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.

This volume covers most areas in the physics of the solar system, with special emphasis on gravitational dynamics; its gist is the rational, in particular mathematical, understanding of the main processes at work. Special stress is given to the variety of objects in the planetary system and their long-term evolution. The unique character of this book is its breadth and depth, which aims at bringing the reader to the threshold of original research; however, special chapters and introductory sections are included for the benefit of the beginner. The volume is generally suitable for post-graduate students and researchers in physics, especially in the field related to the solar system. A large amount of figures and diagrams is included, often compiled with real data.

Introduction to the Mechanics of the Solar System introduces the reader to the mechanics of the solar system and covers topics ranging from the periods of the planets to their flattening and its effects on the orbits of satellites. Kepler's three laws of planetary motion are also discussed, along with the law of gravity; the two-body problem; and perturbations in the motions of the moon and the planets. This book is comprised of four chapters and begins with an analysis of the kinematics of a single planet, focusing on the work of Johannes Kepler, particularly his determination of the orbits of the Earth and Mars and his formulation of his three laws of planetary motion. The following chapters explore systems of ordinary differential equations; determination of orbits using Laplace's method and Gauss' method; the equations of motion and their integrals; the perturbation equations of celestial mechanics; and Lagrange's solution of the three-body problem. The notations of the Earth and the moon are also considered. This monograph is intended for astronomers and astronomy students.

In the last 20 years, researchers in the field of celestial mechanics have achieved spectacular results in their effort to understand the structure and evolution of our solar system. Modern Celestial Mechanics uses a solid theoretical basis to describe recent results on solar system dynamics, and it emphasizes the dynamics of planets and of small bodies. To grasp celestial mechanics, one must comprehend the fundamental concepts of Hamiltonian systems theory, so this volume begins with an explanation of those concepts. Celestial mechanics itself is then considered, including the secular motion of planets and small bodies and mean motion resonances. Graduate students and researchers of astronomy and astrophysics will find Modern Celestial Mechanics an essential addition to their bookshelves.

The Solar System is a complex and fascinating dynamical system. This is the first textbook to describe comprehensively the dynamical features of the Solar System and to provide students with all the mathematical tools and physical models they need to understand how it works. It is a benchmark publication in the field of planetary dynamics and destined to become a classic. Clearly written and well illustrated, Solar System Dynamics shows how a basic knowledge of the two- and three-body problems and perturbation theory can be combined to understand features as diverse as the tidal heating of Jupiter's moon Io, the origin of the Kirkwood gaps in the asteroid belt, and the radial structure of Saturn's rings. Problems at the end of each chapter and a free Internet Mathematica® software package are provided. Solar System Dynamics provides an authoritative textbook for courses on planetary dynamics and celestial mechanics. It also equips students with the mathematical tools to tackle broader courses on dynamics, dynamical systems, applications of chaos theory and non-linear dynamics.

This book develops methods of computing astronomical phenomena from basic ideas. The position of a celestial body is defined by a vector, with components referred to a system of coordinate axes. The relations between various systems in regular use by astronomers are described. In cases where two systems differ in spatial orientation, they are related by a rotation matrix. These matrices are discussed in considerable detail in the mathematical notes. Other topics discussed include: Kepler's Laws and the dynamics of planetary motion, Precession and Nutation, transits of Venus and Mercury, Lagrange points. While no previous knowledge of Astronomy is necessary, it is assumed that the reader is familiar with elementary algebra, trigonometry and calculus.