Astrophysics and Space Science Library 436 Pini Gurfil P Kenneth Seidelmann Celestial Mechanics and Astrodynamics: Theory and Practice Celestial Mechanics and Astrodynamics: Theory and Practice Astrophysics and Space Science Library EDITORIAL BOARD Chairman W B BURTON, National Radio Astronomy Observatory, Charlottesville, Virginia, U.S.A (bburton@nrao.edu); University of Leiden, The Netherlands (burton@strw.leidenuniv.nl) F BERTOLA, University of Padua, Italy C J CESARSKY, Commission for Atomic Energy, Saclay, France P EHRENFREUND, Leiden University, The Netherlands O ENGVOLD, University of Oslo, Norway A HECK, Strasbourg Astronomical Observatory, France E P J VAN DEN HEUVEL, University of Amsterdam, The Netherlands V M KASPI, McGill University, Montreal, Canada J M E KUIJPERS, University of Nijmegen, The Netherlands H VAN DER LAAN, University of Utrecht, The Netherlands P G MURDIN, Institute of Astronomy, Cambridge, UK B V SOMOV, Astronomical Institute, Moscow State University, Russia R A SUNYAEV, Space Research Institute, Moscow, Russia More information about this series at http://www.springer.com/series/5664 Pini Gurfil • P Kenneth Seidelmann Celestial Mechanics and Astrodynamics: Theory and Practice 123 Pini Gurfil Faculty of Aerospace Engineering Technion-Israel Institute of Technology Haifa, Israel P Kenneth Seidelmann Department of Astronomy The University of Virginia Charlottesville, USA ISSN 0067-0057 ISSN 2214-7985 (electronic) Astrophysics and Space Science Library ISBN 978-3-662-50368-3 ISBN 978-3-662-50370-6 (eBook) DOI 10.1007/978-3-662-50370-6 Library of Congress Control Number: 2016943837 © Springer-Verlag Berlin Heidelberg 2016 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 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 The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Cover illustration: Technion’s Space Autonomous Mission for Swarming and Geo-locating Nanosatellites (SAMSON) Credit: Asher Space Research Institute, Technion Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Berlin Heidelberg I dedicate this book to my children, Eytam, Oshri, and Ohav, and to my parents, Arie and Sara Pini Gurfil This book is dedicated to Bobbie Seidelmann and our family, Holly, Kent, Jutta, Alan, Karen, and Sarah P Kenneth Seidelmann Also we dedicate the book to the scientists that preceded us and taught, mentored, and inspired us Foreword The early contributions to artificial satellite orbit theory were mostly made by the celestial mechanicians, e.g., Brouwer, Garfinkel, Vinti and Kozai Then, as aerospace engineering curricula emerged, their astrodynamics graduates began to make contributions Most of the recent astrodynamics books have been written by engineering graduates This book, co-authored by a celestial mechanician, Ken Seidelmann, and an astrodynamicist, Pini Gurfil, is a welcome addition to the aerospace community as it merges the two backgrounds Chapter begins with a short history of celestial mechanics and then transitions to introductions to some of the key topics covered in the book Topics included that are not usually seen in astrodynamics books are stability, chaos, Poincaré sections, KAM (Kolmogorov-Arnold-Moser) theory, and observation systems Chapter covers the basic math and physics concepts needed for the subjects in the book Chapter provides an excellent discussion of coordinate systems and introduces relativity, a subject not usually included in astrodynamics books but certainly present in celestial mechanics, e.g., the precession of Mercury’s perihelion Chapters and provide a thorough discussion of the central force and two-body problems Included is a section on Einstein’s modification of the orbit equation The focus of Chap is initial orbit determination Chapter provides a thorough discussion of the N-body problem and the integrals associated with this problem Chapter then addresses the special case of the circular restricted 3-body problem (CR3BP) The coverage of the CR3BP is more comprehensive than found in most astrodynamics books and includes a discussion of families of periodic orbits Chapter is an introduction to numerical procedures used in astrodynamics and celestial mechanics This chapter is not a comprehensive coverage and comparison of numerical integration methods but an introduction to the methods needed to understand numerical methods and error computation Chapter 10 begins a group of five chapters that this writer considers very important for astrodynamics and celestial mechanics but is often not found in astrodynamics books I believe that the motion under the influence of conservative perturbations, those derivable from a potential, is best addressed and understood vii viii Foreword using Hamiltonian mechanics and perturbation methods such as Lie series Chapter 10 discusses the basics of Hamiltonian mechanics, canonical transformations, generating functions, and Jacobi’s theorem and applies these to the two-body problem The focus of Chap 11 is perturbation methods, and it begins with an excellent discussion of the variation of parameters (VOP), which leads to Lagrange’s planetary equations Then, with the perturbations expressed as specific disturbing accelerations instead of the accelerations obtained from a potential, Gauss’ variational equations are derived for the accelerations in the radial, transverse, and orbit normal directions and the tangential, normal, and orbit normal directions Included is a discussion of Lagrange brackets, which are needed for the VOP Also in this chapter is the presentation of the Kustaanheimo-Stiefel variables Using the foundations developed in Chap 10, Chap 11 addresses the solution for the 3rd body perturbations, atmospheric drag, and gravitational potential Then Chap 12 focuses on the solution for motion about an oblate planet There are many such solutions beginning with Brouwer’s 1959 paper, and presenting even a few solutions would be prohibitive The solution presented here is the Cid-Lahulla radial intermediary Special perturbation (numerical integration) methods are the most accurate and the general perturbation analytical methods, e.g, Brouwer’s solution, are the most efficient Chapter 13 presents the semianalytical approach, which is more efficient than numerical integration and more accurate than the analytical solution The method is then applied to the four problems, a LEO satellite perturbed by drag, frozen orbits, sun-synchronous and repeat ground track orbits, and the motion of a geosynchronous satellite Chapters 10–13 address the problem of the motion of a space object under the influence of forces derivable from a potential except for the section on the effects of atmospheric drag Chapters 14 and 15 consider the problem of the control of a space object using both continuous and impulsive control Chapter 14 considers the control of specific types of orbits such as sun-synchronous orbits, frozen orbits, and geosynchronous orbits, as well as gravity assists Both impulsive and continuous thrust control are addressed Chapter 15 provides a very thorough coverage of the well-known problem of optimal impulsive orbit transfers Chapter 16 addresses the problem of orbit data processing and presents batch least squares and recursive filtering Also discussed is the use of polynomials for the compression/representation of ephemerides Chapter 17 provides a summary of the problem of space debris including probability of collision and collision avoidance maneuvers The book concludes with another discussion of main contributors to celestial mechanics and the early pioneers of astrodynamics Entire books have been written on the subjects presented in many of the chapters in this book Thus, when writing a book on astrodynamics, there has to be a balance between the amount of material presented and the necessary balance of mathematical rigor and its application to the problem at hand I believe this book has achieved such a balance There is a breadth of topics and each one is presented with the necessary depth needed for the reader to understand the topic The book can Foreword ix be used for a senior/1st-year graduate class in astrodynamics and also for a 2nd-year graduate class in astrodynamics It is a pleasure for me to write this Foreword and recommend this book to the astrodynamics community Texas A&M University, College Station, TX, USA Kyle T Alfriend ... laws and Newton’s Principia Celestial mechanics has evolved into a myriad of approaches, methods, and results, some of which are the bases for astrodynamics Indeed, celestial mechanics and astrodynamics. . .Celestial Mechanics and Astrodynamics: Theory and Practice Astrophysics and Space Science Library EDITORIAL BOARD Chairman W B BURTON,... methods and applications common to celestial mechanics and astrodynamics The book includes classical and emerging topics, manifesting the state of the art and beyond The book contains homogenous and