The book "Relativity in Astrometry, Celestial Mechanics and Geodesy" repre­ sents a significant contribution to modern relativistic celestial mechanics and astrometry. In these branches of astronomy the theory of general relativity is used nowadays as an efficient practical framework for constructing accurate dynamical theories of motion of celestial bodies and discussing high-precision observations. The author develops the useful tools for this purpose and intro­ duces the reader into the modern state of the art in these domains. More specifically, the distinctive feature of the book is the wide application of the tetrad formalism to astronomical problems. One may not agree with the author's opinion that this is the only method so far to be able to treat the rel­ ativistic astronomical problems in a consistent and satisfactory manner. (On the contrary, one may foresee in the nearest future other books on relativistic celestial mechanics and astrometry based on different approaches solving the same problems. ) However, we are now at the beginning of practical relativis­ tic astronomy and it will demand much effort to reconstruct in a relativistic manner all Newtonian conceptions of ephemeris astronomy and geodesy. In particular, this concern. s the definitions of reference frames, time scales and astronomical units of measurement. This book is one of the first steps in the correct direction. V. A.

Inhalt

1. Relativity in Astrometry, Celestial Mechanics and Geodesy.- 1.1 Astrometry.- 1.2 Celestial Mechanics.- 1.3 Geodesy.- 2. Newtonian and Relativistic Space-Time.- 2.1 Newtonian Space-Time.- 2.2 Relativistic Space-Time.- 3. Reference Frames and Astrometry.- 3.1 Introduction.- 3.2 Clocks and the Temporal Aspect of Reference Frames.- 3.3 Spatial Reference Directions.- 3.3.1 Gravitational Compass and Geoid.- 3.3.2 The Stellar Compass.- 3.3.3 The Inertial Compass.- 3.4 Reference Frames and Coordinate Systems.- 3.4.1 Frame Induced Coordinates.- 3.4.2 Coordinate Induced Frames.- 3.5 Station Coordinates and the Problem of Length.- 4. Celestial Mechanics.- 4.1 Post-Newtonian Motion of Point Masses.- 4.2 Motion of Satellites.- 4.2.1 Spherical Field of the Earth and the Problem of Coordinates.- 4.2.2 The Gravito-Magnetic Field of the Earth.- 4.2.3 The Post-Newtonian Quadrupole.- 4.3 Lunar Motion.- 4.4 Motion of the Planetary System.- 4.5 Numerically Produced Ephemerides Ill.- 4.6 Timing Observations of Pulsars in Binary Systems.- 4.7 Relativistic Motion of Extended Bodies.- 4.7.1 Translational Motion.- 4.7.2 Spin Motion.- 4.7.3 Beyond the First Post-Newtonian Approximation.- 5. Geodesy.- 5.1 Post-Newtonian Gravimetry.- 5.2 Realisation of Time-Scales.- 5.2.1 Synchronisation of Earthbound Clocks by means of Portable Clocks.- 5.2.2 Comparison of Clocks: Station Clock - Satellite Clock..- 5.2.3 Doppler Measurements in the Vicinity of the Earth.- 5.3 Space Methods.- 5.3.1 Laser Ranging to Satellites and the Moon.- 5.3.2 VLBI.- A.1 PPN-Metric, Christoffel Symbols and Curvature Tensor.- A.2 The PPN Two-Body Problem.- A.2.1 The Wagoner-Will Representation.- A.2.2 The Brumberg Representation.- A.2.3 The Damour-Deruelle Representation.- A.2.4 The Solution with Osculating Elements.- A.3 On the PPN Hill-Brown Theory.- A.3.1 Geocentric EIH Equations for the Restricted Three-Body Problem.- A.3.2 The Geodetic Precession as derived from the EIH Equations.- A.3.3 The PPN Hill-Brown Calculation in the Instantaneous Geocentric System.- A.4 On the PPN Euler Equation.- References.