Preface.Symbols and Abbreviations.
References.
1 Newtonian Celestial Mechanics.
1.1 Prolegomena – Classical Mechanics in a Nutshell.
1.2 The N-body Problem.
1.3 The Reduced Two-Body Problem.
1.4 A Perturbed Two-Body Problem.
1.5 Re-examining the Obvious.
1.6 Epilogue to the Chapter.
References.
2 Introduction to Special Relativity.
2.1 From Newtonian Mechanics to Special Relativity.
2.2 Building the Special Relativity.
2.3 Minkowski Spacetime as a Pseudo-Euclidean Vector Space.
2.4 Tensor Algebra.
2.5 Kinematics.
2.6 Accelerated Frames.
2.7 Relativistic Dynamics.
2.8 Energy-Momentum Tensor.
3 General Relativity.
3.1 The Principle of Equivalence.
3.2 The Principle of Covariance.
3.3 A Differentiable Manifold.
3.4 Affine Connection on Manifold.
3.5 The Levi-Civita Connection.
3.6 Lie Derivative.
3.7 The Riemann Tensor and Curvature of Manifold.
3.8 Mathematical and Physical Foundations of General Relativity.
3.9 Variational Principle in General Relativity.
3.10 GravitationalWaves.
4 Relativistic Reference Frames.
4.1 Historical Background.
4.2 Isolated Astronomical Systems.
4.3 Global Astronomical Coordinates.
4.4 Gravitational Multipoles in the Global Coordinates.
4.5 Local Astronomical Coordinates.
5 Post-Newtonian Coordinate Transformations.
5.1 The Transformation from the Local to Global Coordinates.
5.2 Matching Transformation of the Metric Tensor and Scalar Field.
6 Relativistic Celestial Mechanics.
6.1 Post-Newtonian Equations of Orbital Motion.
6.2 Rotational Equations of Motion of Extended Bodies.
6.3 Motion of Spherically-Symmetric and Rigidly-Rotating Bodies.
6.4 Post-Newtonian Two-Body Problem.
7 Relativistic Astrometry.
7.1 Introduction.
7.2 Gravitational Liénard–Wiechert Potentials.
7.3 Mathematical Technique for Integrating Equations of Propagation of Photons.
7.4 Gravitational Perturbations of Photon’s Trajectory.
7.5 Observable Relativistic Effects.
7.6 Applications to Relativistic Astrophysics and Astrometry.
7.7 Relativistic Astrometry in the Solar System.
7.8 Doppler Tracking of Interplanetary Spacecrafts.
7.9 Astrometric Experiments with the Solar System Planets.
8 Relativistic Geodesy.
8.1 Introduction.
8.2 Basic Equations.
8.3 Geocentric Reference Frame.
8.4 Topocentric Reference Frame.
8.5 Relationship Between the Geocentric and Topocentric Frames.
8.6 Post-Newtonian Gravimetry.
8.7 Post-Newtonian Gradiometry.
8.8 Relativistic Geoid.
9 Relativity in IAU Resolutions.
9.1 Introduction.
9.2 Relativity.
9.3 Time Scales.
9.4 The Fundamental Celestial Reference System.
9.5 Ephemerides of the Major Solar System Bodies.
9.6 Precession and Nutation.
9.7 Modeling the Earth’s Rotation.
Appendix A Fundamental Solution of the Laplace Equation.
References.
Appendix B Astronomical Constants.
References.
Appendix C Text of IAU Resolutions.
C.1 Text of IAU Resolutions of 1997 Adopted at the XXIIIrd General Assembly, Kyoto.
C.2 Text of IAU Resolutions of 2000 Adopted at the XXIVth General Assembly, Manchester.
C.3 Text of IAU Resolutions of 2006 Adopted at the XXVIth General Assembly, Prague.
C.4 Text of IAU Resolutions of 2009 Adopted at the XXVIIth General Assembly, Rio de Janeiro.
Index.