Orbits (eBook)

Guochang Xu graduated in mathematics and geodesy from Wuhan University and the Chinese Academy of Sciences (CAS) in 1982 and 1984 respectively. He obtained his doctorate from the Technical University (TU) Berlin in 1992. Having worked as a research associate at the TU Berlin from 1986 to 1993, as a scientist at the GeoForschungsZentrum (GFZ) Potsdam from 1993 to 1998 and as a senior scientist at the National Survey and Cadastre, Denmark, from 1998 to 1999, he returned to the GFZ as a senior scientist in 1999. He has been involved in geodetic research since 1983 and has authored and co-authored several scientific books and software. He is also an overseas assessor of CAS and Education Ministry China and an adjunct professor of ChangAn University and CAS.

Contents 11
Abbreviations 15
Constants 17
Introduction 18
Coordinate and Time Systems 22
2.1 Geocentric Earth-Fixed Coordinate Systems 22
2.2 Coordinate System Transformations 25
2.3 Local Coordinate System 27
2.4 Earth-Centred Inertial Coordinate System 28
2.5 IAU 2000 Framework 32
2.6 Geocentric Ecliptic Inertial Coordinate System 36
2.7 Satellite Fixed Coordinate System 36
2.8 Time Systems 39
Keplerian Orbits 44
3.1 Keplerian Motion 44
3.2 Satellite Motion in the Orbital Plane 47
3.3 Keplerian Equation 49
3.4 State Vector of the Satellite 52
Perturbations on the Orbits 56
4.1 Perturbed Equation of Satellite Motion 56
4.2 Perturbation Forces of Satellite Motion 63
Solutions of C20 Perturbation 84
5.1 C20 Perturbed Equations of Motion 84
5.2 Solutions of C20 Perturbed Orbit 86
5.3 Properties of the Solutions of C20 Perturbations 99
5.4 Orbit Correction 101
Solutions of Geopotential Perturbations 104
6.1 Principle of the Derivations 104
6.2 Solutions of C30 Perturbation 108
6.3 Solutions of D21 Perturbations 131
6.4 Solutions of D22 Perturbations 146
6.5 Properties of the Solutions of Geopotential Perturbations 160
6.6 Solutions of Geopotential Perturbations of 6 × 6 Order and Degrees 161
6.7 Solutions of Geopotential Perturbations of l × m Order and Degrees 162
Solutions of Extraterrestrial Disturbances 164
7.1 Key Notes to the Problems 164
7.2 Solutions of Disturbance of Solar Radiation Pressure 165
7.3 Solutions of Disturbance of Atmospheric Drag 177
7.4 Solutions of Disturbance of the Sun 180
7.5 Solutions of Disturbance of the Moon 183
7.6 Solutions of Disturbance of Planets 185
7.7 Summary 186
7.8 Ephemeris of the Moon, the Sun and Planets 186
Numerical Orbit Determination 192
8.1 Principle of GPS Precise Orbit Determination 192
8.2 Numerical Integration and Interpolation Algorithms 195
8.3 Orbit-Related Partial Derivatives 207
Analytic Orbit Determination 218
9.1 Principle of Analytic Orbit Determination 218
9.2 Real Time Ability 220
9.3 Properties of Analytic Orbit Determination 221
Singularity-Free Theory and Discussions 224
10.1 Singularity-Free Orbit Theory 224
10.2 Equations of Motion in Non-Inertial Frame 228
10.3 Discussions 229
IAU 1980 Theory of Nutation 232
Bibliography 236
Index 244