Table of Contents

PREFACE page ix

Part I Problem Statement and Requirements 1
1 THE PROBLEM OF ORBIT DETERMINATION 3
1.1 Orbits and observations 3
1.2 The minimum principle 5
1.3 Two interpretations 6
1.4 Classifcation of the problem 7
1.5 How to read this book 13
2 DYNAMICAL SYSTEMS 15
2.1 The equation of motion 15
2.2 Solutions of the equation 16
2.3 The variational equation 18
2.4 Lyapounov exponents 20
2.5 Model problem dynamics 21
3 ERROR MODELS 23
3.1 Continuous random variables 23
3.2 Gaussian random variables 27
3.3 Expected values and transformations 30
4 THE N–BODY PROBLEM 33
4.1 Equation of motion and integrals 33
4.2 Coordinate changes 36
4.3 Barycentric and heliocentric coordinates 40
4.4 Jacobian coordinates 43
4.5 Small parameter perturbation 47
4.6 Solar System dynamical models 54

Part II Basic Theory 57
5 LEAST SQUARES 59
5.1 Linear least squares 59
5.2 Nonlinear least squares 62
5.3 Weighting of the residuals 66
5.4 Confdence ellipsoids 68
5.5 Propagation of covariance 72
5.6 Model problem 74
5.7 Probabilistic interpretation 77
5.8 Gaussian error models and outlier rejection 80
6 RANK DEFICIENCY 87
6.1 Complete rank defciency 87
6.2 Exact symmetries 91
6.3 Approximate rank defciency and symmetries 93
6.4 Scaling and approximate rank defciency 96
6.5 Planetary systems: extrasolar planets 98
6.6 Planetary systems: the Solar System 104

Part III Population Orbit Determination 111
7 THE IDENTIFICATION PROBLEM 113
7.1 Classifcation of the problem 113
7.2 Linear orbit identifcation 116
7.3 Semilinear orbit identifcation 120
7.4 Nonlinear orbit identifcation 124
7.5 Recovery and precovery 130
7.6 Attribution 133
8 LINKAGE 137
8.1 Admissible region 137
8.2 Sampling of the admissible region 144
8.3 Attributable orbital elements 148
8.4 Predictions from an attributable 152
8.5 Linkage by sampling the admissible region 156
8.6 Linkage by the two-body integrals 158
8.7 The space debris problem 163
9 METHODS BY LAPLACE AND GAUSS 171
9.1 Attributables and curvature 171
9.2 The method of Laplace 174
9.3 The method of Gauss 175
9.4 Topocentric Gauss–Laplace methods 177
9.5 Number of solutions 183
9.6 Charlier theory 185
9.7 Generalization of the Charlier theory 188
10 WEAKLY DETERMINED ORBITS 197
10.1 The line of variations 197
10.2 Applications of the constrained solutions 202
10.3 Selection of a metric 208
10.4 Surface of variations 214
10.5 The defnition of discovery 215
11 SURVEYS 219
11.1 Operational constraints of Solar System surveys 219
11.2 Identifcation and orbit determination procedure 221
11.3 Controlling the computational complexity 223
11.4 Identifcation management 226
11.5 Tests for accuracy 232
11.6 Recovery of low confdence detections 235
12 IMPACT MONITORING 237
12.1 Target planes 239
12.2 Minimum orbital intersection distance 242
12.3 Virtual asteroids 248
12.4 Target plane trails 251
12.5 Reliability and completion of impact monitoring 256
12.6 The current monitoring systems 258

Part IV Collaborative Orbit Determination 259
13 THE GRAVITY OF A PLANET 261
13.1 The gravity feld 261
13.2 Spherical harmonics 266
13.3 The Hilbert space of the harmonic functions 276
13.4 The gravity feld along the orbit 280
13.5 Frequency analysis, ground track, and resonance 284
14 NON-GRAVITATIONAL PERTURBATIONS 287
14.1 Direct radiation pressure 288
14.2 Thermal emission 294
14.3 Indirect radiation pressure 299
14.4 Drag 302
14.5 Active spacecraft effects 303
14.6 Case study: asteroid orbiter 306
15 MULTI-ARC STRATEGY 311
15.1 Local–global decomposition 311
15.2 Case study: satellite laser ranging 314
15.3 Perturbation model 315
15.4 Local geodesy 317
15.5 Symmetries and rank defciencies 319
16 SATELLITE GRAVIMETRY 323
16.1 On-board instrumentation 324
16.2 Accelerometer missions 331
16.3 Gradiometer missions 333
16.4 Resonant decomposition 338
16.5 Polar gaps 339
16.6 Satellite-to-satellite tracking 345
17 ORBITERS AROUND OTHER PLANETS 349
17.1 Science goals for an orbiter around Mercury 349
17.2 Interplanetary tracking 351
17.3 The gravimetry experiment 356
17.4 The rotation experiment 360
17.5 The relativity experiment 364
17.6 Global data processing 367
References 371
Index 379

Prezzo del Libro - Euro 69,00

Torna alla pagina precedente

---