Edward Belbruno has been a Visiting Research Collaborator in the Program in Applied and Computational Mathematics at Princeton University since 1998. The author of numerous articles in professional journals in mathematics, astronomy, and aerospace engineering, he received the Laurel Award in 1999 for the salvage of a Hughes satellite in 1998 using lunar transfer.

"You have just launched a multimillion dollar communications satellite into space. A malfunction means your expensive cargo will not reach its required orbit. Who are you going to call? A good choice would be Edward Belbruno, a celestial mechanician who seems to specialize in such lost causes... Capture Dynamics is the first book to describe the necessary theory in the context of the whole process of capture... The result is a brilliant example of the application of chaos theory to practical problems."--Carl Murray, New Scientist "This is a how-to book on how to construct a low energy orbit from the earth to the moon by the man who did just that to save the Japanese space mission in 1990."--Ken Meyer, SIAM Review

• List of Figures vii Foreword xi Preface xiii Chapter 1. Introduction to the N -Body Problem 1 1.1 The N -Body Problem 1 1.2 Planar Three-Body Problem 9 1.3 Two-Body Problem 11 1.4 Regularization of Collision 16 1.5 The Restricted Three-Body Problem: Formulations 24 1.6 The Kepler Problem and Equivalent Geodesic Flows 35 Chapter 2. Bounded Motion, Cantor Sets, and Twist Maps 49 2.1 Quasi-Periodicity and the KAM Theorem 50 2.2 The Moser Twist Theorem, Cantor Sets 59 2.3 Area-Preserving Maps, Fixed Points, Hyperbolicity 66 2.4 Periodic Orbits and Elliptic Fixed Points 78 2.5 Aubrey-Mather Sets and the Restricted Three-Body Problem 91 Chapter 3. Capture 103 3.1 Introduction to Capture 105 3.2 The Weak Stability Boundary 120 3.3 Existence of Primary Interchange Capture and an Application 131 3.4 A Low Energy Lunar Transfer Using Ballistic Capture 144 3.5 Parabolic Motion, Hyperbolic Extension of W 156 3.6 Existence of a Hyperbolic Network on W H 165 Bibliography 193 Index 209

Edward Belbruno has been a Visiting Research Collaborator in the Program in Applied and Computational Mathematics at Princeton University since 1998. The author of numerous articles in professional journals in mathematics, astronomy, and aerospace engineering, he received the Laurel Award in 1999 for the salvage of a Hughes satellite in 1998 using lunar transfer.

"You have just launched a multimillion dollar communications satellite into space. A malfunction means your expensive cargo will not reach its required orbit. Who are you going to call? A good choice would be Edward Belbruno, a celestial mechanician who seems to specialize in such lost causes... Capture Dynamics is the first book to describe the necessary theory in the context of the whole process of capture... The result is a brilliant example of the application of chaos theory to practical problems."--Carl Murray, New Scientist "This is a how-to book on how to construct a low energy orbit from the earth to the moon by the man who did just that to save the Japanese space mission in 1990."--Ken Meyer, SIAM Review

• List of Figures vii Foreword xi Preface xiii Chapter 1. Introduction to the N -Body Problem 1 1.1 The N -Body Problem 1 1.2 Planar Three-Body Problem 9 1.3 Two-Body Problem 11 1.4 Regularization of Collision 16 1.5 The Restricted Three-Body Problem: Formulations 24 1.6 The Kepler Problem and Equivalent Geodesic Flows 35 Chapter 2. Bounded Motion, Cantor Sets, and Twist Maps 49 2.1 Quasi-Periodicity and the KAM Theorem 50 2.2 The Moser Twist Theorem, Cantor Sets 59 2.3 Area-Preserving Maps, Fixed Points, Hyperbolicity 66 2.4 Periodic Orbits and Elliptic Fixed Points 78 2.5 Aubrey-Mather Sets and the Restricted Three-Body Problem 91 Chapter 3. Capture 103 3.1 Introduction to Capture 105 3.2 The Weak Stability Boundary 120 3.3 Existence of Primary Interchange Capture and an Application 131 3.4 A Low Energy Lunar Transfer Using Ballistic Capture 144 3.5 Parabolic Motion, Hyperbolic Extension of W 156 3.6 Existence of a Hyperbolic Network on W H 165 Bibliography 193 Index 209