Text discusses earth's gravitational field; matrices and orbital geometry; satellite orbit dynamics; geometry of satellite observations; statistical implications; and data analysis.

This book on space geodesy presents pioneering geometrical approaches in the modelling of satellite orbits and gravity field of the Earth, based on the gravity field missions CHAMP, GRACE and GOCE in the LEO orbit. Geometrical approach is also extended to precise positioning in space using multi-GNSS constellations and space geodesy techniques in the realization of the terrestrial and celestial reference frame of the Earth. This book addresses major new developments that were taking place in space geodesy in the last decade, namely the availability of GPS receivers onboard LEO satellites, the multitude of the new GNSS satellite navigation systems, the huge improvement in the accuracy of satellite clocks and the revolution in the determination of the Earth's gravity field with dedicated satellite missions.

This book contains theory and applications of gravity both for physical geodesy and geophysics. It identifies classical and modern topics for studying the Earth. Worked-out examples illustrate basic but important concepts of the Earth’s gravity field. In addition, coverage details the Geodetic Reference System 1980, a versatile tool in most applications of gravity data. The authors first introduce the necessary mathematics. They then review classic physical geodesy, including its integral formulas, height systems and their determinations. The next chapter presents modern physical geodesy starting with the original concepts of M.S. Molodensky. A major part of this chapter is a variety of modifying Stokes’ formula for geoid computation by combining terrestrial gravity data and an Earth Gravitational Model. Coverage continues with a discussion that compares today’s methods for modifying Stokes’ formulas for geoid and quasigeoid determination, a description of several modern tools in physical geodesy, and a review of methods for gravity inversion as well as analyses for temporal changes of the gravity field. This book aims to broaden the view of scientists and students in geodesy and geophysics. With a focus on theory, it provides basic and some in-depth knowledge about the field from a geodesist’s perspective. /div

Celestial mechanics aims to predict the motion of every real object in outer space, no matter what causes changes in its orbit. The motion of most planets and natural satellites can be successfully described by conservative celestial mechanics and problems can be studied within the formalism of Hamiltonian mechanics. The few exceptions which experience significant non-gravitational effects call for only very small corrections to the purely gravitational theory. All satellites experience non-gravitational perturbations to their orbits. However, factors such as the relatively high area-to-mass ratio of spacecraft compared with that of even a tiny asteroid significantly increase the relative effect of non-gravitational to gravitational forces on the orbits of artificial satellites. When the orbital tracking is carried out by very accurate techniques, the need arises to model, or at least to estimate, the effects of phenomena such as radiation pressure from solar light and from Earthshine or drag caused by neutral and charged particles. This book presents the basic ideas of the physics of the main non-gravitational perturbations and the mathematics of the methods required to compute their orbital effects. The authors convey to the reader the relevance of the different problems that need to be solved to achieve a given level of accuracy in the orbit determination and in the recovery of geophysically significant parameters. The book will enable readers to assess for themselves the possible geodetic uses of given space missions, or maybe to propose a new one, or to propose a combined geodetic use for a mission envisaged for other purposes. The Authors Andrea Milani is a mathematician, Anna Maria Nobili ad Paolo Farinella are physicists. They began working together in celestial mechanics and satellite geodesy in 1978, when they formed, with others, the Space Mechanics Group now based at the Department of Mathematics of the University of Pisa, Italy. By travelling to many research centres in Europe and in the USA, and by presenting several proposals for space-based experiments to the European Space Agency and to the Italian Space Program, they have learned how to assess the difficulty of an orbit determination and how often the problem is due to poor modelling of very-subtle non-gravitational effects, In this book they try to make their know-how available to others, as well as teaching some basic tools of celestial mechanics on the basis of their experience in basic research. A Milani and A M Nobili also work on the stability of the solar system, P Farinella also studies the dynamics and physics of the asteriod belt.

Based on "Heiskanen/Moritz" which served for more than 30 years as a standard reference Treats physical geodesy encyclopaedically Seamless blend of new ideas and methods (GPS, satellites, collocation)

Advances in space-borne technologies lead to improvements in observations and have a notable impact on geodesy and its applications. As a consequence of these improvements in data accuracies, spatial and temporal resolutions, as well as the developments in the methodologies, more detailed analyses of the Earth and a deeper understanding of its state and dynamic processes are possible today. From this perspective, this book is a collection of the selected reviews and case-study articles that report the advances in methodology and applications in geodesy. The chapters in the book are mainly dedicated to the Earth’s gravity field theory and applications, sea level monitoring and analysis, navigation satellite systems data and applications, and monitoring networks for tectonic deformations. This collection is a current state analysis of the geodetic research in theory and applications in today’s modern world.