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We saw earlier, in Section 2.9, 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, because the equivalent one-body problem is exactly soluble. (See Sections 2.9 and 4.16.) What about a system containing three gravitationally interacting point masses? Despite hundreds of years of research, no useful general solution of this famous problem--which is usually called 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 2016-03-31