Theory Of Satellite Geodesy: Applications Of Satellites To Geodesy

Theory of Satellite Geodesy One of a Special Series of Brief Books Covering Selected Topics in the Pure and Applied Sciences CONSULTING EDITOR GORDON J. F. MAcDONALD University of California nt Los Angeles Theory of Satellite Geodesy APPLICATIONS OF SATELLITES TO GEODESY WILLIAM M. KAULA Institute of Geophysics and Planetary Physics University of California at Los Angeles 14AK/L BLAISDELL PUBLISHING COMPANY A DIVISION OF GINN AND COMPANY IValtham, Massachusetts • Toronto • London COPYRIGHT © 1966 by Blaisdell Publishing Company, A Division of Ginn and Company. All rights reserved. Library of Congress Catalog Card Number: 65-14571 Printed in the United States of America. PREFACE of this text is to . demonstrate the application and development of familiar physics—Newtonian gravitation—and familiar mathematics—Euclidean geometry—in a particular environment: the earth. The second is to collect and explain some orate mathematical techniques developed in recent years in order to utilize artificial satellites for geodesy. To make (his book as useful as possible for the first purpose, it is assumed that the reader has completed only the pertinent parts of a first-year course in physics and a first-year course in calculus. Thus, although it is assumed that the reader is familiar with the fundamentals of potential fields and 'analytic geometry, full explanations are given of certain mathematical techniques, such as spherical harmonics and matrices, that are necessary to apply these fundamentals in the context with which the book deals. The second purpose may interfere with the first in that it introduces more complications than are necessary for an understanding of the physical principles involved. However, the fact that such complications occur in applying simple physics and the fact that certain mathematical techniques are valuable because they cope most effectively with complications are perhaps the most important lessons for the student. In writing this book lam indebted to the following persons; for comments on earlier drafts, to Robert G. Wilson and Bernard F. Cohlan at the University of California in Los Angeles and to C. A. Whitten, Martin Hahne, and others at the United States Coast and Geodetic Survey in Washington, D.C.; to Robert H. Gersten of Aerospace Corporation, Los Angeles, who contributed greatly by carefully reading the final draft; and to Elizabeth Doty for her diligence and patience in preparing the typescript and its .multifarious corrections. -"( W. M. KAMA THE FIRST PURPOSE CONTENTS iX TABLE OF SYMBOLS 'FABLE OE NUMERICAL VALUES xiii THE EARTH'S GRAVITATIONAL FIELD 2 1.1 .Potential Theory 1.2 1.3 Spherical Harmonics Potential of the Ellipsoid 4 8 MATRICES AND ORBITAL GEOMETRY 2.1 2.2 2.3 General Matrix Notation Orbital Geometry 3 , SATELLITE 12 12 16 ORBIT DYNAMICS 3.1 Elliptic Motion 3.2 Perturbed Equations of Motion 3.3 Conversion of Spherical Harmonic Disturbing Function 3.4 Linear Perturbations 3.5 Nonlinear Perturbations 3.6 Resonance 3.7 Miscellaneous Effects 3.8 Summary 4 20 25 30 37 41 49 56 59 GEOMETRY OF SATELLITE OBSERVATION'S 4.1 4.2 — 61 61 General Coordinate Transformations vii Conients viii 4.3 4.4 4.5 4.6 4.7 5 67 73 78 81 87 STATISTICAL IMPLICATIONS 5.1 5.2 5.3 6 Diftrential Relationships and Observation Equations Observation Equations: Directional Observation Equations: Range Rate and Range Time and Precise Definition a Coordinates Observability Conditions General Time Series Quadratic Sum Minimization 92 92 100 DATA