lox-frames 0.1.0-alpha.16

Reference frame transformations for the Lox ecosystem
Documentation 
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

// SPDX-FileCopyrightText: 2023 Angus Morrison <github@angus-morrison.com>
// SPDX-FileCopyrightText: 2024 Helge Eichhorn <git@helgeeichhorn.de>
//
// SPDX-License-Identifier: MPL-2.0

use std::f64::consts::TAU;

use lox_core::types::units::{Arcseconds, JulianCenturies};
use lox_core::units::{Angle, AngleUnits};
use lox_time::{Time, julian_dates::JulianDate, time_scales::Tdb};

use crate::iers::nutation::Nutation;

struct Coefficients {
    /// Coefficients of l, l', F, D and Ω.
    l: f64,
    lp: f64,
    f: f64,
    d: f64,
    om: f64,

    /// Coefficients of longitude, ψ.
    sin_psi: f64,
    sin_psi_t: f64,

    /// Coefficients of obliquity, ε.
    cos_eps: f64,
    cos_eps_t: f64,
}

impl Nutation {
    /// Computes nutation using the IAU 1980 model.
    pub fn iau1980(time: Time<Tdb>) -> Self {
        let t = time.centuries_since_j2000();
        let l = l(t);
        let lp = lp(t);
        let f = f(t);
        let d = d(t);
        let om = omega(t);

        let (dpsi, deps) = COEFFICIENTS
            .iter()
            // The coefficients are given by descending magnitude but folded by ascending
            // magnitude to minimise floating-point error.
            .rev()
            .fold((0.0, 0.0), |(mut dpsi, mut deps), coeff| {
                // Form argument for current term.
                let arg = coeff.l * l + coeff.lp * lp + coeff.f * f + coeff.d * d + coeff.om * om;

                // Accumulate current term.
                let sin = coeff.sin_psi + coeff.sin_psi_t * t;
                let cos = coeff.cos_eps + coeff.cos_eps_t * t;
                dpsi += sin * arg.sin();
                deps += cos * arg.cos();

                (dpsi, deps)
            });

        Self {
            dpsi: (1e-1 * dpsi).mas(),
            deps: (1e-1 * deps).mas(),
        }
    }
}

/// `l`, the mean longitude of the Moon measured from the mean position of the perigee,
/// normalized to the range [0, 2π).
fn l(centuries_since_j2000_tdb: JulianCenturies) -> Angle {
    let l_poly: Arcseconds = fast_polynomial::poly_array(
        centuries_since_j2000_tdb,
        &[485866.733, 715922.633, 31.31, 0.064],
    );
    (l_poly.arcsec() + ((1325.0 * centuries_since_j2000_tdb % 1.0) * TAU).rad())
        .normalize_two_pi(Angle::ZERO)
}

/// `l'`, the mean longitude of the Sun measured from the mean position of the perigee,
/// normalized to the range [0, 2π).
fn lp(centuries_since_j2000_tdb: JulianCenturies) -> Angle {
    let lp_poly: Arcseconds = fast_polynomial::poly_array(
        centuries_since_j2000_tdb,
        &[1287099.804, 1292581.224, -0.577, -0.012],
    );
    (lp_poly.arcsec() + ((99.0 * centuries_since_j2000_tdb % 1.0) * TAU).rad())
        .normalize_two_pi(Angle::ZERO)
}

/// `F`, the mean longitude of the Moon minus the mean longitude of the Moon's ascending node,
/// normalized to the range [0, 2π).
fn f(centuries_since_j2000_tdb: JulianCenturies) -> Angle {
    let f_poly: Arcseconds = fast_polynomial::poly_array(
        centuries_since_j2000_tdb,
        &[335778.877, 295263.137, -13.257, 0.011],
    );
    (f_poly.arcsec() + ((1342.0 * centuries_since_j2000_tdb % 1.0) * TAU).rad())
        .normalize_two_pi(Angle::ZERO)
}

/// `D`, the mean elongation of the Moon from the Sun, normalized to the range [0, 2π).
fn d(centuries_since_j2000_tdb: JulianCenturies) -> Angle {
    let d_poly: Arcseconds = fast_polynomial::poly_array(
        centuries_since_j2000_tdb,
        &[1072261.307, 1105601.328, -6.891, 0.019],
    );
    (d_poly.arcsec() + ((1236.0 * centuries_since_j2000_tdb % 1.0) * TAU).rad())
        .normalize_two_pi(Angle::ZERO)
}

/// `Ω`, the longitude of the mean ascending node of the lunar orbit on the ecliptic, measured from
/// the mean equinox of date.
fn omega(centuries_since_j2000_tdb: JulianCenturies) -> Angle {
    let om_poly: Arcseconds = fast_polynomial::poly_array(
        centuries_since_j2000_tdb,
        &[450160.280, -482890.539, 7.455, 0.008],
    );
    (om_poly.arcsec() + ((-5.0 * centuries_since_j2000_tdb % 1.0) * TAU).rad())
        .normalize_two_pi(Angle::ZERO)
}

#[rustfmt::skip]
// @formatter:off (sometimes RustRover ignores rustfmt::skip)
const COEFFICIENTS: [Coefficients; 106] = [
    Coefficients{ l: 0.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:-171996.0,	sin_psi_t:-174.2,	cos_eps: 92025.0,	cos_eps_t:  8.9 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 2.0,	sin_psi:   2062.0,	sin_psi_t:   0.2,	cos_eps:  -895.0,	cos_eps_t:  0.5 },
    Coefficients{ l: -2.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:     46.0,	sin_psi_t:   0.0,	cos_eps:   -24.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f:-2.0,	d: 0.0,	om: 0.0,	sin_psi:     11.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -2.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp:-1.0,	f: 0.0,	d:-1.0,	om: 0.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp:-2.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:     -2.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f:-2.0,	d: 0.0,	om: 1.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi: -13187.0,	sin_psi_t:  -1.6,	cos_eps:  5736.0,	cos_eps_t: -3.1 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:   1426.0,	sin_psi_t:  -3.4,	cos_eps:    54.0,	cos_eps_t: -0.1 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:   -517.0,	sin_psi_t:   1.2,	cos_eps:   224.0,	cos_eps_t: -0.6 },
    Coefficients{ l: 0.0,	lp:-1.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:    217.0,	sin_psi_t:  -0.5,	cos_eps:   -95.0,	cos_eps_t:  0.3 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:    129.0,	sin_psi_t:   0.1,	cos_eps:   -70.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 0.0,	d:-2.0,	om: 0.0,	sin_psi:     48.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 0.0,	sin_psi:    -22.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 2.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:     17.0,	sin_psi_t:  -0.1,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:    -15.0,	sin_psi_t:   0.0,	cos_eps:     9.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 2.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:    -16.0,	sin_psi_t:   0.1,	cos_eps:     7.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp:-1.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:    -12.0,	sin_psi_t:   0.0,	cos_eps:     6.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -2.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 1.0,	sin_psi:     -6.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp:-1.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:     -5.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 0.0,	d:-2.0,	om: 1.0,	sin_psi:      4.0,	sin_psi_t:   0.0,	cos_eps:    -2.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:      4.0,	sin_psi_t:   0.0,	cos_eps:    -2.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d:-1.0,	om: 0.0,	sin_psi:     -4.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 1.0,	f: 0.0,	d:-2.0,	om: 0.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f:-2.0,	d: 2.0,	om: 1.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f:-2.0,	d: 2.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 0.0,	d: 0.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 0.0,	d: 1.0,	om: 1.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 2.0,	d:-2.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:  -2274.0,	sin_psi_t:  -0.2,	cos_eps:   977.0,	cos_eps_t: -0.5 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:    712.0,	sin_psi_t:   0.1,	cos_eps:    -7.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:   -386.0,	sin_psi_t:  -0.4,	cos_eps:   200.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:   -301.0,	sin_psi_t:   0.0,	cos_eps:   129.0,	cos_eps_t: -0.1 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d:-2.0,	om: 0.0,	sin_psi:   -158.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:    123.0,	sin_psi_t:   0.0,	cos_eps:   -53.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 0.0,	sin_psi:     63.0,	sin_psi_t:   0.0,	cos_eps:    -2.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:     63.0,	sin_psi_t:   0.1,	cos_eps:   -33.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:    -58.0,	sin_psi_t:  -0.1,	cos_eps:    32.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:    -59.0,	sin_psi_t:   0.0,	cos_eps:    26.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:    -51.0,	sin_psi_t:   0.0,	cos_eps:    27.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:    -38.0,	sin_psi_t:   0.0,	cos_eps:    16.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:     29.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:     29.0,	sin_psi_t:   0.0,	cos_eps:   -12.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:    -31.0,	sin_psi_t:   0.0,	cos_eps:    13.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 0.0,	sin_psi:     26.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:     21.0,	sin_psi_t:   0.0,	cos_eps:   -10.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 1.0,	sin_psi:     16.0,	sin_psi_t:   0.0,	cos_eps:    -8.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d:-2.0,	om: 1.0,	sin_psi:    -13.0,	sin_psi_t:   0.0,	cos_eps:     7.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 1.0,	sin_psi:    -10.0,	sin_psi_t:   0.0,	cos_eps:     5.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 1.0,	f: 0.0,	d:-2.0,	om: 0.0,	sin_psi:     -7.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:      7.0,	sin_psi_t:   0.0,	cos_eps:    -3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp:-1.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:     -7.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:     -8.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 0.0,	sin_psi:      6.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:      6.0,	sin_psi_t:   0.0,	cos_eps:    -3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 1.0,	sin_psi:     -6.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 1.0,	sin_psi:     -7.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:      6.0,	sin_psi_t:   0.0,	cos_eps:    -3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 0.0,	d:-2.0,	om: 1.0,	sin_psi:     -5.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp:-1.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:      5.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:     -5.0,	sin_psi_t:   0.0,	cos_eps:     3.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 0.0,	d:-2.0,	om: 0.0,	sin_psi:     -4.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f:-2.0,	d: 0.0,	om: 0.0,	sin_psi:      4.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 0.0,	d: 1.0,	om: 0.0,	sin_psi:     -4.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 1.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 0.0,	sin_psi:      3.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp:-1.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp:-1.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -2.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:     -2.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 3.0,	lp: 0.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp:-1.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:     -3.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 1.0,	f: 2.0,	d: 0.0,	om: 2.0,	sin_psi:      2.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:     -2.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 1.0,	sin_psi:      2.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 2.0,	sin_psi:     -2.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 3.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 0.0,	sin_psi:      2.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 1.0,	om: 2.0,	sin_psi:      2.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 0.0,	d: 0.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d:-4.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -2.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 2.0,	d: 4.0,	om: 2.0,	sin_psi:     -2.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 0.0,	d:-4.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 1.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 1.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -2.0,	lp: 0.0,	f: 2.0,	d: 4.0,	om: 2.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp: 0.0,	f: 4.0,	d: 0.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp:-1.0,	f: 0.0,	d:-2.0,	om: 0.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 1.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:    -1.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 2.0,	d: 2.0,	om: 2.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 1.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 4.0,	d:-2.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 3.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 2.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f: 2.0,	d:-2.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: -1.0,	lp:-1.0,	f: 0.0,	d: 2.0,	om: 1.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f:-2.0,	d: 0.0,	om: 1.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d:-1.0,	om: 2.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 0.0,	d: 2.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f:-2.0,	d:-2.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp:-1.0,	f: 2.0,	d: 0.0,	om: 1.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 1.0,	f: 0.0,	d:-2.0,	om: 1.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 1.0,	lp: 0.0,	f:-2.0,	d: 2.0,	om: 0.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 2.0,	lp: 0.0,	f: 0.0,	d: 2.0,	om: 0.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 0.0,	f: 2.0,	d: 4.0,	om: 2.0,	sin_psi:     -1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
    Coefficients{ l: 0.0,	lp: 1.0,	f: 0.0,	d: 1.0,	om: 0.0,	sin_psi:      1.0,	sin_psi_t:   0.0,	cos_eps:     0.0,	cos_eps_t:  0.0 },
];
// @formatter:on

#[cfg(test)]
mod tests {
    use lox_test_utils::assert_approx_eq;

    use super::*;

    #[test]
    fn test_nutation_iau1980() {
        let time = Time::from_two_part_julian_date(Tdb, 2400000.5, 53736.0);
        let actual = Nutation::iau1980(time);
        let expected = Nutation {
            dpsi: -9.643_658_353_226_563e-6.rad(),
            deps: 4.060_051_006_879_713e-5.rad(),
        };
        assert_approx_eq!(expected, actual, rtol <= 1e-13);
    }
}