The Earth And Its Gravity Field

Since the Czech edition was published four years ago, the authors have revised the original text tobring it up to date. During these four years, thanks to satellite altimetry the accuracy of the global descrip tion of the gravity field (model GEM-T2), of the fundamental astro geodetic constants, of the principal moments of inertia of the Earth and, in particular, of their differences, of the precession constant, and of a number of other dynamical parameters of the Earth have been improved. The authors have included most of these improvements in the revised English edition. They have, of course, also made factual, formal and other corrections and have modified some of the figures. Additions to the index and references have also been made. Praha, Czech Republic M. BuRSA and K. PF:c August 1993 Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals of Determining the Parameters 1 Defining the Earth's Gravitational Field by Satellite Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 1 Satellite Equations of Motion . . . . . . . . . . . . . . . . . 6 1. 2 Perturbing Function and Perturbing Potential . . . . 23 1. 3 General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 3. 1 Perturbing Gravitational Potential of the Earth in 1. 3. 2 Outer Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Perturbations due to the Moon and the Sun . . . . . . 27 1. 3. 3 Solution of the Perturbed Motion . . . . . . . . . . . . . . 28 1. 4 1. 5 Transformation of the Perturbing Gravitational Potential into the Function of the Satellite's Orbital Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1. 5. 1 Transformation of Potential Rs$ . . . . . . . . . . . . . . . 32 1. 5. 2 Transformation of Potentials L1 Vs»' L1 Vso . . . . . . . .

The author of this history of mankind’s increasingly successful attempts to understand, to measure and to map the Earth’s gravity field (commonly known as ‘little g’ or just ‘g’) has been following in the footsteps of the pioneers, intermittently and with a variety of objectives, for more than fifty years. It is a story that begins with Galileo’s early experiments with pendulums and falling bodies, progresses through the conflicts between Hooke and Newton and culminates in the measurements that are now being made from aircraft and satellites. The spectacular increases in accuracy that have been achieved during this period provide the context, but the main focus is on the people, many of whom were notable eccentrics. Also covered are the reasons WHY these people thought their measurements would be useful, with emphasis in the later chapters on the place of ‘g’ in today’s applied geology, and on the ways in which it is providing new and spectacular visions of our planet. It is also, in part, a personal memoir that explores the parallels between the way fieldwork is being done now and the difficulties that accompanied its execution in the past. Selected topics in the mathematics of ‘g’ are discussed in a series of short Codas.

Volume resulting from an ISSI Workshop, 11-15 March 2002, Bern, Switzerland

International Geophysics Series, Volume 10: The Gravity Field of the Earth: From Classical and Modern Methods explores the theory of the gravity field of the earth based on both classical and modern methods. Classical method involves observations of gravity taken over the earth's surface, while the modern method uses observations of variation of orbital elements of artificial satellites caused by the gravity field of the earth. This book is organized into two parts encompassing 12 chapters. Part I describes the solution of physical problems that are treated as Dirichlet problems or solved by means of integral equations. This part also deals with the determination of the geoid form from ground gravity measurements using the Stokes formula. The method of obtaining the Stokes formula by means of an integral equation is also outlined. Part II contains modern mathematical techniques developed to utilize the observations of artificial satellites for geodetic purposes. This book could be used as a textbook for students in the fields of geodesy, geophysics, or astronomy.

Volume resulting from an ISSI Workshop, 11-15 March 2002, Bern, Switzerland