Fundamentals of astrodynamics

Abstract

This book deals with the motion of the center of mass of a spacecraft; this discipline is generally called astrodynamics. The book focuses on an analytical treatment of the motion of spacecraft and provides insight into the fundamentals of spacecraft orbit dynamics. A large number of topics are treated in a uniform and consistent way. The text is intended for senior undergraduate or graduate engineering students, and is based on course notes that have been used in various versions since 1976 for courses given for M.Sc. students at the Faculty of Aerospace Engineering of Delft University of Technology. It is a typical student study book: the knowledge of mathematics and mechanics required from the reader corresponds to that of students having a B.Sc. degree, and full derivations of the formulas are given. However, the book is also useful for astrodynamicists and is a valuable resource for anyone interested in astrodynamics. The text starts with a treatment of the foundation of dynamics. It continues with the clas-sical topics of the many-body problem and the three-body problem, and modern applications of the three-body problem for spaceflight are presented. Then, it is proved that the motion of planets, satellites and interplanetary spacecraft can generally be approximated by a two-body problem. This problem is analyzed in full detail and many useful relations for circular, elliptical, parabolic and hyperbolic motion are derived. Next, the motion of a satellite relative to another satellite is discussed and analyzed, and the more modern topic of regularization is treated. Then, the basic astronomical concepts of reference frames, coordinate systems, orbital elements and time are presented, and various topics which are crucial in modern astrodynamics are addressed. Next, the application of rocket engines to change the orbit of a spacecraft is treated, both for coplanar and for three-dimensional maneuvers. Subsequently, the theory of phasing orbits is presented and various cases are analyzed. Next, rendez-vous flights between two satellites are analyzed. Then, the launching of satellites is discussed and analyzed, as well as the execution of lunar and interplanetary flights, and the flight of space-craft along low-thrust trajectories. The last four chapters deal with various aspects of orbit perturbations. The perturbing forces acting on a satellite are discussed and special and general perturbations methods are described. An elementary analysis of the character¬istic effects of the perturbing forces on a satellite orbit is given. The general method of variation of orbital elements is described in detail and an application to orbit maneuvers is presented. Finally, a detailed analysis of orbit perturbations due to the Earth=s gravity field is given. The book concludes with three appendices, containing additional information.