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Guochang Xu

Orbits

With 26 Figures and 6 Tables

123

Dr. Guochang Xu GeoForschungsZentrum Potsdam Dept. 1 Geodesy and Remote Sensing Telegrafenberg A 17 14473 Potsdam Germany [email protected]

ISBN: 978-3-540-78521-7

e-ISBN: 978-3-540-78522-4

Library of Congress Control Number: 2008930175 c 2008 Springer-Verlag Berlin Heidelberg  This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

To Liping, Jia, Yuxi, Pan and Yan

Preface

The purpose of this reference and handbook is to describe and to derive the analytic solutions of the equations of satellite motion perturbed by extraterrestrial and geopotential disturbances of the second order. The equations of satellite motion perturbed by extraterrestrial disturbances are solved by means of discretization and approximated potential function as well as Gaussian equations. The equations perturbed by geopotential disturbances are solved by symbolic mathematical operations. The traditional problem of singularity in the solutions is solved by so-called singularityfree orbit theory. Simplified disturbed equations of motion are proposed to simplify the solutions. Applications of the theory for analytic orbit determination are also discussed. Indeed, this is the first book since the satellite era, which describes systematically the orbit theory with analytical solutions, with respect to all of extraterrestrial and geopotential disturbances of the second order, and the solutions are free of singularity. Based on such a theory, the algorithms of orbit determination can be renewed; deeper insight into the physics of disturbances becomes possible; the way to a variety of new applications and refinements is opened. My primary knowledge of the orbit theory came from my education of mathematics while studying physics and theoretical mechanics (1981). My first practical experience with orbit came from the research activity at the Technical University (TU) Berlin on orbit corrections of the satellite altimetry data (1988–1992). The extensive experience on orbit came from the GPS/Galileo software development for orbit determination and geopotential mapping at the GFZ (2001–2004). The traditional adjustment mode