Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, two stars orbiting each other, and a classical electron orbiting an atomic nucleus. The two-body problem can be re-formulated as two independent one-body problems, which involve solving for the motion of one particle in an external potential. Since many one-body problems can be solved exactly, the corresponding two-body problem can also be solved. By contrast, the three-body problem cannot be solved, except in special cases.

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