Trajectories of three point masses , , interacting via Newtonian force fields in 2D (planar three-body problem). This Demonstration allows you to vary the initial positions and velocities of the three bodies and their masses. We start the dance with a choreography by Chenciner and Montgomery.

The three-body problem is one of the simplest mechanical systems that exhibit nonintegrability and chaos. (The two-body problem with retardation is conceptually simpler but trickier to calculate.) Depending on the initial conditions, the system exhibits periodic orbits, escape to infinity in finite time, collision singularities, triple collisions, quasi-bound states, …