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/* Nutation, IAU 2000b model */
/* Translated from Pat Wallace's Fortran subroutine iau_nut00b (June 26 2007)
into C by Jessica Mink on September 5, 2008 */
#define NLS 77 /* number of terms in the luni-solar nutation model */
void
compnut (dj, dpsi, deps, eps0)
double dj; /* Julian Date */
double *dpsi; /* Nutation in longitude in radians (returned) */
double *deps; /* Nutation in obliquity in radians (returned) */
double *eps0; /* Mean obliquity in radians (returned) */
/* This routine is translated from the International Astronomical Union's
* SOFA (Standards Of Fundamental Astronomy) software collection.
*
* notes:
*
* 1) the nutation components in longitude and obliquity are in radians
* and with respect to the equinox and ecliptic of date. the
* obliquity at j2000 is assumed to be the lieske et al. (1977) value
* of 84381.448 arcsec. (the errors that result from using this
* routine 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).
*
* 2) this routine is an implementation of the iau 2000b abridged
* nutation model formally adopted by the iau general assembly in
* 2000. the routine 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 mean poles.
*
* 3) 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 routine 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 routine
* iau_nut00a (q.v.), delivers considerably greater accuracy at
* current epochs; however, to realize this improved accuracy,
* corrections for the essentially unpredictable free-core-nutation
* (fcn) must also be included.
*
* 4) the present routine 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 routines
* iau_bi00 and iau_pr00.
*
* 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 iau_pmat76, to deliver gcrs-to-
* true predictions of mas accuracy at current epochs. however, for
* symmetry with the iau_nut00a routine (q.v. for the reasons), the
* sofa routines do not generate the "total nutations" directly.
* should they be required, they could of course easily be generated
* by calling iau_bi00, iau_pr00 and the present routine 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 from original Fortran subroutines:
*
* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
*
* 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)
*
*/
{
double as2r = 0.000004848136811095359935899141; /* arcseconds to radians */
double dmas2r = as2r / 1000.0; /* milliarcseconds to radians */
double as2pi = 1296000.0; /* arc seconds in a full circle */
double d2pi = 6.283185307179586476925287; /* 2pi */
double u2r = as2r / 10000000.0; /* units of 0.1 microarcsecond to radians */
double dj0 = 2451545.0; /* reference epoch (j2000), jd */
double djc = 36525.0; /* Days per julian century */
/* Miscellaneous */
double t, el, elp, f, d, om, arg, dp, de, sarg, carg;
double dpsils, depsls, dpsipl, depspl;
int i, j;
int nls = NLS; /* number of terms in the luni-solar nutation model */
/* Fixed offset in lieu of planetary terms (radians) */
double dpplan = - 0.135 * dmas2r;
double deplan = + 0.388 * dmas2r;
/* Tables of argument and term coefficients */
/* Coefficients for fundamental arguments
/* Luni-solar argument multipliers: */
/* l l' f d om */
static int nals[5*NLS]=
{0, 0, 0, 0, 1,
0, 0, 2, -2, 2,
0, 0, 2, 0, 2,
0, 0, 0, 0, 2,
0, 1, 0, 0, 0,
0, 1, 2, -2, 2,
1, 0, 0, 0, 0,
0, 0, 2, 0, 1,
1, 0, 2, 0, 2,
0, -1, 2, -2, 2,
0, 0, 2, -2, 1,
-1, 0, 2, 0, 2,
-1, 0, 0, 2, 0,
1, 0, 0, 0, 1,
-1, 0, 0, 0, 1,
-1, 0, 2, 2, 2,
1, 0, 2, 0, 1,
-2, 0, 2, 0, 1,
0, 0, 0, 2, 0,
0, 0, 2, 2, 2,
0, -2, 2, -2, 2,
-2, 0, 0, 2, 0,
2, 0, 2, 0, 2,
1, 0, 2, -2, 2,
-1, 0, 2, 0, 1,
2, 0, 0, 0, 0,
0, 0, 2, 0, 0,
0, 1, 0, 0, 1,
-1, 0, 0, 2, 1,
0, 2, 2, -2, 2,
0, 0, -2, 2, 0,
1, 0, 0, -2, 1,
0, -1, 0, 0, 1,
-1, 0, 2, 2, 1,
0, 2, 0, 0, 0,
1, 0, 2, 2, 2,
-2, 0, 2, 0, 0,
0, 1, 2, 0, 2,
0, 0, 2, 2, 1,
0, -1, 2, 0, 2,
0, 0, 0, 2, 1,
1, 0, 2, -2, 1,
2, 0, 2, -2, 2,
-2, 0, 0, 2, 1,
2, 0, 2, 0, 1,
0, -1, 2, -2, 1,
0, 0, 0, -2, 1,
-1, -1, 0, 2, 0,
2, 0, 0, -2, 1,
1, 0, 0, 2, 0,
0, 1, 2, -2, 1,
1, -1, 0, 0, 0,
-2, 0, 2, 0, 2,
3, 0, 2, 0, 2,
0, -1, 0, 2, 0,
1, -1, 2, 0, 2,
0, 0, 0, 1, 0,
-1, -1, 2, 2, 2,
-1, 0, 2, 0, 0,
0, -1, 2, 2, 2,
-2, 0, 0, 0, 1,
1, 1, 2, 0, 2,
2, 0, 0, 0, 1,
-1, 1, 0, 1, 0,
1, 1, 0, 0, 0,
1, 0, 2, 0, 0,
-1, 0, 2, -2, 1,
1, 0, 0, 0, 2,
-1, 0, 0, 1, 0,
0, 0, 2, 1, 2,
-1, 0, 2, 4, 2,
-1, 1, 0, 1, 1,
0, -2, 2, -2, 1,
1, 0, 2, 2, 1,
-2, 0, 2, 2, 2,
-1, 0, 0, 0, 2,
1, 1, 2, -2, 2};
/* Luni-solar nutation coefficients, in 1e-7 arcsec */
/* longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin) */
static double cls[6*NLS]=
{-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0,
-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0,
-2276413.0, -234.0, 2796.0, 978459.0, -485.0, 1374.0,
2074554.0, 207.0, -698.0, -897492.0, 470.0, -291.0,
1475877.0, -3633.0, 11817.0, 73871.0, -184.0, -1924.0,
-516821.0, 1226.0, -524.0, 224386.0, -677.0, -174.0,
711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0,
-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0,
-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0,
215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0,
128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0,
123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0,
156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0,
63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0,
-57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0,
-59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0,
-51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0,
45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0,
63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0,
-38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0,
32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0,
-47722.0, 0.0, -18.0, 477.0, 0.0, -25.0,
-31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0,
28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0,
20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0,
29243.0, 0.0, -74.0, -609.0, 0.0, 13.0,
25887.0, 0.0, -66.0, -550.0, 0.0, 11.0,
-14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0,
15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0,
-15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0,
21783.0, 0.0, 13.0, -167.0, 0.0, 13.0,
-12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0,
-12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0,
-10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0,
16707.0, -85.0, -10.0, 168.0, -1.0, 10.0,
-7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0,
-11024.0, 0.0, -14.0, 104.0, 0.0, 2.0,
7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0,
-6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0,
-7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0,
-6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0,
5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0,
6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0,
-5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0,
-5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0,
-4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0,
-4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0,
7350.0, 0.0, -8.0, -51.0, 0.0, 4.0,
4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0,
6579.0, 0.0, -24.0, -199.0, 0.0, 2.0,
3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0,
4725.0, 0.0, -6.0, -41.0, 0.0, 3.0,
-3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0,
-2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0,
4348.0, 0.0, -10.0, -81.0, 0.0, 2.0,
-2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0,
-4230.0, 0.0, 5.0, -20.0, 0.0, -2.0,
-2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0,
-4056.0, 0.0, 5.0, 40.0, 0.0, -2.0,
-2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0,
-2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0,
2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0,
2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0,
3276.0, 0.0, 1.0, -9.0, 0.0, 0.0,
-3389.0, 0.0, 5.0, 35.0, 0.0, -2.0,
3339.0, 0.0, -13.0, -107.0, 0.0, 1.0,
-1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0,
-1981.0, 0.0, 0.0, 854.0, 0.0, 0.0,
4026.0, 0.0, -353.0, -553.0, 0.0, -139.0,
1660.0, 0.0, -5.0, -710.0, 0.0, -2.0,
-1521.0, 0.0, 9.0, 647.0, 0.0, 4.0,
1314.0, 0.0, 0.0, -700.0, 0.0, 0.0,
-1283.0, 0.0, 0.0, 672.0, 0.0, 0.0,
-1331.0, 0.0, 8.0, 663.0, 0.0, 4.0,
1383.0, 0.0, -2.0, -594.0, 0.0, -2.0,
1405.0, 0.0, 4.0, -610.0, 0.0, 2.0,
1290.0, 0.0, 0.0, -556.0, 0.0, 0.0};
/* Interval between fundamental epoch J2000.0 and given date (JC) */
t = (dj - dj0) / djc;
/* Luni-solar nutation */
/* Fundamental (delaunay) arguments from Simon et al. (1994) */
/* Mean anomaly of the moon */
el = fmod (485868.249036 + (1717915923.2178 * t), as2pi) * as2r;
/* Mean anomaly of the sun */
elp = fmod (1287104.79305 + (129596581.0481 * t), as2pi) * as2r;
/* Mean argument of the latitude of the moon */
f = fmod (335779.526232 + (1739527262.8478 * t), as2pi) * as2r;
/* Mean elongation of the moon from the sun */
d = fmod (1072260.70369 + (1602961601.2090 * t), as2pi ) * as2r;
/* Mean longitude of the ascending node of the moon */
om = fmod (450160.398036 - (6962890.5431 * t), as2pi ) * as2r;
/* Initialize the nutation values */
dp = 0.0;
de = 0.0;
/* Summation of luni-solar nutation series (in reverse order) */
for (i = nls; i > 0; i=i-1) {
j = i - 1;
/* Argument and functions */
arg = fmod ( (double) (nals[5*j]) * el +
(double) (nals[1+5*j]) * elp +
(double) (nals[2+5*j]) * f +
(double) (nals[3+5*j]) * d +
(double) (nals[4+5*j]) * om, d2pi);
sarg = sin (arg);
carg = cos (arg);
/* Terms */
dp = dp + (cls[6*j] + cls[1+6*j] * t) * sarg + cls[2+6*j] * carg;
de = de + (cls[3+6*j] + cls[4+6*j] * t) * carg + cls[5+6*j] * 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;
/* Mean Obliquity in radians (IAU 2006, Hilton, et al.) */
*eps0 = ( 84381.406 +
( -46.836769 +
( -0.0001831 +
( 0.00200340 +
( -0.000000576 +
( -0.0000000434 ) * t ) * t ) * t ) * t ) * t ) * as2r;
}
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