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
use crate::gp;
use crate::model;
use crate::propagator;
#[cfg(not(feature = "std"))]
use num_traits::Float;
#[allow(clippy::too_many_arguments)]
pub(crate) fn constants(
geopotential: model::Geopotential,
drag_term: f64,
orbit_0: propagator::Orbit,
p1: f64,
a0: f64,
s: f64,
xi: f64,
eta: f64,
c1: f64,
c4: f64,
k0: f64,
k1: f64,
k6: f64,
k14: f64,
p2: f64,
p3: f64,
p7: f64,
p9: f64,
p14: f64,
p15: f64,
) -> propagator::Constants {
propagator::Constants {
geopotential,
// Ω̇ = p₁₄
right_ascension_dot: p14,
// ω̇ = k₁₄
argument_of_perigee_dot: k14,
// Ṁ = p₁₅
mean_anomaly_dot: p15,
c1,
c4,
k0,
k1,
method: propagator::Method::NearEarth {
a0,
// 1 J₃
// k₂ = - - -- sin I₀
// 2 J₂
k2: -0.5 * (geopotential.j3 / geopotential.j2) * orbit_0.inclination.sin(),
// k₃ = 1 - p₁²
k3: 1.0 - p1.powi(2),
// k₄ = 7 p₁² - 1
k4: 7.0 * p1.powi(2) - 1.0,
// │ 1 J₃ 3 + 5 p₁
// k₅ = │ - - -- sin I₀ -------- if |1 + p₁| > 1.5 × 10⁻¹²
// │ 4 J₂ 1 + p₁
// │ 1 J₃ 3 + 5 p₁
// │ - - -- sin I₀ ----------- otherwise
// │ 4 J₂ 1.5 × 10⁻¹²
k5: if (1.0 + p1).abs() > 1.5e-12 {
-0.25
* (geopotential.j3 / geopotential.j2)
* orbit_0.inclination.sin()
* (3.0 + 5.0 * p1)
/ (1.0 + p1)
} else {
-0.25
* (geopotential.j3 / geopotential.j2)
* orbit_0.inclination.sin()
* (3.0 + 5.0 * p1)
/ 1.5e-12
},
k6,
// p₃ < 220 / (aₑ + 1)
high_altitude: if p3 < 220.0 / geopotential.ae + 1.0 {
propagator::HighAltitude::No {}
} else {
// D₂ = 4 a₀" ξ C₁²
let d2 = 4.0 * a0 * xi * c1.powi(2);
// p₁₆ = D₂ ξ C₁ / 3
let p16 = d2 * xi * c1 / 3.0;
// D₃ = (17 a + s) p₁₆
let d3 = (17.0 * a0 + s) * p16;
// D₄ = ¹/₂ p₁₆ a₀" ξ (221 a₀" + 31 s) C₁
let d4 = 0.5 * p16 * a0 * xi * (221.0 * a0 + 31.0 * s) * c1;
propagator::HighAltitude::Yes {
// C₅ = 2 B* p₉ a₀" p₂ (1 + 2.75 (η² + η e₀) + e₀ η³)
c5: drag_term
* (2.0
* p9
* a0
* p2
* (1.0
+ 2.75 * (eta.powi(2) + eta * orbit_0.eccentricity)
+ eta * orbit_0.eccentricity * eta.powi(2))),
d2,
d3,
d4,
eta,
// k₇ = sin M₀
k7: orbit_0.mean_anomaly.sin(),
// k₈ = D₂ + 2 C₁²
k8: d2 + 2.0 * c1.powi(2),
// k₉ = ¹/₄ (3 D₃ + C₁ (12 D₂ + 10 C₁²))
k9: 0.25 * (3.0 * d3 + c1 * (12.0 * d2 + 10.0 * c1.powi(2))),
// k₁₀ = ¹/₅ (3 D₄ + 12 C₁ D₃ + 6 D₂² + 15 C₁² (2 D₂ + C₁²))
k10: 0.2
* (3.0 * d4
+ 12.0 * c1 * d3
+ 6.0 * d2.powi(2)
+ 15.0 * c1.powi(2) * (2.0 * d2 + c1.powi(2))),
elliptic: if orbit_0.eccentricity > 1.0e-4 {
propagator::Elliptic::Yes {
// k₁₁ = (1 + η cos M₀)³
k11: (1.0 + eta * orbit_0.mean_anomaly.cos()).powi(3),
// J₃ p₇ ξ n₀" sin I₀
// k₁₂ = - 2 B* cos ω₀ -- ----------------
// J₂ e₀
k12: drag_term
* (-2.0
* p7
* xi
* (geopotential.j3 / geopotential.j2)
* orbit_0.mean_motion
* orbit_0.inclination.sin()
/ orbit_0.eccentricity)
* orbit_0.argument_of_perigee.cos(),
// 2 p₇ B*
// k₁₃ = - - -----
// 3 e₀ η
k13: -2.0 / 3.0 * p7 * drag_term / (orbit_0.eccentricity * eta),
}
} else {
propagator::Elliptic::No {}
},
}
},
},
orbit_0,
}
}
impl propagator::Constants {
#[allow(clippy::too_many_arguments, clippy::type_complexity)]
pub(crate) fn near_earth_orbital_elements(
&self,
a0: f64,
k2: f64,
k3: f64,
k4: f64,
k5: f64,
k6: f64,
high_altitude: &propagator::HighAltitude,
t: f64,
p22: f64,
p23: f64,
) -> core::result::Result<(propagator::Orbit, f64, f64, f64, f64, f64, f64), gp::Error> {
// p₂₄ = M₀ + Ṁ t
let p24 = self.orbit_0.mean_anomaly + self.mean_anomaly_dot * t;
let (argument_of_perigee, mean_anomaly, a, p27) = match high_altitude {
propagator::HighAltitude::No {} => (
// ω = p₂₃
p23,
// M = p₂₄ + n₀" k₁ t²
p24 + self.orbit_0.mean_motion * self.k1 * t.powi(2),
// a = a₀" (1 - C₁ t)²
a0 * (1.0 - self.c1 * t).powi(2),
// p₂₇ = e₀ - C₄ t
self.orbit_0.eccentricity - self.c4 * t,
),
propagator::HighAltitude::Yes {
c5,
d2,
d3,
d4,
eta,
k7,
k8,
k9,
k10,
elliptic,
} => {
// ω = │ p₂₃ - p₂₅ if e₀ > 10⁻⁴
// │ p₂₃ otherwise
// p₂₆ = │ p₂₄ + p₂₅ if e₀ > 10⁻⁴
// │ p₂₄ otherwise
let (argument_of_perigee, p26) = match elliptic {
propagator::Elliptic::Yes { k11, k12, k13 } => {
// p₂₅ = k₁₃ ((1 + η cos p₂₄)³ - k₁₁) + k₁₂ t
let p25 = k13 * ((1.0 + eta * p24.cos()).powi(3) - k11) + k12 * t;
(p23 - p25, p24 + p25)
}
propagator::Elliptic::No {} => (p23, p24),
};
(
argument_of_perigee,
// M = p₂₆ + n₀" (k₁ t² + k₈ t³ + t⁴ (k₉ + t k₁₀)
p26 + self.orbit_0.mean_motion
* (self.k1 * t.powi(2) + k8 * t.powi(3) + t.powi(4) * (k9 + t * k10)),
// a = a₀" (1 - C₁ t - D₂ t² - D₃ t³ - D₄ t⁴)²
a0 * (1.0 - self.c1 * t - d2 * t.powi(2) - d3 * t.powi(3) - d4 * t.powi(4))
.powi(2),
// p₂₇ = e₀ - (C₄ t + C₅ (sin p₂₆ - k₇))
self.orbit_0.eccentricity - (self.c4 * t + c5 * (p26.sin() - k7)),
)
}
};
if !(-0.001..1.0).contains(&p27) {
Err(gp::Error::OutOfRangeEccentricity {
eccentricity: p27,
t,
})
} else {
// e = │ 10⁻⁶ if p₂₇ < 10⁻⁶
// │ p₂₇ otherwise
let eccentricity = p27.max(1.0e-6);
Ok((
propagator::Orbit {
// I = I₀
inclination: self.orbit_0.inclination,
// Ω = p₂₂
right_ascension: p22,
eccentricity,
argument_of_perigee,
mean_anomaly,
// n = kₑ / a³ᐟ²
mean_motion: self.geopotential.ke / a.powf(1.5),
},
a,
// p₃₂ = k₂
k2,
// p₃₃ = k₃
k3,
// p₃₄ = k₄
k4,
// p₃₅ = k₅
k5,
// p₃₆ = k₆
k6,
))
}
}
}