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Relativistic Celestial Mechanics of the Solar Systemкнига
- Авторы: Kopeikin Sergei, Efroimsky Michael, Kaplan George
- Год издания: 2011
- Издательство: WILEY-V C H VERLAG GMBH
- Местоположение издательства: PO BOX 10 11 61, WEINHEIM, GERMANY,D-69451
- Объём: 892 страниц
- ISBN: 978-3-527-40856-6
- Монография
- Академическое издание
- DOI: 10.1002/9783527634569
- Аннотация: The book by Kopeikin, Efroimsky and Kaplan is a remarkable account on relativity in the solar system. On about 850 pages, the book covers all aspects of relativistic celestial mechanics in the solar system, from the Newtonian framework up to the general relativity based IAU resolutions. I do not remember any book on that subject that can be regarded as deeper or more exhaustive. Very many references went into the book which are most conveniently presented at the end of each chapter or appendix in author-named alphabetic order. Worth to be mentioned is also that the book is not at all overloaded with formulae, rather the text dominates and delivers a plethora of authoritatively presented highly useful information. Additionally, the layout of the book is very appealing and nicely supports its quite readable content. The first five chapters of the book, of more than 450 pages, are devoted to Newtonian celestial mechanics, special and general relativity as well as relativistic reference frames and post-Newtonian coordinate transformations. These chapters do lay a perfect ground for the main part of the book. To elucidate the originality and depth of the treated subjects, some topics may be selected for illustration: In the Ch. Newtonian Celestial Mechanics topics are the perturbated two-body problem, the Lagrange constraint in celestial mechanics, Delaunay equations, gauge-invariant pertubation equations, osculating and contact orbital elements; in the Ch. Introduction to Special Relativity selected topics are the Lorentz and Poincaré group, covectors, Rindler and radar coordinates, nonperfect fluids and solids; in the Ch. General Relativity one finds various equivalence principles, the covariance principle, the Mach principle, torsion tensor, nonmetricity tensor, holonomy of a connection, Jacobi equation, Weyl tensor and Ricci decomposition, the general relativity principle, principles of measurement of gravitational field, Killing vectors and conservation laws, energy-momentum tensors of various systems, multipolar expansion of the gravitational field, and variational principles for matter and fields; in the Ch. Relativistic Reference Frames topics of special interest are the basic principles of the post-Newtonian approximation, local and global astronomical coordinates, external and internal solutions of the metric tensor; and in the Ch. Post-Newtonian Coordinate Transformations selected topics are the method of matched asymptotic expansion, matching and transformation of the external and internal potentials. Indeed, the mentioned chapters deliver a profound understanding of the theory of relativity. They are indispensable for the next 400 pages in which relativistic celestial mechanics, astrometry, geodesy, and relativity in IAU resolutions are treated. It is much appealing that in an Appendix the text of the IAU Resolutions from 1997 through 2009 are given. Already within the Ch. Relativistic Reference Frames general relativity is generalized to scalar-tensor gravity which supplies a very useful dynamical model for the often applied parametrized post-Newtonian formalism within quantitative tests of general relativity. The Ch. Relativistic Celestial Mechanics treats some fundamental topics like rotational equations of motion or the various post-Newtonian orbital parametrizations in the two-body dynamics. A voluminous chapter of 150 pages, about the same as the Ch. General Relativity, deals with relativistic astrometry. Herein gravitational time delay, bending, deflection, frequency shift, and lensing of light as well as pulsar timing, Doppler tracking, and tests of general relativity are developed in great detail. In a footnote therein, in the context of the Jupiter’s experiment, the authors claim “a number of misconceptions in the physical interpretation of the experiment presented in Will (2006).” The reader is strongly adviced to explore the correctness of that idiosyncratic statement. The Ch. Relativistic Geodesy contains post-Newtonian gravimetry, gradiometry, and geoids. The Ch. Relativity in IAU Resolutions presents time scales, various coordinate systems, the fundamental celestial reference system, the ephemerides of the major solar system bodies, precession and nutation, and modelling of the Earth’s rotation. All these topics are crucial for a precise understanding of astronomy-related measurements on the Earth. Finally, there is an Appendix which gives the fundamental solution of the Laplace equation in terms of both spherical harmonics and symmetric trace-free tensors, and there is another Appendix showing a lot of astronomical constants including mass ratios of many bodies of the solar system. The book ideally fits to all scientists who are interested in relativity in the solar system and still need to learn some more relativity or, even relativity at all. For those readers, but also for experts in relativity, the book is most valuable. The book is right an overwhelmingly rich and thorough treatise on the modern dynamics of the solar system.
- Добавил в систему: Копейкин Сергей Михайлович