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#include "erfa.h"
void eraNut80(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - -
** e r a N u t 8 0
** - - - - - - - - -
**
** Nutation, IAU 1980 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:
** eraAnpm normalize angle into range +/- pi
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222 (p111).
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, el, elp, f, d, om, dp, de, arg, s, c;
int j;
/* Units of 0.1 milliarcsecond to radians */
const double U2R = ERFA_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 - ERFA_DJ00) + date2) / ERFA_DJC;
/* --------------------- */
/* Fundamental arguments */
/* --------------------- */
/* Mean longitude of Moon minus mean longitude of Moon's perigee. */
el = eraAnpm(
(485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t)
* ERFA_DAS2R + fmod(1325.0 * t, 1.0) * ERFA_D2PI);
/* Mean longitude of Sun minus mean longitude of Sun's perigee. */
elp = eraAnpm(
(1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t)
* ERFA_DAS2R + fmod(99.0 * t, 1.0) * ERFA_D2PI);
/* Mean longitude of Moon minus mean longitude of Moon's node. */
f = eraAnpm(
(335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t)
* ERFA_DAS2R + fmod(1342.0 * t, 1.0) * ERFA_D2PI);
/* Mean elongation of Moon from Sun. */
d = eraAnpm(
(1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t)
* ERFA_DAS2R + fmod(1236.0 * t, 1.0) * ERFA_D2PI);
/* Longitude of the mean ascending node of the lunar orbit on the */
/* ecliptic, measured from the mean equinox of date. */
om = eraAnpm(
(450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t)
* ERFA_DAS2R + fmod(-5.0 * t, 1.0) * ERFA_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) 2013-2016, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/
|
