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. |
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 anomaly applied arbitrary assume basis body calculation called Celestial Mechanics Chap components condition conic connection consider constant coordinates corresponding covariant covector curve defined definition denoted depend derivative differential direction distance effect Einstein elements energy equal equations equations of motion example existence expression field Figure force function fundamental gauge given gravitational indices inertial frame integral interval introduced invariant Lagrange le-tex light linear manifold mass mathematical matrix matter means measured metric tensor Minkowski spacetime momentum motion moving Newtonian observer obtains operator orbital origin parameters partial derivatives particle perturbed physical plane position potential principle problem proper reduced reference frame relativistic respect rest rotation scalar side Solar System solution space spatial Special Relativity speed taking theory tion transformation unit variables variation vector velocity