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. Poincaré'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. This book should be essential reading for students in a rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level. 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. Poincaré'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. 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. "How do three celestial bodies move under their mutual gravitational attraction? It is a problem that 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 new possibilities of dealing with it: a statistical approach. For the first time such methods are presented in a systematic way. The book surveys statistical methods as well as more traditional methods, suitable for students of celestial mechanics at advanced undergraduate level."-- Jaquette "How do three celestial bodies move under their mutual gravitational attraction? It is a problem that 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 new possibilities of dealing with it: a statistical approach. For the first time such methods are presented in a systematic way. The book surveys statistical methods as well as more traditional methods, suitable for students of celestial mechanics at advanced undergraduate level."--Jacket The book 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 is essential reading for students in this rapidly expanding field. The three-body problem arises in many different contexts in nature.