Mauri Valtonen, Hannu Karttunen - The Three-Body Problem

How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincare's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. The book begins by providing an introduction to celestial mechanics, including Lagrangian and Hamiltonian methods, and both the two and restricted three body problems. It then surveys statistical and perturbation methods for the solution of the general three body problem, providing solutions based on combining orbit calculations with semi-analytic methods for the first time. This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.

Review
"In The Three-Body Problem, readers will find the necessary theoretical ingredients and will also enjoy the variety of technical explanations for phenomena in the solar system and beyond. The book would be useful for a graduate course in modern astrophysics and makes interesting reading for an amateur who has some background in classical physics." - Martin Gutzwiller, Physics Today