IAU S261 summarizes the present state of applied relativity, and discusses the applications and future tests of general relativity.

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.

In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.

Introduction to Relativity is intended to teach physics and astronomy majors at the freshman, sophomore or upper-division levels how to think about special and general relativity in a fundamental, but accessible, way. Designed to render any reader a "master of relativity", everything on the subject is comprehensible and derivable from first principles. The book emphasizes problem solving, contains abundant problem sets, and is conveniently organized to meet the needs of both student and instructor. - Simplicity: the book teaches space and time in relativity in a physical fashion with minimal mathematics - Conciseness: the book teaches relativity by emphasizing the basic simplicity of the principles at work - Visualization: space-time diagrams (Minkowski) illustrate phenomena from simultaneity to the resolution of the twin paradox in a concrete fashion - Worked problems: two chapters of challenging problems solved in several ways illustrate and teach the principles - Problem sets: each chapter is accompanied by a full set of problems for the student that teach the principles and some new phenonmena

Providing a broad overview of foundational concepts, this second edition of Fundamentals of Astronomy covers topics ranging from spherical astronomy to reference systems, and celestial mechanics to astronomical photometry and spectroscopy. It expounds arguments of classical astronomy that provided the foundation for modern astrometry, whilst presenting the latest results of the very-long-baseline interferometry (VLBI) radio technique, optical interferometers and satellites such as Hipparcos and GAIA, and recent resolutions of the IAU and IERS regarding precession, forced and free nutation, and Earth figure and rotation. Concepts of general relativity are explored, such as the advance of Mercury’s perihelion, light deflection and black holes, in addition to the physical properties, orbits, and ephemerides of planets, comets and asteroids with an extension to visual binary stars orbital reconstruction. Extrasolar planets are also discussed, with reference to radial velocity and transits measurements by ground and space telescopes. Basic concepts of astronomical photometry, spectroscopy and polarimetry are given, including the influence of the terrestrial atmosphere. Classical works, such as Hipparchus, are mentioned in order to provide a flavor of the historical development of the field. It is an ideal textbook for undergraduate and graduate students studying astronomy, astrophysics, mathematics, and engineering. Supplementary and explanatory notes provide readers with references to additional material published in other literature and scientific journals, whilst solved and unsolved exercises allow students to review their understanding of the material. Features: Provides an introductory vision of arguments from spherical astronomy to celestial mechanics to astronomical photometry and spectroscopy Presents the information at an introductory level without sacrificing scientific rigor Fully updated throughout with the latest results in the field

Relativistic Astrophysics and Cosmology offers a succinct and self-contained treatment of general relativity and its application to compact objects, gravitational waves and cosmology. The required mathematical concepts are introduced informally, following geometrical intuition as much as possible. The approach is theoretical, but there is ample discussion of observational aspects and of instrumental issues where appropriate. The book includes such topical issues as the Gravity Probe B mission, interferometer detectors of gravitational waves, and the physics behind the angular power spectrum of the cosmic microwave background (CMB). Written for advanced undergraduates and beginning graduate students in (astro)physics, it is ideally suited for a lecture course and contains 140 exercises with extensive hints. The reader is assumed to be familiar with linear algebra and analysis, ordinary differential equations, special relativity, and basic thermal physics.

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.