| Description |
1 online resource (894 pages) |
| Contents |
Relativistic Celestial Mechanics of the Solar System; Contents; Preface; Symbols and Abbreviations; References; 1 Newtonian Celestial Mechanics; 1.1 Prolegomena -- Classical Mechanics in a Nutshell; 1.1.1 Kepler's Laws; 1.1.2 Fundamental Laws of Motion -- from Descartes, Newton, and Leibniz to Poincaré and Einstein; 1.1.3 Newton's Law of Gravity; 1.2 The N-body Problem; 1.2.1 Gravitational Potential; 1.2.2 Gravitational Multipoles; 1.2.3 Equations of Motion; 1.2.4 The Integrals of Motion; 1.2.5 The Equations of Relative Motion with Perturbing Potential; 1.2.6 The Tidal Potential and Force |
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1.3 The Reduced Two-Body Problem1.3.1 Integrals of Motion and Kepler's Second Law; 1.3.2 The Equations of Motion and Kepler's First Law; 1.3.3 The Mean and Eccentric Anomalies -- Kepler's Third Law; 1.3.4 The Laplace-Runge-Lenz Vector; 1.3.5 Parameterizations of the Reduced Two-Body Problem; 1.3.6 The Freedom of Choice of the Anomaly; 1.4 A Perturbed Two-Body Problem; 1.4.1 Prefatory Notes; 1.4.2 Variation of Constants -- Osculating Conics; 1.4.3 The Lagrange and Poisson Brackets; 1.4.4 Equations of Perturbed Motion for Osculating Elements |
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1.4.5 Equations for Osculating Elements in the Euler-Gauss Form1.4.6 The Planetary Equations in the Form of Lagrange; 1.4.7 The Planetary Equations in the Form of Delaunay; 1.4.8 Marking a Minefield; 1.5 Re-examining the Obvious; 1.5.1 Why Did Lagrange Impose His Constraint? Can It Be Relaxed?; 1.5.2 Example -- the Gauge Freedom of a Harmonic Oscillator; 1.5.3 Relaxing the Lagrange Constraint in Celestial Mechanics; 1.5.4 The Gauge-Invariant Perturbation Equation in Terms of the Disturbing Force; 1.5.5 The Gauge-Invariant Perturbation Equation in Terms of the Disturbing Function |
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1.5.6 The Delaunay Equations without the Lagrange Constraint1.5.7 Contact Orbital Elements; 1.5.8 Osculation and Nonosculation in Rotational Dynamics; 1.6 Epilogue to the Chapter; References; 2 Introduction to Special Relativity; 2.1 From Newtonian Mechanics to Special Relativity; 2.1.1 The Newtonian Spacetime; 2.1.2 The Newtonian Transformations; 2.1.3 The Galilean Transformations; 2.1.4 Form-Invariance of the Newtonian Equations of Motion; 2.1.5 The Maxwell Equations and the Lorentz Transformations; 2.2 Building the Special Relativity |
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2.2.1 Basic Requirements to a New Theory of Space and Time2.2.2 On the "Single-Postulate" Approach to Special Relativity; 2.2.3 The Difference in the Interpretation of Special Relativity by Einstein, Poincaré and Lorentz; 2.2.4 From Einstein's Postulates to Minkowski's Spacetime of Events; 2.3 Minkowski Spacetime as a Pseudo-Euclidean Vector Space; 2.3.1 Axioms of Vector Space; 2.3.2 Dot-Products and Norms; 2.3.3 The Vector Basis; 2.3.4 The Metric Tensor; 2.3.5 The Lorentz Group; 2.3.6 The Poincaré Group; 2.4 Tensor Algebra; 2.4.1 Warming up in Three Dimensions -- Scalars, Vectors, What Next? |
| Summary |
This 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 re |
| Notes |
2.4.2 Covectors |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Celestial mechanics.
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Relativity (Physics)
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Celestial mechanics
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Relativity (Physics)
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| Form |
Electronic book
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| Author |
Efroimsky, Michael
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Kaplan, George
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| ISBN |
9783527634583 |
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3527634584 |
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3527408568 |
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9783527408566 |
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3527634576 |
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9783527634576 |
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1283370530 |
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9781283370530 |
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9786613370532 |
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6613370533 |
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3527634568 |
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9783527634569 |
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