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#include "sofa.h"
void iauNut00b(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - - -
** i a u N u t 0 0 b
** - - - - - - - - - -
**
** Nutation, IAU 2000B 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,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 iauNut00a (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 SOFA functions
** iauBi00 and iauPr00.
**
** 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 iauPmat76, to deliver GCRS-
** to-true predictions of mas accuracy at current epochs. However,
** for symmetry with the iauNut00a function (q.v. for the reasons),
** the SOFA functions do not generate the "total nutations"
** directly. Should they be required, they could of course easily
** be generated by calling iauBi00, iauPr00 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 SOFA 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 SOFA
** 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)
**
** This revision: 2019 June 23
**
** SOFA release 2020-07-21
**
** Copyright (C) 2020 IAU SOFA Board. See notes at end.
*/
{
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 = DAS2R / 1e7;
/* ---------------------------------------- */
/* Fixed offsets in lieu of planetary terms */
/* ---------------------------------------- */
static const double DPPLAN = -0.135 * DMAS2R;
static const double DEPLAN = 0.388 * 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 - DJ00) + date2) / DJC;
/* --------------------*/
/* LUNI-SOLAR NUTATION */
/* --------------------*/
/* Fundamental (Delaunay) arguments from Simon et al. (1994) */
/* Mean anomaly of the Moon. */
el = fmod(485868.249036 + (1717915923.2178) * t, TURNAS) * DAS2R;
/* Mean anomaly of the Sun. */
elp = fmod(1287104.79305 + (129596581.0481) * t, TURNAS) * DAS2R;
/* Mean argument of the latitude of the Moon. */
f = fmod(335779.526232 + (1739527262.8478) * t, TURNAS) * DAS2R;
/* Mean elongation of the Moon from the Sun. */
d = fmod(1072260.70369 + (1602961601.2090) * t, TURNAS) * DAS2R;
/* Mean longitude of the ascending node of the Moon. */
om = fmod(450160.398036 + (-6962890.5431) * t, TURNAS) * 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, 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) 2020
** 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: sofa@ukho.gov.uk
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}