n-body problem

This article is about the problem in classical mechanics. For the problem in quantum mechanics, see Many-body problem. For engineering problems and simulations involving many components, see Multibody system and Multibody simulation.

In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars.

The classical physical problem can be stated as follows:

Each particle in a system of a finite number of particles is subjected to a Newtonian gravitational attraction from all the other particles, and to no other forces. If the initial state of the system is given, how will the particles move?

The two-body problem has been completely solved and is discussed below. For three or more bodies the problem can only be solved completely in particular cases. In general, the problem is chaotic and can only be solved numerically.

The n-body problem in general relativity is considerably more difficult to solve.

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