Planar Three-Body Problem in Phase Space

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Trajectories of three point masses , , interacting via Newtonian force fields in 2D (planar three‚Äźbody 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.

Contributed by: Michael Trott (September 2007)
Suggested by: Stephen Wolfram
Open content licensed under CC BY-NC-SA


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The three-body problem is one of the simplest mechanical systems that exhibits 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, …



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