The Geometry of Celestial Mechanics

Description

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 Content: Preface 1. The central force problem 2. Conic sections 3. The Kepler problem 4. The dynamics of the Kepler problem 5. The two-body problem 6. The n-body problem 7. The three-body problem 8. The differential geometry of the Kepler problem 9. Hamiltonian mechanics 10. The topology of the Kepler problem Bibliography Index.