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three-body problem

The three-body problem is the mathematical problem of finding the positions and velocities of three massive bodies, which are interacting with each other gravitationally, at any point in the future or the past, given their present positions, masses, and velocities. An example would be to completely solve the behavior of the Sun-Jupiter-Saturn system, or that of three mutually orbiting stars. It is a vastly more difficult exercise than the two-body problem. In fact, as Henri Poincaré and others showed, the three-body problem is impossible to solve in the general case; that is, given three bodies in a random configuration, the resulting motion nearly always turns out to be chaotic: no one can predict precisely what paths those bodies would follow. However, the problem becomes tractable in certain special cases. (Encyclopedia of Science, by David Darling, https://www.daviddarling.info/encyclopedia/T/three-body_problem.html)

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