There is no general closed-form solution to the three-body problem, meaning there is no general solution that can be expressed in terms of a finite number of standard mathematical operations. For these reasons, it has occupied an important role in the historical development of the three-body problem. It is of practical interest as well since it accurately describes many real-world problems, the most important example being the Earth–Moon–Sun system.
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The restricted three-body problem is easier to analyze theoretically than the full problem. Usually this two-body motion is taken to consist of circular orbits around the center of mass, and the planetoid is assumed to move in the plane defined by the circular orbits. Having negligible mass, the force that the planetoid exerts on the two massive bodies may be neglected, and the system can be analysed and can therefore be described in terms of a two-body motion. In the restricted three-body problem, a body of negligible mass (the "planetoid") moves under the influence of two massive bodies.
In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun. Unlike two-body problems, no general closed-form solution exists, as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required. The three-body problem is a special case of the n-body problem. In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. For other uses, see Three-body problem (disambiguation). For the Chinese science fiction novel by Liu Cixin, see The Three-Body Problem (novel).
This article is about the physics and classical mechanics theory.
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