double eraS00(double date1, double date2, double x, double y)
/*
** - - - - - - -
** e r a S 0 0
** - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, given the CIP's X,Y
** coordinates. Compatible with IAU 2000A precession-nutation.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** x,y double CIP coordinates (Note 3)
**
** 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 quantity s remains below 0.1 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. This
** function requires X,Y to be supplied by the caller, who is
** responsible for providing values that are consistent with the
** supplied date.
**
** 4) The model is consistent with the IAU 2000A precession-nutation.
**
** Called:
** eraFal03 mean anomaly of the Moon
** eraFalp03 mean anomaly of the Sun
** eraFaf03 mean argument of the latitude of the Moon
** eraFad03 mean elongation of the Moon from the Sun
** eraFaom03 mean longitude of the Moon's ascending node
** eraFave03 mean longitude of Venus
** eraFae03 mean longitude of Earth
** eraFapa03 general accumulated precession in longitude
**
** 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.
*/
{
/* Time since J2000.0, in Julian centuries */
double t;
/* Miscellaneous */
int i, j;
double a, w0, w1, w2, w3, w4, w5;
/* Fundamental arguments */
double fa[8];
/* Returned value */
double s;
/* --------------------- */
/* The series for s+XY/2 */
/* --------------------- */
typedef struct {
int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
double s, c; /* sine and cosine coefficients */
} TERM;
/* Polynomial coefficients */
static const double sp[] = {
/* 1-6 */
94.00e-6,
3808.35e-6,
-119.94e-6,
-72574.09e-6,
27.70e-6,
15.61e-6
};
/* Terms of order t^0 */
static const TERM s0[] = {
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 },
{{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 },
{{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 },
{{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 },
{{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 },
/* 11-20 */
{{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 },
{{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 },
{{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 },
{{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 },
{{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 },
/* 21-30 */
{{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 },
{{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 },
{{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 },
/* 31-33 */
{{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 }
};
/* Terms of order t^1 */
static const TERM s1[] ={
/* 1-3 */
{{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 },
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.71e-6, -0.03e-6 },
{{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 }
};
/* Terms of order t^2 */
static const TERM s2[] ={
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.53e-6, -0.17e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 },
{{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 },
{{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 },
/* 11-20 */
{{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 },
{{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 },
{{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 },
{{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 },
{{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 },
{{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 },
{{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
{{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 },
/* 21-25 */
{{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 },
{{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 },
{{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 },
{{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 }
};
/* Terms of order t^3 */
static const TERM s3[] ={
/* 1-4 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.51e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.39e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.24e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.22e-6 }
};
/* Terms of order t^4 */
static const TERM s4[] ={
/* 1-1 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 }
};
/* Number of terms in the series */
const int NS0 = (int) (sizeof s0 / sizeof (TERM));
const int NS1 = (int) (sizeof s1 / sizeof (TERM));
const int NS2 = (int) (sizeof s2 / sizeof (TERM));
const int NS3 = (int) (sizeof s3 / sizeof (TERM));
const int NS4 = (int) (sizeof s4 / sizeof (TERM));
/*--------------------------------------------------------------------*/
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = eraFal03(t);
/* Mean anomaly of the Sun. */
fa[1] = eraFalp03(t);
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = eraFaf03(t);
/* Mean elongation of the Moon from the Sun. */
fa[3] = eraFad03(t);
/* Mean longitude of the ascending node of the Moon. */
fa[4] = eraFaom03(t);
/* Mean longitude of Venus. */
fa[5] = eraFave03(t);
/* Mean longitude of Earth. */
fa[6] = eraFae03(t);
/* General precession in longitude. */
fa[7] = eraFapa03(t);
/* Evaluate s. */
w0 = sp[0];
w1 = sp[1];
w2 = sp[2];
w3 = sp[3];
w4 = sp[4];
w5 = sp[5];
for (i = NS0-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s0[i].nfa[j] * fa[j];
}
w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
}
for (i = NS1-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s1[i].nfa[j] * fa[j];
}
w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
}
for (i = NS2-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s2[i].nfa[j] * fa[j];
}
w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
}
for (i = NS3-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s3[i].nfa[j] * fa[j];
}
w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
}
for (i = NS4-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s4[i].nfa[j] * fa[j];
}
w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
}
s = (w0 +
(w1 +
(w2 +
(w3 +
(w4 +
w5 * t) * t) * t) * t) * t) * ERFA_DAS2R - x*y/2.0;
return s;
}
double eraEect00(double date1, double date2)
/*
** - - - - - - - - - -
** e r a E e c t 0 0
** - - - - - - - - - -
**
** Equation of the equinoxes complementary terms, consistent with
** IAU 2000 resolutions.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double complementary terms (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 "complementary terms" are part of the equation of the
** equinoxes (EE), classically the difference between apparent and
** mean Sidereal Time:
**
** GAST = GMST + EE
**
** with:
**
** EE = dpsi * cos(eps)
**
** where dpsi is the nutation in longitude and eps is the obliquity
** of date. However, if the rotation of the Earth were constant in
** an inertial frame the classical formulation would lead to
** apparent irregularities in the UT1 timescale traceable to side-
** effects of precession-nutation. In order to eliminate these
** effects from UT1, "complementary terms" were introduced in 1994
** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
** 1993):
**
** GAST = GMST + CT + EE
**
** By convention, the complementary terms are included as part of
** the equation of the equinoxes rather than as part of the mean
** Sidereal Time. This slightly compromises the "geometrical"
** interpretation of mean sidereal time but is otherwise
** inconsequential.
**
** The present function computes CT in the above expression,
** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
** IERS Conventions 2003).
**
** Called:
** eraFal03 mean anomaly of the Moon
** eraFalp03 mean anomaly of the Sun
** eraFaf03 mean argument of the latitude of the Moon
** eraFad03 mean elongation of the Moon from the Sun
** eraFaom03 mean longitude of the Moon's ascending node
** eraFave03 mean longitude of Venus
** eraFae03 mean longitude of Earth
** eraFapa03 general accumulated precession in longitude
**
** References:
**
** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
** 645-650 (1993)
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** IAU Resolution C7, Recommendation 3 (1994)
**
** 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.
*/
{
/* Time since J2000.0, in Julian centuries */
double t;
/* Miscellaneous */
int i, j;
double a, s0, s1;
/* Fundamental arguments */
double fa[14];
/* Returned value. */
double eect;
/* ----------------------------------------- */
/* The series for the EE complementary terms */
/* ----------------------------------------- */
typedef struct {
int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
double s, c; /* sine and cosine coefficients */
} TERM;
/* Terms of order t^0 */
static const TERM e0[] = {
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 },
{{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 },
{{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 },
{{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 },
{{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 },
/* 11-20 */
{{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
{{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 },
{{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 },
{{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 },
{{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 },
/* 21-30 */
{{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 },
{{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 },
{{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 },
/* 31-33 */
{{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 }
};
/* Terms of order t^1 */
static const TERM e1[] = {
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 }
};
/* Number of terms in the series */
const int NE0 = (int) (sizeof e0 / sizeof (TERM));
const int NE1 = (int) (sizeof e1 / sizeof (TERM));
/*--------------------------------------------------------------------*/
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = eraFal03(t);
/* Mean anomaly of the Sun. */
fa[1] = eraFalp03(t);
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = eraFaf03(t);
/* Mean elongation of the Moon from the Sun. */
fa[3] = eraFad03(t);
/* Mean longitude of the ascending node of the Moon. */
fa[4] = eraFaom03(t);
/* Mean longitude of Venus. */
fa[5] = eraFave03(t);
/* Mean longitude of Earth. */
fa[6] = eraFae03(t);
/* General precession in longitude. */
fa[7] = eraFapa03(t);
/* Evaluate the EE complementary terms. */
s0 = 0.0;
s1 = 0.0;
for (i = NE0-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)(e0[i].nfa[j]) * fa[j];
}
s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
}
for (i = NE1-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)(e1[i].nfa[j]) * fa[j];
}
s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
}
eect = (s0 + s1 * t ) * ERFA_DAS2R;
return eect;
}
