The **two-body problem** is simple; its solution is that each body travels along a conic section which has a focus at the centre of mass of the system.

The **three-body problem** is much more complicated; its solution can be chaotic. The general three-body problem has not been solved analytically,
although approximate solutions can be calculated by numerical methods or perturbation methods.

A restricted three-body problem, in which two of the bodies are in circular orbits and the third is of negligible mass (approximated by the Sun - Earth - Moon system) was solved analytically by Lagrange in the 18th century. The points where the smallest object can orbit the other two with the same period are called Lagrangian points.