1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
use crate*;
use *;
/// Precession angles, IAU 2006, equinox based.
///
/// Given:
/// date1,date2 double TT as a 2-part Julian Date (Note 1)
///
/// Returned (see Note 2):
/// eps0 double epsilon_0
/// psia double psi_A
/// oma double omega_A
/// bpa double P_A
/// bqa double Q_A
/// pia double pi_A
/// bpia double Pi_A
/// epsa double obliquity epsilon_A
/// chia double chi_A
/// za double z_A
/// zetaa double zeta_A
/// thetaa double theta_A
/// pa double p_A
/// gam double F-W angle gamma_J2000
/// phi double F-W angle phi_J2000
/// psi double F-W angle psi_J2000
///
/// 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) This function returns the set of equinox based angles for the
/// Capitaine et al. "P03" precession theory, adopted by the IAU in
/// 2006. The angles are set out in Table 1 of Hilton et al. (2006):
///
/// eps0 epsilon_0 obliquity at J2000.0
/// psia psi_A luni-solar precession
/// oma omega_A inclination of equator wrt J2000.0 ecliptic
/// bpa P_A ecliptic pole x, J2000.0 ecliptic triad
/// bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
/// pia pi_A angle between moving and J2000.0 ecliptics
/// bpia Pi_A longitude of ascending node of the ecliptic
/// epsa epsilon_A obliquity of the ecliptic
/// chia chi_A planetary precession
/// za z_A equatorial precession: -3rd 323 Euler angle
/// zetaa zeta_A equatorial precession: -1st 323 Euler angle
/// thetaa theta_A equatorial precession: 2nd 323 Euler angle
/// pa p_A general precession (n.b. see below)
/// gam gamma_J2000 J2000.0 RA difference of ecliptic poles
/// phi phi_J2000 J2000.0 codeclination of ecliptic pole
/// psi psi_J2000 longitude difference of equator poles, J2000.0
///
/// The returned values are all radians.
///
/// Note that the t^5 coefficient in the series for p_A from
/// Capitaine et al. (2003) is incorrectly signed in Hilton et al.
/// (2006).
///
/// 3) Hilton et al. (2006) Table 1 also contains angles that depend on
/// models distinct from the P03 precession theory itself, namely the
/// IAU 2000A frame bias and nutation. The quoted polynomials are
/// used in other ERFA functions:
///
/// . eraXy06 contains the polynomial parts of the X and Y series.
///
/// . eraS06 contains the polynomial part of the s+XY/2 series.
///
/// . eraPfw06 implements the series for the Fukushima-Williams
/// angles that are with respect to the GCRS pole (i.e. the variants
/// that include frame bias).
///
/// 4) The IAU resolution stipulated that the choice of parameterization
/// was left to the user, and so an IAU compliant precession
/// implementation can be constructed using various combinations of
/// the angles returned by the present function.
///
/// 5) The parameterization used by ERFA is the version of the Fukushima-
/// Williams angles that refers directly to the GCRS pole. These
/// angles may be calculated by calling the function eraPfw06. ERFA
/// also supports the direct computation of the CIP GCRS X,Y by
/// series, available by calling eraXy06.
///
/// 6) The agreement between the different parameterizations is at the
/// 1 microarcsecond level in the present era.
///
/// 7) When constructing a precession formulation that refers to the GCRS
/// pole rather than the dynamical pole, it may (depending on the
/// choice of angles) be necessary to introduce the frame bias
/// explicitly.
///
/// 8) It is permissible to re-use the same variable in the returned
/// arguments. The quantities are stored in the stated order.
///
/// References:
///
/// Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
/// Astron.Astrophys., 412, 567
///
/// Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
///
/// Called:
/// eraObl06 mean obliquity, IAU 2006
///
/// This revision: 2021 May 11