Orbits

Contents......Page 10
1. Introduction......Page 16
2.1 Geocentric Earth-Fixed Coordinate Systems......Page 19
2.2 Coordinate System Transformations......Page 22
2.3 Local Coordinate System......Page 24
2.4 Earth-Centred Inertial Coordinate System......Page 25
2.5 IAU 2000 Framework......Page 29
2.7 Satellite Fixed Coordinate System......Page 33
2.8 Time Systems......Page 36
3.1 Keplerian Motion......Page 40
3.2 Satellite Motion in the Orbital Plane......Page 43
3.3 Keplerian Equation......Page 45
3.4 State Vector of the Satellite......Page 48
4.1 Perturbed Equation of Satellite Motion......Page 51
4.1.1 Lagrangian Perturbed Equation of Satellite Motion......Page 52
4.1.2 Gaussian Perturbed Equation of Satellite Motion......Page 54
4.2.1 Perturbation of the Earth's Gravitational Field......Page 58
4.2.2 Perturbation of the Sun and the Moon as well as Planets......Page 62
4.2.3 Earth Tide and Ocean Tide Perturbations......Page 63
4.2.4 Solar Radiation Pressure......Page 67
4.2.5 Atmospheric Drag......Page 72
4.2.6 Additional Perturbations......Page 75
4.2.7 Order Estimations of Perturbations......Page 76
5.1 C[sub(20)] Perturbed Equations of Motion......Page 78
5.2 Solutions of C[sub(20)] Perturbed Orbit......Page 80
5.3 Properties of the Solutions of C[sub(20)] Perturbations......Page 93
5.4 Orbit Correction......Page 95
6.1 Principle of the Derivations......Page 98
6.2 Solutions of C[sub(30)] Perturbation......Page 102
6.3 Solutions of D[sub(21)] Perturbations......Page 125
6.4 Solutions of D[sub(22)] Perturbations......Page 140
6.5 Properties of the Solutions of Geopotential Perturbations......Page 154
6.6 Solutions of Geopotential Perturbations of 6 × 6 Order and Degrees......Page 155
6.7 Solutions of Geopotential Perturbations of l × m Order and Degrees......Page 156
7.1 Key Notes to the Problems......Page 158
7.2 Solutions of Disturbance of Solar Radiation Pressure......Page 159
7.2.1 Solutions via Gaussian Perturbed Equations......Page 161
7.3 Solutions of Disturbance of Atmospheric Drag......Page 171
7.3.1 Solutions via Gaussian Perturbed Equations......Page 172
7.4 Solutions of Disturbance of the Sun......Page 174
7.5 Solutions of Disturbance of the Moon......Page 177
7.6 Solutions of Disturbance of Planets......Page 179
7.8 Ephemeris of the Moon, the Sun and Planets......Page 180
8.1 Principle of GPS Precise Orbit Determination......Page 185
8.1.1 Algebraic Solution of the Variation Equation......Page 187
8.2 Numerical Integration and Interpolation Algorithms......Page 188
8.2.1 Runge-Kutta Algorithms......Page 189
8.2.2 Adams Algorithms......Page 193
8.2.3 Cowell Algorithms......Page 196
8.2.4 Mixed Algorithms and Discussions......Page 197
8.2.5 Interpolation Algorithms......Page 198
8.3 Orbit-Related Partial Derivatives......Page 200
9.1 Principle of Analytic Orbit Determination......Page 210
9.2 Real Time Ability......Page 212
9.3 Properties of Analytic Orbit Determination......Page 213
10.1.1 Problem of Singularity of the Solutions......Page 215
10.1.3 Disturbed Equations in the Case of Equatorial Orbit......Page 216
10.1.4 Disturbed Equations in the Case of Circular and Equatorial Orbit......Page 217
10.1.6 Simplified Singularity-Free Disturbed Equations of Motion......Page 218
10.2 Equations of Motion in Non-Inertial Frame......Page 219
10.3 Discussions......Page 220
Appendix 1: IAU 1980 Theory of Nutation......Page 223
Bibliography......Page 226
G......Page 234
S......Page 235
Z......Page 236