FACT++  1.0
nut00b.c
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1 #include "erfa.h"
2 
3 void eraNut00b(double date1, double date2, double *dpsi, double *deps)
4 /*
5 ** - - - - - - - - - -
6 ** e r a N u t 0 0 b
7 ** - - - - - - - - - -
8 **
9 ** Nutation, IAU 2000B model.
10 **
11 ** Given:
12 ** date1,date2 double TT as a 2-part Julian Date (Note 1)
13 **
14 ** Returned:
15 ** dpsi,deps double nutation, luni-solar + planetary (Note 2)
16 **
17 ** Notes:
18 **
19 ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
20 ** convenient way between the two arguments. For example,
21 ** JD(TT)=2450123.7 could be expressed in any of these ways,
22 ** among others:
23 **
24 ** date1 date2
25 **
26 ** 2450123.7 0.0 (JD method)
27 ** 2451545.0 -1421.3 (J2000 method)
28 ** 2400000.5 50123.2 (MJD method)
29 ** 2450123.5 0.2 (date & time method)
30 **
31 ** The JD method is the most natural and convenient to use in
32 ** cases where the loss of several decimal digits of resolution
33 ** is acceptable. The J2000 method is best matched to the way
34 ** the argument is handled internally and will deliver the
35 ** optimum resolution. The MJD method and the date & time methods
36 ** are both good compromises between resolution and convenience.
37 **
38 ** 2) The nutation components in longitude and obliquity are in radians
39 ** and with respect to the equinox and ecliptic of date. The
40 ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
41 ** value of 84381.448 arcsec. (The errors that result from using
42 ** this function with the IAU 2006 value of 84381.406 arcsec can be
43 ** neglected.)
44 **
45 ** The nutation model consists only of luni-solar terms, but
46 ** includes also a fixed offset which compensates for certain long-
47 ** period planetary terms (Note 7).
48 **
49 ** 3) This function is an implementation of the IAU 2000B abridged
50 ** nutation model formally adopted by the IAU General Assembly in
51 ** 2000. The function computes the MHB_2000_SHORT luni-solar
52 ** nutation series (Luzum 2001), but without the associated
53 ** corrections for the precession rate adjustments and the offset
54 ** between the GCRS and J2000.0 mean poles.
55 **
56 ** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400
57 ** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
58 ** 77 terms, plus additional simplifications, yet still delivers
59 ** results of 1 mas accuracy at present epochs. This combination of
60 ** accuracy and size makes the IAU 2000B abridged nutation model
61 ** suitable for most practical applications.
62 **
63 ** The function delivers a pole accurate to 1 mas from 1900 to 2100
64 ** (usually better than 1 mas, very occasionally just outside
65 ** 1 mas). The full IAU 2000A model, which is implemented in the
66 ** function eraNut00a (q.v.), delivers considerably greater accuracy
67 ** at current dates; however, to realize this improved accuracy,
68 ** corrections for the essentially unpredictable free-core-nutation
69 ** (FCN) must also be included.
70 **
71 ** 5) The present function provides classical nutation. The
72 ** MHB_2000_SHORT algorithm, from which it is adapted, deals also
73 ** with (i) the offsets between the GCRS and mean poles and (ii) the
74 ** adjustments in longitude and obliquity due to the changed
75 ** precession rates. These additional functions, namely frame bias
76 ** and precession adjustments, are supported by the ERFA functions
77 ** eraBi00 and eraPr00.
78 **
79 ** 6) The MHB_2000_SHORT algorithm also provides "total" nutations,
80 ** comprising the arithmetic sum of the frame bias, precession
81 ** adjustments, and nutation (luni-solar + planetary). These total
82 ** nutations can be used in combination with an existing IAU 1976
83 ** precession implementation, such as eraPmat76, to deliver GCRS-
84 ** to-true predictions of mas accuracy at current epochs. However,
85 ** for symmetry with the eraNut00a function (q.v. for the reasons),
86 ** the ERFA functions do not generate the "total nutations"
87 ** directly. Should they be required, they could of course easily
88 ** be generated by calling eraBi00, eraPr00 and the present function
89 ** and adding the results.
90 **
91 ** 7) The IAU 2000B model includes "planetary bias" terms that are
92 ** fixed in size but compensate for long-period nutations. The
93 ** amplitudes quoted in McCarthy & Luzum (2003), namely
94 ** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
95 ** the "total nutations" method described in Note 6. The Luzum
96 ** (2001) values used in this ERFA implementation, namely -0.135 mas
97 ** and +0.388 mas, are optimized for the "rigorous" method, where
98 ** frame bias, precession and nutation are applied separately and in
99 ** that order. During the interval 1995-2050, the ERFA
100 ** implementation delivers a maximum error of 1.001 mas (not
101 ** including FCN).
102 **
103 ** References:
104 **
105 ** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
106 ** for the precession quantities based upon the IAU /1976/ system of
107 ** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
108 **
109 ** Luzum, B., private communication, 2001 (Fortran code
110 ** MHB_2000_SHORT)
111 **
112 ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
113 ** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
114 ** 85, 37-49 (2003)
115 **
116 ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
117 ** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
118 **
119 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
120 ** Derived, with permission, from the SOFA library. See notes at end of file.
121 */
122 {
123  double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
124  dpsils, depsls, dpsipl, depspl;
125  int i;
126 
127 /* Units of 0.1 microarcsecond to radians */
128  static const double U2R = ERFA_DAS2R / 1e7;
129 
130 /* ---------------------------------------- */
131 /* Fixed offsets in lieu of planetary terms */
132 /* ---------------------------------------- */
133 
134  static const double DPPLAN = -0.135 * ERFA_DMAS2R;
135  static const double DEPLAN = 0.388 * ERFA_DMAS2R;
136 
137 /* --------------------------------------------------- */
138 /* Luni-solar nutation: argument and term coefficients */
139 /* --------------------------------------------------- */
140 
141 /* The units for the sine and cosine coefficients are */
142 /* 0.1 microarcsec and the same per Julian century */
143 
144  static const struct {
145  int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
146  double ps,pst,pc; /* longitude sin, t*sin, cos coefficients */
147  double ec,ect,es; /* obliquity cos, t*cos, sin coefficients */
148 
149  } x[] = {
150 
151  /* 1-10 */
152  { 0, 0, 0, 0,1,
153  -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0},
154  { 0, 0, 2,-2,2,
155  -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0},
156  { 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0},
157  { 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0},
158  { 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0},
159  { 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0},
160  { 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0},
161  { 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0},
162  { 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0},
163  { 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0},
164 
165  /* 11-20 */
166  { 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0},
167  {-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0},
168  {-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0},
169  { 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0},
170  {-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0},
171  {-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0},
172  { 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0},
173  {-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0},
174  { 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0},
175  { 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0},
176 
177  /* 21-30 */
178  { 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0},
179  {-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0},
180  { 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0},
181  { 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0},
182  {-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0},
183  { 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0},
184  { 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0},
185  { 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0},
186  {-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0},
187  { 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0},
188 
189  /* 31-40 */
190  { 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0},
191  { 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0},
192  { 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0},
193  {-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0},
194  { 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0},
195  { 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0},
196  {-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0},
197  { 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0},
198  { 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0},
199  { 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0},
200 
201  /* 41-50 */
202  { 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0},
203  { 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0},
204  { 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0},
205  {-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0},
206  { 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0},
207  { 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0},
208  { 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0},
209  {-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0},
210  { 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0},
211  { 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0},
212 
213  /* 51-60 */
214  { 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0},
215  { 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0},
216  {-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0},
217  { 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0},
218  { 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0},
219  { 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0},
220  { 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0},
221  {-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0},
222  {-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0},
223  { 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0},
224 
225  /* 61-70 */
226  {-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0},
227  { 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0},
228  { 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0},
229  {-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0},
230  { 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0},
231  { 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0},
232  {-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0},
233  { 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0},
234  {-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0},
235  { 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0},
236 
237  /* 71-77 */
238  {-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0},
239  {-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0},
240  { 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0},
241  { 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0},
242  {-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0},
243  {-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0},
244  { 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0}
245  };
246 
247 /* Number of terms in the series */
248  const int NLS = (int) (sizeof x / sizeof x[0]);
249 
250 /*--------------------------------------------------------------------*/
251 
252 /* Interval between fundamental epoch J2000.0 and given date (JC). */
253  t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
254 
255 /* --------------------*/
256 /* LUNI-SOLAR NUTATION */
257 /* --------------------*/
258 
259 /* Fundamental (Delaunay) arguments from Simon et al. (1994) */
260 
261 /* Mean anomaly of the Moon. */
262  el = fmod(485868.249036 + (1717915923.2178) * t, ERFA_TURNAS) * ERFA_DAS2R;
263 
264 /* Mean anomaly of the Sun. */
265  elp = fmod(1287104.79305 + (129596581.0481) * t, ERFA_TURNAS) * ERFA_DAS2R;
266 
267 /* Mean argument of the latitude of the Moon. */
268  f = fmod(335779.526232 + (1739527262.8478) * t, ERFA_TURNAS) * ERFA_DAS2R;
269 
270 /* Mean elongation of the Moon from the Sun. */
271  d = fmod(1072260.70369 + (1602961601.2090) * t, ERFA_TURNAS) * ERFA_DAS2R;
272 
273 /* Mean longitude of the ascending node of the Moon. */
274  om = fmod(450160.398036 + (-6962890.5431) * t, ERFA_TURNAS) * ERFA_DAS2R;
275 
276 /* Initialize the nutation values. */
277  dp = 0.0;
278  de = 0.0;
279 
280 /* Summation of luni-solar nutation series (smallest terms first). */
281  for (i = NLS-1; i >= 0; i--) {
282 
283  /* Argument and functions. */
284  arg = fmod( (double)x[i].nl * el +
285  (double)x[i].nlp * elp +
286  (double)x[i].nf * f +
287  (double)x[i].nd * d +
288  (double)x[i].nom * om, ERFA_D2PI );
289  sarg = sin(arg);
290  carg = cos(arg);
291 
292  /* Term. */
293  dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg;
294  de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg;
295  }
296 
297 /* Convert from 0.1 microarcsec units to radians. */
298  dpsils = dp * U2R;
299  depsls = de * U2R;
300 
301 /* ------------------------------*/
302 /* IN LIEU OF PLANETARY NUTATION */
303 /* ------------------------------*/
304 
305 /* Fixed offset to correct for missing terms in truncated series. */
306  dpsipl = DPPLAN;
307  depspl = DEPLAN;
308 
309 /* --------*/
310 /* RESULTS */
311 /* --------*/
312 
313 /* Add luni-solar and planetary components. */
314  *dpsi = dpsils + dpsipl;
315  *deps = depsls + depspl;
316 
317  return;
318 
319 }
320 /*----------------------------------------------------------------------
321 **
322 **
323 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
324 ** All rights reserved.
325 **
326 ** This library is derived, with permission, from the International
327 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
328 ** available from http://www.iausofa.org.
329 **
330 ** The ERFA version is intended to retain identical functionality to
331 ** the SOFA library, but made distinct through different function and
332 ** file names, as set out in the SOFA license conditions. The SOFA
333 ** original has a role as a reference standard for the IAU and IERS,
334 ** and consequently redistribution is permitted only in its unaltered
335 ** state. The ERFA version is not subject to this restriction and
336 ** therefore can be included in distributions which do not support the
337 ** concept of "read only" software.
338 **
339 ** Although the intent is to replicate the SOFA API (other than
340 ** replacement of prefix names) and results (with the exception of
341 ** bugs; any that are discovered will be fixed), SOFA is not
342 ** responsible for any errors found in this version of the library.
343 **
344 ** If you wish to acknowledge the SOFA heritage, please acknowledge
345 ** that you are using a library derived from SOFA, rather than SOFA
346 ** itself.
347 **
348 **
349 ** TERMS AND CONDITIONS
350 **
351 ** Redistribution and use in source and binary forms, with or without
352 ** modification, are permitted provided that the following conditions
353 ** are met:
354 **
355 ** 1 Redistributions of source code must retain the above copyright
356 ** notice, this list of conditions and the following disclaimer.
357 **
358 ** 2 Redistributions in binary form must reproduce the above copyright
359 ** notice, this list of conditions and the following disclaimer in
360 ** the documentation and/or other materials provided with the
361 ** distribution.
362 **
363 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
364 ** the International Astronomical Union nor the names of its
365 ** contributors may be used to endorse or promote products derived
366 ** from this software without specific prior written permission.
367 **
368 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
369 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
370 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
371 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
372 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
373 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
374 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
375 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
376 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
377 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
378 ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
379 ** POSSIBILITY OF SUCH DAMAGE.
380 **
381 */
ERFA_DJ00
#define ERFA_DJ00
Definition: erfam.h:87
i
int i
Definition: db_dim_client.c:21
ERFA_TURNAS
#define ERFA_TURNAS
Definition: erfam.h:66
ERFA_DAS2R
#define ERFA_DAS2R
Definition: erfam.h:60
ERFA_DMAS2R
#define ERFA_DMAS2R
Definition: erfam.h:69
eraNut00b
void eraNut00b(double date1, double date2, double *dpsi, double *deps)
Definition: nut00b.c:3
ERFA_D2PI
#define ERFA_D2PI
Definition: erfam.h:48
ERFA_DJC
#define ERFA_DJC
Definition: erfam.h:81
t
TT t
Definition: test_client.c:26