Essential Relativistic Celestial Mechanics

by Victor Brumberg

Overview

Essential Relativistic Celestial Mechanics presents a systematic exposition of the essential questions of relativistic celestial mechanics and their relation to relativistic astrometry. The book focuses on the comparison of calculated and measurable quantities that is of paramount importance in using general relativity as a necessary framework in the discussion of high-precision observations and for the construction of accurate dynamical ephemerides. It discusses the results of the general relativistic theory of motion of celestial bodies and describes the relativistic theory of astronomical reference frames, time scales, and the reduction of observations.

Product Details

ISBN-13:	9780367403065
Publisher:	Taylor & Francis
Publication date:	09/05/2019
Pages:	274
Product dimensions:	6.12(w) x 9.19(h) x (d)

Table of Contents

Preface vii

1 Mathematical Tools 1

1.1 Elements of Newtonian celestial mechanics 1

1.2 Elements of Riemannian geometry and tensor analysis 11

1.3 Elements of the special theory of relativity 25

2 GRT Field Equations 37

2.1 Basic principles of GRT 37

2.2 Weak gravitational field 48

2.3 Problem of measurable quantities in GRT 58

3 One-body Problem 73

3.1 Schwarzschild problem 73

3.2 Light propagation in the Schwarzschild problem 96

3.3 Field of a rotating spheroid 106

4 Approximate Solutions of the Field Equations and Approximate Equations of Motion 116

4.1 N-body problem 116

4.2 Geocentric reference frame 130

4.3 Equations in variations for the spherically symmetrical metric 139

4.4 Gravitational radiation and motion in a binary system 149

5 Equations of Motion of Solar System Bodies 162

5.1 Equations of motion of Earth's artificial satellites 162

5.2 Motion of the major planets 175

5.3 Motion of the Moon 180

6 Relativistic Reduction of Astrometric Measurements 197

6.1 General principles of reduction 197

6.2 Relativistic theory of astronomical reference systems 202

6.3 Relativistic reduction of astrometric observations 211

6.4 Relativistic reduction of radio observations 217

7 Relativistic Effects in Geodynamics 226

7.1 Timescales of the Earth 226

7.2 Clocks and satellites in circumterrestrial space 238

Postscript 250

References 251

Index 261