Three-body problem

In physics, specifically classical mechanics, the three-body problem involves taking the initial positions and velocities (or momenta) of three point masses and calculating their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.^[1]

Unlike the two-body problem, the three-body problem has no general closed-form solution,^[1] and it is impossible to write a standard equation that gives the exact movements of three bodies orbiting each other in space. When three bodies orbit each other, the resulting dynamical system is chaotic for most initial conditions, and the only way to predict the motions of the bodies is to calculate them using numerical methods.

The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun.^[2] 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.