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E-raamat: Relativistic Celestial Mechanics of the Solar System

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(U.S. Naval Observatory, Washington, USA), (U.S. Naval Observatory, Washington, USA), (University of Missouri, Columbia, USA)
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  • Ilmumisaeg: 24-Jun-2011
  • Kirjastus: Blackwell Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783527634583
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Relativistic Celestial Mechanics of the Solar SystemSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 24-Jun-2011
  • Kirjastus: Blackwell Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783527634583
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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 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.

Arvustused

The book is intended for graduate students and researchers working in gravitational physics applied in modern astronomy.  (Zentralblatt MATH, 1 December 2012)

Preface xvii
Symbols and Abbreviations xxiii
References xxxi
1 Newtonian Celestial Mechanics
1(80)
1.1 Prolegomena - Classical Mechanics in a Nutshell
1(9)
1.1.1 Kepler's Laws
1(1)
1.1.2 Fundamental Laws of Motion - from Descartes, Newton, and Leibniz to Poincare and Einstein
2(5)
1.1.3 Newton's Law of Gravity
7(3)
1.2 The N-body Problem
10(14)
1.2.1 Gravitational Potential
11(2)
1.2.2 Gravitational Multipoles
13(2)
1.2.3 Equations of Motion
15(4)
1.2.4 The Integrals of Motion
19(2)
1.2.5 The Equations of Relative Motion with Perturbing Potential
21(1)
1.2.6 The Tidal Potential and Force
22(2)
1.3 The Reduced Two-Body Problem
24(21)
1.3.1 Integrals of Motion and Kepler's Second Law
24(3)
1.3.2 The Equations of Motion and Kepler's First Law
27(4)
1.3.3 The Mean and Eccentric Anomalies - Kepler's Third Law
31(4)
1.3.4 The Laplace-Runge-Lenz Vector
35(2)
1.3.5 Parameterizations of the Reduced Two-Body Problem
37(1)
1.3.5.1 A Keplerian Orbit in the Euclidean Space
37(2)
1.3.5.2 A Keplerian Orbit in the Projective Space
39(4)
1.3.6 The Freedom of Choice of the Anomaly
43(2)
1.4 A Perturbed Two-Body Problem
45(13)
1.4.1 Prefatory Notes
45(2)
1.4.2 Variation of Constants - Osculating Conics
47(2)
1.4.3 The Lagrange and Poisson Brackets
49(2)
1.4.4 Equations of Perturbed Motion for Osculating Elements
51(2)
1.4.5 Equations for Osculating Elements in the Euler-Gauss Form
53(2)
1.4.6 The Planetary Equations in the Form of Lagrange
55(1)
1.4.7 The Planetary Equations in the Form of Delaunay
56(1)
1.4.8 Marking a Minefield
57(1)
1.5 Re-examining the Obvious
58(18)
1.5.1 Why Did Lagrange Impose His Constraint? Can It Be Relaxed?
58(1)
1.5.2 Example - the Gauge Freedom of a Harmonic Oscillator
59(3)
1.5.3 Relaxing the Lagrange Constraint in Celestial Mechanics
62(1)
1.5.3.1 The Gauge Freedom
62(2)
1.5.3.2 The Gauge Transformations
64(2)
1.5.4 The Gauge-Invariant Perturbation Equation in Terms of the Disturbing Force
66(1)
1.5.5 The Gauge-Invariant Perturbation Equation in Terms of the Disturbing Function
67(2)
1.5.6 The Delaunay Equations without the Lagrange Constraint
69(3)
1.5.7 Contact Orbital Elements
72(3)
1.5.8 Osculation and Nonosculation in Rotational Dynamics
75(1)
1.6 Epilogue to the
Chapter
76(5)
References
77(4)
2 Introduction to Special Relativity
81(118)
2.1 From Newtonian Mechanics to Special Relativity
81(13)
2.1.1 The Newtonian Spacetime
81(3)
2.1.2 The Newtonian Transformations
84(1)
2.1.3 The Galilean Transformations
85(3)
2.1.4 Form-Invariance of the Newtonian Equations of Motion
88(1)
2.1.5 The Maxwell Equations and the Lorentz Transformations
89(5)
2.2 Building the Special Relativity
94(9)
2.2.1 Basic Requirements to a New Theory of Space and Time
94(2)
2.2.2 On the "Single-Postulate" Approach to Special Relativity
96(1)
2.2.3 The Difference in the Interpretation of Special Relativity by Einstein, Poincare and Lorentz
97(2)
2.2.4 From Einstein's Postulates to Minkowski's Spacetime of Events
99(1)
2.2.4.1 Dimension of the Minkowski Spacetime
99(1)
2.2.4.2 Homogeneity and Isotropy of the Minkowski Spacetime
99(1)
2.2.4.3 Coordinates and Reference Frames
100(1)
2.2.4.4 Spacetime Interval
100(1)
2.2.4.5 The Null Cone
101(1)
2.2.4.6 The Proper Time
102(1)
2.2.4.7 The Proper Distance
103(1)
2.2.4.8 Causal Relationship
103(1)
2.3 Minkowski Spacetime as a Pseudo-Euclidean Vector Space
103(17)
2.3.1 Axioms of Vector Space
103(2)
2.3.2 Dot-Products and Norms
105(1)
2.3.2.1 Euclidean Space
106(1)
2.3.2.2 Pseudo-Euclidean Space
107(1)
2.3.3 The Vector Basis
108(3)
2.3.4 The Metric Tensor
111(2)
2.3.5 The Lorentz Group
113(1)
2.3.5.1 General Properties
113(2)
2.3.5.2 Parametrization of the Lorentz Group
115(3)
2.3.6 The Poincare Group
118(2)
2.4 Tensor Algebra
120(14)
2.4.1 Warming up in Three Dimensions - Scalars, Vectors, What Next?
120(3)
2.4.2 Covectors
123(1)
2.4.2.1 Axioms of Covector Space
123(2)
2.4.2.2 The Basis in the Covector Space
125(1)
2.4.2.3 Duality of Covectors and Vectors
126(1)
2.4.2.4 The Transformation Law of Covectors
127(1)
2.4.3 Bilinear Forms
128(1)
2.4.4 Tensors
129(1)
2.4.4.1 Definition of Tensors as Linear Mappings
129(1)
2.4.4.2 Transformations of Tensors Under a Change of the Basis
130(1)
2.4.4.3 Rising and Lowering Indices of Tensors
131(1)
2.4.4.4 Contraction of Tensor Indices
132(1)
2.4.4.5 Tensor Equations
133(1)
2.5 Kinematics
134(18)
2.5.1 The Proper Frame of Observer
134(2)
2.5.2 Four-Velocity and Four-Acceleration
136(2)
2.5.3 Transformation of Velocity
138(2)
2.5.4 Transformation of Acceleration
140(2)
2.5.5 Dilation of Time
142(1)
2.5.6 Simultaneity and Synchronization of Clocks
143(3)
2.5.7 Contraction of Length
146(2)
2.5.8 Aberration of Light
148(2)
2.5.9 The Doppler Effect
150(2)
2.6 Accelerated Frames
152(14)
2.6.1 Worldline of a Uniformly-Accelerated Observer
155(2)
2.6.2 A Tetrad Comoving with a Uniformly-Accelerated Observer
157(1)
2.6.3 The Rindler Coordinates
158(4)
2.6.4 The Radar Coordinates
162(4)
2.7 Relativistic Dynamics
166(18)
2.7.1 Linear Momentum and Energy
166(3)
2.7.2 Relativistic Force and Equations of Motion
169(3)
2.7.3 The Relativistic Transformation of the Minkowski Force
172(2)
2.7.4 The Lorentz Force and Transformation of Electromagnetic Field
174(2)
2.7.5 The Aberration of the Minkowski Force
176(2)
2.7.6 The Center-of-Momentum Frame
178(4)
2.7.7 The Center-of-Mass Frame
182(2)
2.8 Energy-Momentum Tensor
184(15)
2.8.1 Noninteracting Particles
184(4)
2.8.2 Perfect Fluid
188(1)
2.8.3 Nonperfect Fluid and Solids
189(1)
2.8.4 Electromagnetic Field
190(1)
2.8.5 Scalar Field
191(3)
References
194(5)
3 General Relativity
199(172)
3.1 The Principle of Equivalence
199(8)
3.1.1 The Inertial and Gravitational Masses
199(2)
3.1.2 The Weak Equivalence Principle
201(1)
3.1.3 The Einstein Equivalence Principle
202(1)
3.1.4 The Strong Equivalence Principle
203(1)
3.1.5 The Mach Principle
204(3)
3.2 The Principle of Covariance
207(10)
3.2.1 Lorentz Covariance in Special Relativity
208(1)
3.2.2 Lorentz Covariance in Arbitrary Coordinates
209(2)
3.2.2.1 Covariant Derivative and the Christoffel Symbols in Special Relativity
211(1)
3.2.2.2 Relationship Between the Christoffel Symbols and the Metric Tensor
212(1)
3.2.2.3 Covariant Derivative of the Metric Tensor
213(1)
3.2.3 From Lorentz to General Covariance
214(1)
3.2.4 Two Approaches to Gravitation in General Relativity
215(2)
3.3 A Differentiable Manifold
217(12)
3.3.1 Topology of Manifold
217(1)
3.3.2 Local Charts and Atlas
218(1)
3.3.3 Functions
218(1)
3.3.4 Tangent Vectors
219(1)
3.3.5 Tangent Space
220(2)
3.3.6 Covectors and Cotangent Space
222(2)
3.3.7 Tensors
224(1)
3.3.8 The Metric Tensor
224(1)
3.3.8.1 Operation of Rising and Lowering Indices
225(1)
3.3.8.2 Magnitude of a Vector and an Angle Between Vectors
226(1)
3.3.8.3 The Riemann Normal Coordinates
226(3)
3.4 Affine Connection on Manifold
229(9)
3.4.1 Axiomatic Definition of the Affine Connection
230(2)
3.4.2 Components of the Connection
232(1)
3.4.3 Covariant Derivative of Tensors
233(1)
3.4.4 Parallel Transport of Tensors
234(1)
3.4.4.1 Equation of the Parallel Transport
234(1)
3.4.4.2 Geodesics
235(2)
3.4.5 Transformation Law for Connection Components
237(1)
3.5 The Levi-Civita Connection
238(7)
3.5.1 Commutator of Two Vector Fields
238(2)
3.5.2 Torsion Tensor
240(2)
3.5.3 Nonmetricity Tensor
242(1)
3.5.4 Linking the Connection with the Metric Structure
243(2)
3.6 Lie Derivative
245(8)
3.6.1 A Vector Flow
245(1)
3.6.2 The Directional Derivative of a Function
246(1)
3.6.3 Geometric Interpretation of the Commutator of Two Vector Fields
247(2)
3.6.4 Definition of the Lie Derivative
249(2)
3.6.5 Lie Transport of Tensors
251(2)
3.7 The Riemann Tensor and Curvature of Manifold
253(13)
3.7.1 Noncommutation of Covariant Derivatives
253(2)
3.7.2 The Dependence of the Parallel Transport on the Path
255(1)
3.7.3 The Holonomy of a Connection
256(2)
3.7.4 The Riemann Tensor as a Measure of Flatness
258(3)
3.7.5 The Jacobi Equation and the Geodesies Deviation
261(1)
3.7.6 Properties of the Riemann Tensor
262(1)
3.7.6.1 Algebraic Symmetries
262(2)
3.7.6.2 The Weyl Tensor and the Ricci Decomposition
264(1)
3.7.6.3 The Bianchi Identities
265(1)
3.8 Mathematical and Physical Foundations of General Relativity
266(34)
3.8.1 General Covariance on Curved Manifolds
267(2)
3.8.2 General Relativity Principle Links Gravity to Geometry
269(4)
3.8.3 The Equations of Motion of Test Particles
273(4)
3.8.4 The Correspondence Principle - the Interaction of Matter and Geometry
277(1)
3.8.4.1 The Newtonian Gravitational Potential and the Metric Tensor
277(2)
3.8.4.2 The Newtonian Gravity and the Einstein Field Equations
279(3)
3.8.5 The Principle of the Gauge Invariance
282(4)
3.8.6 Principles of Measurement of Gravitational Field
286(1)
3.8.6.1 Clocks and Rulers
286(3)
3.8.6.2 Time Measurements
289(1)
3.8.6.3 Space Measurements
290(4)
3.8.6.4 Are Coordinates Measurable?
294(3)
3.8.7 Experimental Testing of General Relativity
297(3)
3.9 Variational Principle in General Relativity
300(39)
3.9.1 The Action Functional
300(3)
3.9.2 Variational Equations
303(1)
3.9.2.1 Variational Equations for Matter
303(4)
3.9.2.2 Variational Equations for Gravitational Field
307(1)
3.9.3 The Hilbert Action and the Einstein Equations
307(1)
3.9.3.1 The Hilbert Lagrangian
307(2)
3.9.3.2 The Einstein Lagrangian
309(1)
3.9.3.3 The Einstein Tensor
310(3)
3.9.3.4 The Generalizations of the Hilbert Lagrangian
313(3)
3.9.4 The Noether Theorem and Conserved Currents
316(1)
3.9.4.1 The Anatomy of the Infinitesimal Variation
316(3)
3.9.4.2 Examples of the Gauge Transformations
319(1)
3.9.4.3 Proof of the Noether Theorem
320(2)
3.9.5 The Metrical Energy-Momentum Tensor
322(1)
3.9.5.1 Hardcore of the Metrical Energy-Momentum Tensor
322(2)
3.9.5.2 Gauge Invariance of the Metrical Energy Momentum Tensor
324(1)
3.9.5.3 Electromagnetic Energy-Momentum Tensor
325(1)
3.9.5.4 Energy-Momentum Tensor of a Perfect Fluid
326(3)
3.9.5.5 Energy-Momentum Tensor of a Scalar Field
329(1)
3.9.6 The Canonical Energy-Momentum Tensor
329(1)
3.9.6.1 Definition
329(2)
3.9.6.2 Relationship to the Metrical Energy-Momentum Tensor
331(1)
3.9.6.3 Killing Vectors and the Global Laws of Conservation
332(1)
3.9.6.4 The Canonical Energy-Momentum Tensor for Electromagnetic Field
333(1)
3.9.6.5 The Canonical Energy-Momentum Tensor for Perfect Fluid
334(2)
3.9.7 Pseudotensor of Landau and Lifshitz
336(3)
3.10 Gravitational Waves
339(32)
3.10.1 The Post-Minkowskian Approximations
340(4)
3.10.2 Multipolar Expansion of a Retarded Potential
344(1)
3.10.3 Multipolar Expansion of Gravitational Field
345(5)
3.10.4 Gravitational Field in Transverse-Traceless Gauge
350(2)
3.10.5 Gravitational Radiation and Detection of Gravitational Waves
352(6)
References
358(13)
4 Relativistic Reference Frames
371(58)
4.1 Historical Background
371(7)
4.2 Isolated Astronomical Systems
378(13)
4.2.1 Field Equations in the Scalar-Tensor Theory of Gravity
378(2)
4.2.2 The Energy-Momentum Tensor
380(2)
4.2.3 Basic Principles of the Post-Newtonian Approximations
382(5)
4.2.4 Gauge Conditions and Residual Gauge Freedom
387(2)
4.2.5 The Reduced Field Equations
389(2)
4.3 Global Astronomical Coordinates
391(5)
4.3.1 Dynamic and Kinematic Properties of the Global Coordinates
391(4)
4.3.2 The Metric Tensor and Scalar Field in the Global Coordinates
395(1)
4.4 Gravitational Multipoles in the Global Coordinates
396(10)
4.4.1 General Description of Multipole Moments
396(3)
4.4.2 Active Multipole Moments
399(2)
4.4.3 Scalar Multipole Moments
401(1)
4.4.4 Conformal Multipole Moments
402(2)
4.4.5 Post-Newtonian Conservation Laws
404(2)
4.5 Local Astronomical Coordinates
406(23)
4.5.1 Dynamic and Kinematic Properties of the Local Coordinates
406(3)
4.5.2 The Metric Tensor and Scalar Field in the Local Coordinates
409(1)
4.5.2.1 The Scalar Field: Internal and External Solutions
410(1)
4.5.2.2 The Metric Tensor: Internal Solution
411(1)
4.5.2.3 The Metric Tensor: External Solution
412(7)
4.5.2.4 The Metric Tensor: The Coupling Terms
419(1)
4.5.3 Multipolar Expansion of Gravitational Field in the Local Coordinates
420(3)
References
423(6)
5 Post-Newtonian Coordinate Transformations
429(34)
5.1 The Transformation from the Local to Global Coordinates
429(7)
5.1.1 Preliminaries
429(2)
5.1.2 General Structure of the Coordinate Transformation
431(3)
5.1.3 Transformation of the Coordinate Basis
434(2)
5.2 Matching Transformation of the Metric Tensor and Scalar Field
436(27)
5.2.1 Historical Background
436(3)
5.2.2 Method of the Matched Asymptotic Expansions in the PPN Formalism
439(3)
5.2.3 Transformation of Gravitational Potentials from the Local to Global Coordinates
442(1)
5.2.3.1 Transformation of the Internal Potentials
442(4)
5.2.3.2 Transformation of the External Potentials
446(1)
5.2.4 Matching for the Scalar Field
447(1)
5.2.5 Matching for the Metric Tensor
447(1)
5.2.5.1 Matching g00 (t, x) and gαβ(u, w) in the Newtonian Approximation
447(3)
5.2.5.2 Matching gij (t, x) and gαβ(u, w)
450(1)
5.2.5.3 Matching g0i (t, x) and gαβ(u, w)
451(2)
5.2.5.4 Matching g00 (t, x) and gαβ(u, w) in the Post-Newtonian Approximation
453(4)
5.2.6 Final Form of the PPN Coordinate Transformation
457(1)
References
458(5)
6 Relativistic Celestial Mechanics
463(56)
6.1 Post-Newtonian Equations of Orbital Motion
463(16)
6.1.1 Introduction
463(4)
6.1.2 Macroscopic Post-Newtonian Equations of Motion
467(1)
6.1.3 Mass and the Linear Momentum of a Self-Gravitating Body
468(5)
6.1.4 Translational Equation of Motion in the Local Coordinates
473(4)
6.1.5 Orbital Equation of Motion in the Global Coordinates
477(2)
6.2 Rotational Equations of Motion of Extended Bodies
479(4)
6.2.1 The Angular Momentum of a Self-Gravitating Body
479(1)
6.2.2 Equations of Rotational Motion in the Local Coordinates
480(3)
6.3 Motion of Spherically-Symmetric and Rigidly-Rotating Bodies
483(18)
6.3.1 Definition of a Spherically-Symmetric and Rigidly-Rotating Body
483(4)
6.3.2 Coordinate Transformation of the Multipole Moments
487(3)
6.3.3 Gravitational Multipoles in the Global Coordinates
490(2)
6.3.4 Orbital Post-Newtonian Equations of Motion
492(8)
6.3.5 Rotational Equations of Motion
500(1)
6.4 Post-Newtonian Two-Body Problem
501(18)
6.4.1 Introduction
501(2)
6.4.2 Perturbing Post-Newtonian Force
503(2)
6.4.3 Orbital Solution in the Two-Body Problem
505(1)
6.4.3.1 Osculating Elements Parametrization
505(3)
6.4.3.2 The Damour-Deruelle Parametrization
508(3)
6.4.3.3 The Epstein-Haugan Parametrization
511(1)
6.4.3.4 The Brumberg Parametrization
512(1)
References
513(6)
7 Relativistic Astrometry
519(152)
7.1 Introduction
519(5)
7.2 Gravitational Lienard-Wiechert Potentials
524(5)
7.3 Mathematical Technique for Integrating Equations of Propagation of Photons
529(9)
7.4 Gravitational Perturbations of Photon's Trajectory
538(3)
7.5 Observable Relativistic Effects
541(16)
7.5.1 Gravitational Time Delay
541(6)
7.5.2 Gravitational Bending and the Deflection Angle of Light
547(5)
7.5.3 Gravitational Shift of Electromagnetic-Wave Frequency
552(5)
7.6 Applications to Relativistic Astrophysics and Astrometry
557(27)
7.6.1 Gravitational Time Delay in Binary Pulsars
557(1)
7.6.1.1 Pulsars - Rotating Radio Beacons
557(3)
7.6.1.2 The Approximation Scheme
560(5)
7.6.1.3 Post-Newtonian Versus Post-Minkowski Calculations of Time Delay in Binary Systems
565(2)
7.6.1.4 Time Delay in the Parameterized Post-Keplerian Formalism
567(5)
7.6.2 Moving Gravitational Lenses
572(1)
7.6.2.1 Gravitational Lens Equation
572(8)
7.6.2.2 Gravitational Shift of Frequency by Moving Bodies
580(4)
7.7 Relativistic Astrometry in the Solar System
584(20)
7.7.1 Near-Zone and Far-Zone Astrometry
584(6)
7.7.2 Pulsar Timing
590(3)
7.7.3 Very Long Baseline Interferometry
593(7)
7.7.4 Relativistic Space Astrometry
600(4)
7.8 Doppler Tracking of Interplanetary Spacecrafts
604(15)
7.8.1 Definition and Calculation of the Doppler Shift
607(2)
7.8.2 The Null Cone Partial Derivatives
609(2)
7.8.3 Doppler Effect in Spacecraft-Planetary Conjunctions
611(2)
7.8.4 The Doppler Effect Revisited
613(4)
7.8.5 The Explicit Doppler Tracking Formula
617(2)
7.9 Astrometric Experiments with the Solar System Planets
619(52)
7.9.1 Motivations
619(5)
7.9.2 The Unperturbed Light-Ray Trajectory
624(2)
7.9.3 The Gravitational Field
626(1)
7.9.3.1 The Field Equations
626(2)
7.9.3.2 The Planet's Gravitational Multipoles
628(3)
7.9.4 The light-Ray Gravitational Perturbations
631(1)
7.9.4.1 The Light-Ray Propagation Equation
631(1)
7.9.4.2 The Null Cone Integration Technique
632(4)
7.9.4.3 The Speed of Gravity, Causality, and the Principle of Equivalence
636(4)
7.9.5 Light-Ray Deflection Patterns
640(1)
7.9.5.1 The Deflection Angle
640(2)
7.9.5.2 Snapshot Patterns
642(4)
7.9.5.3 Dynamic Patterns of the Light Deflection
646(4)
7.9.6 Testing Relativity and Reference Frames
650(2)
7.9.6.1 The Monopolar Deflection
652(1)
7.9.6.2 The Dipolar Deflection
653(2)
7.9.6.3 The Quadrupolar Deflection
655(1)
References
656(15)
8 Relativistic Geodesy
671(44)
8.1 Introduction
671(5)
8.2 Basic Equations
676(5)
8.3 Geocentric Reference Frame
681(3)
8.4 Topocentric Reference Frame
684(3)
8.5 Relationship Between the Geocentric and Topocentric Frames
687(2)
8.6 Post-Newtonian Gravimetry
689(5)
8.7 Post-Newtonian Gradiometry
694(9)
8.8 Relativistic Geoid
703(12)
8.8.1 Definition of a Geoid in the Post-Newtonian Gravity
703(1)
8.8.2 Post-Newtonian u-Geoid
704(1)
8.8.3 Post-Newtonian a-Geoid
705(1)
8.8.4 Post-Newtonian Level Surface
706(1)
8.8.5 Post-Newtonian Clairaut's Equation
707(2)
References
709(6)
9 Relativity in IAU Resolutions
715(98)
9.1 Introduction
715(5)
9.1.1 Overview of the Resolutions
716(2)
9.1.2 About this
Chapter
718(1)
9.1.3 Other Resources
719(1)
9.2 Relativity
720(8)
9.2.1 Background
720(2)
9.2.2 The BCRS and the GCRS
722(2)
9.2.3 Computing Observables
724(3)
9.2.4 Other Considerations
727(1)
9.3 Time Scales
728(15)
9.3.1 Different Flavors of Time
729(1)
9.3.2 Time Scales Based on the SI Second
730(3)
9.3.3 Time Scales Based on the Rotation of the Earth
733(2)
9.3.4 Coordinated Universal Time (UTC)
735(1)
9.3.5 To Leap or not to Leap
735(2)
9.3.6 Formulas
737(1)
9.3.6.1 Formulas for Time Scales Based on the SI Second
737(3)
9.3.6.2 Formulas for Time Scales Based on the Rotation of the Earth
740(3)
9.4 The Fundamental Celestial Reference System
743(15)
9.4.1 The ICRS, ICRF, and the HCRF
744(2)
9.4.2 Background: Reference Systems and Reference Frames
746(2)
9.4.3 The Effect of Catalogue Errors on Reference Frames
748(2)
9.4.4 Late Twentieth Century Developments
750(2)
9.4.5 ICRS Implementation
752(1)
9.4.5.1 The Defining Extragalactic Frame
752(1)
9.4.5.2 The Frame at Optical Wavelengths
753(1)
9.4.6 Standard Algorithms
753(1)
9.4.7 Relationship to Other Systems
754(1)
9.4.8 Data in the ICRS
755(2)
9.4.9 Formulas
757(1)
9.5 Ephemerides of the Major Solar System Bodies
758(5)
9.5.1 The JPL Ephemerides
759(1)
9.5.2 DE405
760(1)
9.5.3 Recent Ephemeris Development
761(1)
9.5.4 Sizes, Shapes, and Rotational Data
762(1)
9.6 Precession and Nutation
763(23)
9.6.1 Aspects of Earth Rotation
764(1)
9.6.2 Which Pole?
765(3)
9.6.3 The New Models
768(3)
9.6.4 Formulas
771(3)
9.6.5 Formulas for Precession
774(4)
9.6.6 Formulas for Nutation
778(3)
9.6.7 Alternative Combined Transformation
781(1)
9.6.8 Observational Corrections to Precession-Nutation
782(1)
9.6.9 Sample Nutation Terms
783(3)
9.7 Modeling the Earth's Rotation
786(27)
9.7.1 A Messy Business
786(2)
9.7.2 Nonrotating Origins
788(2)
9.7.3 The Path of the CIO on the Sky
790(1)
9.7.4 Transforming Vectors Between Reference Systems
791(3)
9.7.5 Formulas
794(1)
9.7.5.1 Location of Cardinal Points
795(1)
9.7.5.2 CIO Location Relative to the Equinox
795(2)
9.7.5.3 CIO Location from Numerical Integration
797(1)
9.7.5.4 CIO Location from the Arc-Difference s
798(1)
9.7.5.5 Geodetic Position Vectors and Polar Motion
799(2)
9.7.5.6 Complete Terrestrial to Celestial Transformation
801(1)
9.7.5.7 Hour Angle
802(3)
References
805(8)
Appendix A Fundamental Solution of the Laplace Equation
813(6)
References
817(2)
Appendix B Astronomical Constants
819(6)
References
823(2)
Appendix C Text of IAU Resolutions
825(26)
C.1 Text of IAU Resolutions of 1997 Adopted at the XXIIIrd General Assembly, Kyoto
825(4)
C.2 Text of IAU Resolutions of 2000 Adopted at the XXIVth General Assembly, Manchester
829(12)
C.3 Text of IAU Resolutions of 2006 Adopted at the XXVIth General Assembly, Prague
841(6)
C.4 Text of IAU Resolutions of 2009 Adopted at the XXVIIth General Assembly, Rio de Janeiro
847(4)
Index 851
Sergei Kopeikin studied general relativity at the Department of Astronomy of Moscow State University, Russia. He obtained his PhD in relativistic astrophysics from Moscow State University in 1986, where he was then employed as an associate professor. In 1993, he moved to Japan to teach astronomy at Hitotsubashi University, Tokyo. He was an adjunct staff member and thereafter visiting professor at the National Astronomical Observatory of Japan. In 1997, Professor Kopeikin moved to Germany and worked at the Institute of Theoretical Physics of the Friedrich Schiller University, Jena. Three years later he accepted the position of a professor of physics at the University of Missouri, Columbia, USA.

Michael Efroimsky is a research scientist at the United States Naval Observatory. His research focuses on celestial mechanics and solar system studies. He received his Ph.D. from Oxford in 1995 and he subsequently worked at Tufts, Harvard, and the University of Minnesota. An experienced teacher, having taught numerous courses to Harvard and Tufts students, Dr. Efroimsky is in a unique position to convey this complicated topic to interested readers."

George Kaplan was a staff astronomer at the U.S. Naval Observatory in Washington, D.C., from 1971 to 2007, and now works as an independent consultant. He received his PhD degree from the University of Maryland, USA, in 1985. His professional interests focus on the fi eld of positional astronomy, both its observational and theoretical aspects. His work includes publications in astrometry, celestial reference systems, solar system ephemerides, Earth rotation, navigation algorithms, and astronomical software. Dr. Kaplan is currently the president of Commission 4 (Ephemerides) of the International Astronomical Union. The minor planet 16074 is named in his honor.
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