The units for the sine and cosine coefficients are 0.1 mas and */
/* the same per Julian century */
static const struct {
int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
double sp,spt; /* longitude sine, 1 and t coefficients */
double ce,cet; /* obliquity cosine, 1 and t coefficients */
} x[] = {
/* 1-10 */
{ 0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9 },
{ 0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5 },
{ -2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0 },
{ 2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0 },
{ -2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 },
{ 1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0 },
{ 0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 },
{ 2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0 },
{ 0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1 },
{ 0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1 },
/* 11-20 */
{ 0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6 },
{ 0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3 },
{ 0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0 },
{ 2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0 },
{ 0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0 },
{ 0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0 },
{ 0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0 },
{ 0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0 },
{ 0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0 },
{ -2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 },
/* 21-30 */
{ 0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0 },
{ 2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0 },
{ 0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0 },
{ 1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0 },
{ 2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 },
{ 0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0 },
{ 0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 },
{ 0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0 },
{ -1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0 },
{ 0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 },
/* 31-40 */
{ 0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5 },
{ 1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0 },
{ 0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0 },
{ 1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1 },
{ 1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0 },
{ -1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0 },
{ 0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0 },
{ 1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0 },
{ -1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0 },
{ -1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0 },
/* 41-50 */
{ 1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0 },
{ 0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0 },
{ 2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0 },
{ 1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0 },
{ 2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0 },
{ 0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0 },
{ -1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0 },
{ -1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0 },
{ 1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0 },
{ -1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0 },
/* 51-60 */
{ 1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0 },
{ 0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0 },
{ 0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0 },
{ 1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0 },
{ 1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0 },
{ 2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0 },
{ 0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 },
{ 0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0 },
{ 1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0 },
{ 0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0 },
/* 61-70 */
{ 1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0 },
{ 2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0 },
{ 0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0 },
{ 1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0 },
{ 0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0 },
{ 1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0 },
{ 1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0 },
{ 1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 },
{ -1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 },
{ -2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0 },
/* 71-80 */
{ 3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 },
{ 0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 },
{ 1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0 },
{ -1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 },
{ 2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0 },
{ 1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0 },
{ 3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0 },
{ 0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0 },
{ -1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0 },
{ 1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 },
/* 81-90 */
{ -2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0 },
{ -1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0 },
{ 2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 },
{ 1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0 },
{ 1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0 },
{ -2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0 },
{ -1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0 },
{ 1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 },
{ 2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0 },
{ 2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0 },
/* 91-100 */
{ 1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0 },
{ 0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0 },
{ 3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0 },
{ 1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 },
{ 0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0 },
{ -1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0 },
{ 0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0 },
{ 0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0 },
{ 0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0 },
{ 1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0 },
/* 101-106 */
{ 0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0 },
{ 1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0 },
{ 1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 },
{ 2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0 },
{ 0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0 },
{ 0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0 }
};
/* Number of terms in the series */
const int NT = (int) (sizeof x / sizeof x[0]);
/*--------------------------------------------------------------------*/
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC;
/* --------------------- */
/* Fundamental arguments */
/* --------------------- */
/* Mean longitude of Moon minus mean longitude of Moon's perigee. */
el = iauAnpm(
(485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t)
* DAS2R + fmod(1325.0 * t, 1.0) * D2PI);
/* Mean longitude of Sun minus mean longitude of Sun's perigee. */
elp = iauAnpm(
(1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t)
* DAS2R + fmod(99.0 * t, 1.0) * D2PI);
/* Mean longitude of Moon minus mean longitude of Moon's node. */
f = iauAnpm(
(335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t)
* DAS2R + fmod(1342.0 * t, 1.0) * D2PI);
/* Mean elongation of Moon from Sun. */
d = iauAnpm(
(1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t)
* DAS2R + fmod(1236.0 * t, 1.0) * D2PI);
/* Longitude of the mean ascending node of the lunar orbit on the */
/* ecliptic, measured from the mean equinox of date. */
om = iauAnpm(
(450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t)
* DAS2R + fmod(-5.0 * t, 1.0) * D2PI);
/* --------------- */
/* Nutation series */
/* --------------- */
/* Initialize nutation components. */
dp = 0.0;
de = 0.0;
/* Sum the nutation terms, ending with the biggest. */
for (j = NT-1; j >= 0; j--) {
/* Form argument for current term. */
arg = (double)x[j].nl * el
+ (double)x[j].nlp * elp
+ (double)x[j].nf * f
+ (double)x[j].nd * d
+ (double)x[j].nom * om;
/* Accumulate current nutation term. */
s = x[j].sp + x[j].spt * t;
c = x[j].ce + x[j].cet * t;
if (s != 0.0) dp += s * sin(arg);
if (c != 0.0) de += c * cos(arg);
}
/* Convert results from 0.1 mas units to radians. */
*dpsi = dp * U2R;
*deps = de * U2R;
return;
/*----------------------------------------------------------------------
**
** 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
**
**--------------------------------------------------------------------*/
}
double iauEe06a(double date1, double date2)
/*
** - - - - - - - - -
** i a u E e 0 6 a
** - - - - - - - - -
**
** Equation of the equinoxes, compatible with IAU 2000 resolutions and
** IAU 2006/2000A precession-nutation.
**
** 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
**
** Called:
** iauAnpm normalize angle into range +/- pi
** iauGst06a Greenwich apparent sidereal time, IAU 2006/2000A
** iauGmst06 Greenwich mean sidereal time, IAU 2006
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** This revision: 2008 May 18
**
** SOFA release 2016-05-03
**
** Copyright (C) 2016 IAU SOFA Board. See notes at end.
*/
{
double gst06a, gmst06, ee;
/* Apparent and mean sidereal times. */
gst06a = iauGst06a(0.0, 0.0, date1, date2);
gmst06 = iauGmst06(0.0, 0.0, date1, date2);
/* Equation of the equinoxes. */
ee = iauAnpm(gst06a - gmst06);
return ee;
/*----------------------------------------------------------------------
**
** Copyright (C) 2016
** 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
**
**--------------------------------------------------------------------*/
}
double iauEqeq94(double date1, double date2)
/*
** - - - - - - - - - -
** i a u E q e q 9 4
** - - - - - - - - - -
**
** Equation of the equinoxes, IAU 1994 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TDB date (Note 1)
**
** Returned (function value):
** double equation of the equinoxes (Note 2)
**
** Notes:
**
** 1) The 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
**
** Called:
** iauNut80 nutation, IAU 1980
** iauObl80 mean obliquity, IAU 1980
**
** References:
**
** IAU Resolution C7, Recommendation 3 (1994).
**
** Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275,
** 645-650.
**
** This revision: 2008 May 24
**
** SOFA release 2012-03-01
**
** Copyright (C) 2012 IAU SOFA Board. See notes at end.
*/
{
double t, om, dpsi, deps, eps0, ee;
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC;
/* Longitude of the mean ascending node of the lunar orbit on the */
/* ecliptic, measured from the mean equinox of date. */
om = iauAnpm((450160.280 + (-482890.539
+ (7.455 + 0.008 * t) * t) * t) * DAS2R
+ fmod(-5.0 * t, 1.0) * D2PI);
/* Nutation components and mean obliquity. */
iauNut80(date1, date2, &dpsi, &deps);
eps0 = iauObl80(date1, date2);
/* Equation of the equinoxes. */
ee = dpsi*cos(eps0) + DAS2R*(0.00264*sin(om) + 0.000063*sin(om+om));
return ee;
/*----------------------------------------------------------------------
**
** Copyright (C) 2012
** 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
**
**--------------------------------------------------------------------*/
}
void iauLteqec(double epj, double dr, double dd, double *dl, double *db)
/*
** - - - - - - - - - -
** i a u L t e q e c
** - - - - - - - - - -
**
** Transformation from ICRS equatorial coordinates to ecliptic
** coordinates (mean equinox and ecliptic of date) using a long-term
** precession model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** epj double Julian epoch (TT)
** dr,dd double ICRS right ascension and declination (radians)
**
** Returned:
** dl,db double ecliptic longitude and latitude (radians)
**
** 1) No assumptions are made about whether the coordinates represent
** starlight and embody astrometric effects such as parallax or
** aberration.
**
** 2) The transformation is approximately that from mean J2000.0 right
** ascension and declination to ecliptic longitude and latitude
** (mean equinox and ecliptic of date), with only frame bias (always
** less than 25 mas) to disturb this classical picture.
**
** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model
** agrees with the IAU 2006 precession at J2000.0 and stays within
** 100 microarcseconds during the 20th and 21st centuries. It is
** accurate to a few arcseconds throughout the historical period,
** worsening to a few tenths of a degree at the end of the
** +/- 200,000 year time span.
**
** Called:
** iauS2c spherical coordinates to unit vector
** iauLtecm J2000.0 to ecliptic rotation matrix, long term
** iauRxp product of r-matrix and p-vector
** iauC2s unit vector to spherical coordinates
** iauAnp normalize angle into range 0 to 2pi
** iauAnpm normalize angle into range +/- pi
**
** References:
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
** expressions, valid for long time intervals, Astron.Astrophys. 534,
** A22
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
** expressions, valid for long time intervals (Corrigendum),
** Astron.Astrophys. 541, C1
**
** This revision: 2016 February 9
**
** SOFA release 2016-05-03
**
** Copyright (C) 2016 IAU SOFA Board. See notes at end.
*/
{
double rm[3][3], v1[3], v2[3], a, b;
/* Spherical to Cartesian. */
iauS2c(dr, dd, v1);
/* Rotation matrix, ICRS equatorial to ecliptic. */
iauLtecm(epj, rm);
/* The transformation from ICRS to ecliptic. */
iauRxp(rm, v1, v2);
/* Cartesian to spherical. */
iauC2s(v2, &a, &b);
/* Express in conventional ranges. */
*dl = iauAnp(a);
*db = iauAnpm(b);
/*----------------------------------------------------------------------
**
** Copyright (C) 2016
** 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
**
**--------------------------------------------------------------------*/
}
