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#include "erfa.h"
void eraNut00b(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - - -
** e r a N u t 0 0 b
** - - - - - - - - - -
**
** Nutation, IAU 2000B model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation, luni-solar + planetary (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 nutation components in longitude and obliquity are in radians
** and with respect to the equinox and ecliptic of date. The
** obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
** value of 84381.448 arcsec. (The errors that result from using
** this function with the IAU 2006 value of 84381.406 arcsec can be
** neglected.)
**
** The nutation model consists only of luni-solar terms, but
** includes also a fixed offset which compensates for certain long-
** period planetary terms (Note 7).
**
** 3) This function is an implementation of the IAU 2000B abridged
** nutation model formally adopted by the IAU General Assembly in
** 2000. The function computes the MHB_2000_SHORT luni-solar
** nutation series (Luzum 2001), but without the associated
** corrections for the precession rate adjustments and the offset
** between the GCRS and J2000.0 mean poles.
**
** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400
** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
** 77 terms, plus additional simplifications, yet still delivers
** results of 1 mas accuracy at present epochs. This combination of
** accuracy and size makes the IAU 2000B abridged nutation model
** suitable for most practical applications.
**
** The function delivers a pole accurate to 1 mas from 1900 to 2100
** (usually better than 1 mas, very occasionally just outside
** 1 mas). The full IAU 2000A model, which is implemented in the
** function eraNut00a (q.v.), delivers considerably greater accuracy
** at current dates; however, to realize this improved accuracy,
** corrections for the essentially unpredictable free-core-nutation
** (FCN) must also be included.
**
** 5) The present function provides classical nutation. The
** MHB_2000_SHORT algorithm, from which it is adapted, deals also
** with (i) the offsets between the GCRS and mean poles and (ii) the
** adjustments in longitude and obliquity due to the changed
** precession rates. These additional functions, namely frame bias
** and precession adjustments, are supported by the ERFA functions
** eraBi00 and eraPr00.
**
** 6) The MHB_2000_SHORT algorithm also provides "total" nutations,
** comprising the arithmetic sum of the frame bias, precession
** adjustments, and nutation (luni-solar + planetary). These total
** nutations can be used in combination with an existing IAU 1976
** precession implementation, such as eraPmat76, to deliver GCRS-
** to-true predictions of mas accuracy at current epochs. However,
** for symmetry with the eraNut00a function (q.v. for the reasons),
** the ERFA functions do not generate the "total nutations"
** directly. Should they be required, they could of course easily
** be generated by calling eraBi00, eraPr00 and the present function
** and adding the results.
**
** 7) The IAU 2000B model includes "planetary bias" terms that are
** fixed in size but compensate for long-period nutations. The
** amplitudes quoted in McCarthy & Luzum (2003), namely
** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
** the "total nutations" method described in Note 6. The Luzum
** (2001) values used in this ERFA implementation, namely -0.135 mas
** and +0.388 mas, are optimized for the "rigorous" method, where
** frame bias, precession and nutation are applied separately and in
** that order. During the interval 1995-2050, the ERFA
** implementation delivers a maximum error of 1.001 mas (not
** including FCN).
**
** References:
**
** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
** for the precession quantities based upon the IAU /1976/ system of
** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
**
** Luzum, B., private communication, 2001 (Fortran code
** MHB_2000_SHORT)
**
** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
** 85, 37-49 (2003)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
dpsils, depsls, dpsipl, depspl;
int i;
/* Units of 0.1 microarcsecond to radians */
static const double U2R = ERFA_DAS2R / 1e7;
/* ---------------------------------------- */
/* Fixed offsets in lieu of planetary terms */
/* ---------------------------------------- */
static const double DPPLAN = -0.135 * ERFA_DMAS2R;
static const double DEPLAN = 0.388 * ERFA_DMAS2R;
/* --------------------------------------------------- */
/* Luni-solar nutation: argument and term coefficients */
/* --------------------------------------------------- */
/* The units for the sine and cosine coefficients are */
/* 0.1 microarcsec and the same per Julian century */
static const struct {
int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
double ps,pst,pc; /* longitude sin, t*sin, cos coefficients */
double ec,ect,es; /* obliquity cos, t*cos, sin coefficients */
} x[] = {
/* 1-10 */
{ 0, 0, 0, 0,1,
-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0},
{ 0, 0, 2,-2,2,
-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0},
{ 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0},
{ 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0},
{ 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0},
{ 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0},
{ 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0},
{ 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0},
{ 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0},
{ 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0},
/* 11-20 */
{ 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0},
{-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0},
{-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0},
{ 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0},
{-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0},
{-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0},
{ 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0},
{-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0},
{ 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0},
{ 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0},
/* 21-30 */
{ 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0},
{-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0},
{ 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0},
{ 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0},
{-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0},
{ 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0},
{ 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0},
{ 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0},
{-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0},
{ 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0},
/* 31-40 */
{ 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0},
{ 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0},
{ 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0},
{-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0},
{ 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0},
{ 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0},
{-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0},
{ 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0},
{ 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0},
{ 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0},
/* 41-50 */
{ 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0},
{ 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0},
{ 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0},
{-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0},
{ 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0},
{ 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0},
{ 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0},
{-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0},
{ 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0},
{ 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0},
/* 51-60 */
{ 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0},
{ 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0},
{-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0},
{ 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0},
{ 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0},
{ 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0},
{ 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0},
{-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0},
{-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0},
{ 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0},
/* 61-70 */
{-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0},
{ 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0},
{ 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0},
{-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0},
{ 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0},
{ 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0},
{-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0},
{ 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0},
{-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0},
{ 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0},
/* 71-77 */
{-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0},
{-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0},
{ 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0},
{ 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0},
{-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0},
{-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0},
{ 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0}
};
/* Number of terms in the series */
const int NLS = (int) (sizeof x / sizeof x[0]);
/*--------------------------------------------------------------------*/
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* --------------------*/
/* LUNI-SOLAR NUTATION */
/* --------------------*/
/* Fundamental (Delaunay) arguments from Simon et al. (1994) */
/* Mean anomaly of the Moon. */
el = fmod(485868.249036 + (1717915923.2178) * t, ERFA_TURNAS) * ERFA_DAS2R;
/* Mean anomaly of the Sun. */
elp = fmod(1287104.79305 + (129596581.0481) * t, ERFA_TURNAS) * ERFA_DAS2R;
/* Mean argument of the latitude of the Moon. */
f = fmod(335779.526232 + (1739527262.8478) * t, ERFA_TURNAS) * ERFA_DAS2R;
/* Mean elongation of the Moon from the Sun. */
d = fmod(1072260.70369 + (1602961601.2090) * t, ERFA_TURNAS) * ERFA_DAS2R;
/* Mean longitude of the ascending node of the Moon. */
om = fmod(450160.398036 + (-6962890.5431) * t, ERFA_TURNAS) * ERFA_DAS2R;
/* Initialize the nutation values. */
dp = 0.0;
de = 0.0;
/* Summation of luni-solar nutation series (smallest terms first). */
for (i = NLS-1; i >= 0; i--) {
/* Argument and functions. */
arg = fmod( (double)x[i].nl * el +
(double)x[i].nlp * elp +
(double)x[i].nf * f +
(double)x[i].nd * d +
(double)x[i].nom * om, ERFA_D2PI );
sarg = sin(arg);
carg = cos(arg);
/* Term. */
dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg;
de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg;
}
/* Convert from 0.1 microarcsec units to radians. */
dpsils = dp * U2R;
depsls = de * U2R;
/* ------------------------------*/
/* IN LIEU OF PLANETARY NUTATION */
/* ------------------------------*/
/* Fixed offset to correct for missing terms in truncated series. */
dpsipl = DPPLAN;
depspl = DEPLAN;
/* --------*/
/* RESULTS */
/* --------*/
/* Add luni-solar and planetary components. */
*dpsi = dpsils + dpsipl;
*deps = depsls + depspl;
return;
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2014, 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.
**
*/
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