Handbook of Satellite Orbits from Kepler to GPS Michel Capderou
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Handbook of Satellite Orbits From Kepler to GPS Michel Capderou Handbook of Satellite Orbits From Kepler to GPS Translated by Stephen Lyle Foreword by Charles Elachi, Director, NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA 123 Michel Capderou Universite´ Pierre et Marie Curie Paris, France ISBN 978-3-319-03415-7 ISBN 978-3-319-03416-4 (eBook) DOI 10.1007/978-3-319-03416-4 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014930341 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microﬁlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied speciﬁcally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this pub- lication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permis- sions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publica- tion, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Foreword Since the dawn of the space age with the launch of Sputnik 1 and Ex- plorer 1, orbital mechanics became a major discipline in space exploration. This book reﬂects many years of research and teaching in this ﬁeld by Michel Capderou. It is a comprehensive and modern treatment of the theory of or- bital mechanics, its application, and current day samples of how it is used in the ﬁeld. In that sense, it is not just a textbook for classroom-style lectures; it is truly a handbook for practitioners. It is full of fascinating historical information and references that intrigue the readers to follow the anecdotes and details on how this particular disci- pline evolved from the collective genius of giants in mathematics, physics and astronomy such as Tycho Brahe, Kepler, Newton, Galileo, Lagrange, Laplace, Gauss, Poincar´e and Einstein. This story telling not only makes reading in- teresting but also challenges the readers to understand the fundamentals used by these giants before the advent of computers. Most classroom-style textbook would skip intermediate steps in the deriva- tion of equations or refer the readers to the original papers or textbooks. This book provides suﬃcient intermediate steps so readers with basic freshman mathematics can follow the logical steps. Its treatment of geodesy, geopoten- tial and perturbation methods connects theory to physical measurements and observables. The chapter on Orbit and Mission is unique in that it provides a comprehensive survey of how theory is applied to real-life missions. It connects this discipline to science and inspires the reader to appreciate how a satellite orbit provides a special vantage point for conducting scientiﬁc measurements. Orbital mechanics is not just about getting into space, but it is integral to the measurement technique such as altimetry, radar topography, radio occul- tation, interferometry and gravity ﬁeld through radiometric observables. The comprehensive treatment on designing an orbit for systematic ground track control and target point visibility is unique. In the past, practitioners had to conduct a literature search and examine multiple publications. Its treatment on GPS begs the reader to further explore the world of precision orbit deter- mination, timing and terrestrial reference frame. The book is sprinkled with stories of much innovative use of “tricks” in orbital mechanics such as frozen orbit, sun-synchronicity, aerobraking, libration point and Lissajous orbits, and gravity assist that enables missions like Voyager Grand Tour, Galileo, Cassini- V VI Foreword Huygens and tours of their satellites. This book has superb illustrations and graphics enhanced by colorful photographs. Since the ﬂight of Explorer 1, JPL prides itself in pioneering techniques in orbital mechanics and its applications to carry out NASA’s mission in space-borne observation of our Earth; in ﬂy-by, orbiting and landing of plan- etary bodies and their satellites; in astronomical telescopes that can observe our galaxy and the early Universe. We continue to recruit the best and the brightest graduates in this discipline from universities around the world, who understand not only the physics and mathematics of orbital mechanics but also its applications of real-life missions. The Handbook of Satellite Orbits: From Kepler to GPS is exactly what is needed for all graduates of this disci- pline. Michel Capderou’s book is an essential treatise in orbital mechanics for all students, lecturers and practitioners in this ﬁeld, as well as other aerospace systems engineers. Charles Elachi Director NASA Jet Propulsion Laboratory California Institute of Technology Pasadena, CA, USA Preface Of all the ﬁelds of modern science and technology, space exploration is the one that most clearly displays the following fundamental contrast: on the one hand, its theoretical basis is underpinned by long-established, historically tested and almost immutable, one might even say timeless, principles; on the other, the whole ﬁeld of space science is undergoing meteoric technological evolution, with exponential growth, bringing with it a broad mix of commer- cial, political and ideological considerations. And so we have come from Kepler to GPS. Regarding the “immutable foundations”, we know that the notion of geopotential or the solution of Lagrange’s equations is no easy matter. We just hope that, with teaching experience among the ingredients, we have suc- ceeded in presenting these issues in a suﬃciently clear and interesting way. To illustrate unbridled technological progress, we supply a wealth of examples. The book falls into six main parts: • The ﬁrst part, consisting of Chaps. 1–3, is devoted to geodesy. We begin with the ellipse and its geometrical properties and work our way to the Earth’s gravitational potential and the geoid. • The second part, Chaps. 4–8, focuses on the motion of the satellite, working from the ideal, Keplerian case to the real, perturbed case. • The third part, Chaps. 9–11, takes us into the actual running and func- tioning of satellites, discussing their missions and the ways that orbits are designed to fulﬁl those missions. We consider some novel issues, such as the constant of Sun-synchronicity kh and, for recurrent satellites, the constant κ and the index Φ. Abundant illustrations are provided, always relating to past, present or future space programmes. VII VIII Preface • The fourth part, Chaps. 12 and 13, considers the instruments carried aboard the satellite from a geometrical point of view. We begin with the diﬀerent ways of observing the Earth from a satellite, then move on to sampling, i.e. the conditions under which a given point on the Earth can view the satellite, considering the viewing angle and frequency of visibility. • We then devote the whole of Chap. 14 to GPS. This navigation system, entirely satellite-based, appeals to almost all branches of modern physics. • In the ﬁnal part, Chaps. 15 and 16, we leave the conﬁnes of our own planet to apply all these theories ﬁrst to Mars, then to the other planets of the Solar System, and even to the natural satellites of those planets, around which artiﬁcial satellites may gravitate. The orbit and sampling software Ixion forms the backbone of this book. We ﬁrst developed it as a teaching tool for an M.Sc. in climatology and space observation, and also in the research context, as an aid to understanding issues of orbital elements, satellite–pixel–Sun conﬁguration, and so on, which arise when processing the data transmitted to us by our satellites. But once the accuracy of Ixion had been proven in the context of real data, by the confrontation with pixels, one might say, we extended it to all types of orbit and included some didactic features that would make it accessible and useful to a broader audience. The software Ixion has since been used for preliminary studies of orbital strategy, as it is known, which serve to match orbital elements in the best possible way to the physical phenomena we need to observe. Among the orbits studied in this context, we cite the French–Indian satellite Megha-Tropiques and the planned Mars missions Premier-07 and MEMO. Ixion isoftenusedby our colleagues for calibration and validation campaigns in the ﬁeld, as for the satellites Calipso, MetOp-A and -B, Megha-Tropiques, and others. Ixion/Web is the part of Ixion that is now accessible online. Our mapping software Atlas has been coupled with Ixion to produce graphical representa- tions of orbits and their ground tracks. We hope the maps it produces will be pleasant and useful to the reader.