## Relativistic Celestial Mechanics of the Solar SystemThis authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping. |

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### Contents

Contents | 56 |

Introduction to Special Relativity | 81 |

i | 117 |

Contents | 189 |

i | 199 |

i | 255 |

i | 257 |

i | 371 |

Relativistic Astrometry | 519 |

i | 645 |

Relativistic Geodesy | 671 |

Relativity in IAU Resolutions | 715 |

i | 804 |

Appendix A Fundamental Solution of the Laplace Equation | 813 |

Appendix B Astronomical Constants | 819 |

Contents | 501 |

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### Common terms and phrases

acceleration ćther affine connection anomaly arbitrary astronomical body Cartesian coordinates Celestial Mechanics center of mass Chap Christoffel symbols components conic constant covariant derivative covector curve defined Delaunay denoted density depend differential dot-product Efroimsky Einstein electromagnetic energy-momentum tensor equations of motion Euclidean force four-velocity frame S0 Galilean geometric gravitational field gravitational potential inertial frame inertial reference frame instantaneous integral introduced Introduction to Special Keplerian Kopeikin Lagrange le-tex linear Lorentz transformations mathematical matrix metric tensor Minkowski metric Minkowski spacetime momentum moving multipole moments Newton Newtonian Celestial Mechanics observer orbital elements orthogonal osculating parameterized parameters partial derivatives particle perturbed physical plane Poincaré post-Newtonian principle relativistic respect rotation scalar field Section Solar System solution spatial Special Relativity tangent theory timelike tion two-body problem unit vector variables vector field vector space velocity worldline ηα