| Preface | p. ix |
| Problem Statement and Requirements | p. 1 |
| The Problem of Orbit Determination | p. 3 |
| Orbits and observations | p. 3 |
| The minimum principle | p. 5 |
| Two interpretations | p. 6 |
| Classification of the problem | p. 7 |
| How to read this book | p. 13 |
| Dynamical Systems | p. 15 |
| The equation of motion | p. 15 |
| Solutions of the equation | p. 16 |
| The variational equation | p. 18 |
| Lyapounov exponents | p. 20 |
| Model problem dynamics | p. 21 |
| Error Models | p. 23 |
| Continuous random variables | p. 23 |
| Gaussian random variables | p. 27 |
| Expected values and transformations | p. 30 |
| The N-Body Problem | p. 33 |
| Equation of motion and integrals | p. 33 |
| Coordinate changes | p. 36 |
| Barycentric and heliocentric coordinates | p. 40 |
| Jacobian coordinates | p. 43 |
| Small parameter perturbation | p. 47 |
| Solar System dynamical models | p. 54 |
| Basic Theory | p. 57 |
| Least Squares | p. 59 |
| Linear least squares | p. 59 |
| Nonlinear least squares | p. 62 |
| Weighting of the residuals | p. 66 |
| Confidence ellipsoids | p. 68 |
| Propagation of covariance | p. 72 |
| Model problem | p. 74 |
| Probabilistic interpretation | p. 77 |
| Gaussian error models and outlier rejection | p. 80 |
| Rank Deficiency | p. 87 |
| Complete rank deficiency | p. 87 |
| Exact symmetries | p. 91 |
| Approximate rank deficiency and symmetries | p. 93 |
| Scaling and approximate rank deficiency | p. 96 |
| Planetary systems: extrasolar planets | p. 98 |
| Planetary systems: the Solar System | p. 104 |
| Population Orbit Determination | p. 111 |
| The Identification Problem | p. 113 |
| Classification of the problem | p. 113 |
| Linear orbit identification | p. 116 |
| Semilinear orbit identification | p. 120 |
| Nonlinear orbit identification | p. 124 |
| Recovery and precovery | p. 130 |
| Attribution | p. 133 |
| Linkage | p. 137 |
| Admissible region | p. 137 |
| Sampling of the admissible region | p. 144 |
| Attributable orbital elements | p. 148 |
| Predictions from an attributable | p. 152 |
| Linkage by sampling the admissible region | p. 156 |
| Linkage by the two-body integrals | p. 158 |
| The space debris problem | p. 163 |
| Methods by Laplace and Gauss | p. 171 |
| Attributables and curvature | p. 171 |
| The method of Laplace | p. 174 |
| The method of Gauss | p. 175 |
| Topocentric Gauss-Laplace methods | p. 177 |
| Number of solutions | p. 183 |
| Charlier theory | p. 185 |
| Generalization of the Charlier theory | p. 188 |
| Weakly Determined Orbits | p. 197 |
| The line of variations | p. 197 |
| Applications of the constrained solutions | p. 202 |
| Selection of a metric | p. 208 |
| Surface of variations | p. 214 |
| The definition of discovery | p. 215 |
| Surveys | p. 219 |
| Operational constraints of Solar System surveys | p. 219 |
| Identification and orbit determination procedure | p. 221 |
| Controlling the computational complexity | p. 223 |
| Identification management | p. 226 |
| Tests for accuracy | p. 232 |
| Recovery of low confidence detections | p. 235 |
| Impact Monitoring | p. 237 |
| Target planes | p. 239 |
| Minimum orbital intersection distance | p. 242 |
| Virtual asteroids | p. 248 |
| Target plane trails | p. 251 |
| Reliability and completion of impact monitoring | p. 256 |
| The current monitoring systems | p. 258 |
| Collaborative Orbit Determination | p. 259 |
| The Gravity of a Planet | p. 261 |
| The gravity field | p. 261 |
| Spherical harmonics | p. 266 |
| The Hilbert space of the harmonic functions | p. 276 |
| The gravity field along the orbit | p. 280 |
| Frequency analysis, ground track, and resonance | p. 284 |
| Non-Gravitational Perturbations | p. 287 |
| Direct radiation pressure | p. 288 |
| Thermal emission | p. 294 |
| Indirect radiation pressure | p. 299 |
| Drag | p. 302 |
| Active spacecraft effects | p. 303 |
| Case study: asteroid orbiter | p. 306 |
| Multi-Arc Strategy | p. 311 |
| Local-global decomposition | p. 311 |
| Case study: satellite laser ranging | p. 314 |
| Perturbation model | p. 315 |
| Local geodesy | p. 317 |
| Symmetries and rank deficiencies | p. 319 |
| Satellite Gravimetry | p. 323 |
| On-board instrumentation | p. 324 |
| Accelerometer missions | p. 331 |
| Gradiometer missions | p. 333 |
| Resonant decomposition | p. 338 |
| Polar gaps | p. 339 |
| Satellite-to-satellite tracking | p. 345 |
| Orbiters around Other Planets | p. 349 |
| Science goals for an orbiter around Mercury | p. 349 |
| Interplanetary tracking | p. 351 |
| The gravimetry experiment | p. 356 |
| The rotation experiment | p. 360 |
| The relativity experiment | p. 364 |
| Global data processing | p. 367 |
| References | p. 371 |
| Index | p. 379 |
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