The Geometry of Celestial Mechanics (London Mathematical Society Student Texts, Series Number 83)

"Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics." --From publisher's description Front Matter 1 Contents 5 Preface 7 1 The Central Force Problem 15 2 Conic Sections 24 3 The Kepler Problem 37 4 The Dynamics of the Kepler Problem 50 5 The Two-body Problem 65 6 The N-body problem 69 7 The Three-body problem 91 8 The Differential Geometry of the Kepler Problem 115 9 Hamiltonian Mechanics 180 10 The Topology of the Kepler Problem 208 References 223 Index 229 Hansjörg Geiges, University Of Cologne. Includes Bibliographical References And Index.