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We saw earlier, in Section 6.2, that an isolated dynamical system consisting of two freely moving point masses exerting forces on one another--which is usually referred to as a two-body problem--can always be converted into an equivalent one-body problem. In particular, this implies that we can exactly solve a dynamical system containing two gravitationally interacting point masses, since the equivalent one-body problem is exactly soluble--see Chapter 5 and Section 6.3. What about a system containing three gravitationally interacting point masses? Despite hundreds of years of research, no exact solution of this famous problem--which is generally known as the three-body problem--has ever been found. It is, however, possible to make some progress by severely restricting the problem's scope.

Richard Fitzpatrick 2011-03-31