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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