Three-Body Choreographies
The three-body problem has no general closed-form solution, but it hides a handful of exact periodic solutions of startling beauty. This tool integrates three equal masses under Newtonian gravity and starts them on famous "choreographies" — orbits where the bodies chase each other around a single shared curve. The most famous is the figure-eight, discovered numerically by Moore in 1993 and proved to exist by Chenciner and Montgomery in 2000, in which three stars trace the same figure-eight forever. Pick a preset, watch the bodies weave with their trails, then nudge the launch slightly and see the delicate orbit dissolve into chaotic scattering, the generic fate of three gravitating bodies.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- A choreography is a periodic n-body orbit in which every body follows the same closed curve, evenly spaced in time; the figure-eight is the simplest and most stable known example for three equal masses.
- These orbits are measure-zero islands of order in a sea of chaos: an arbitrarily small change to the initial positions or velocities almost always leads to exponential divergence and eventual ejection of one body.
- The energy and angular momentum are conserved by a symplectic integrator here, which is what keeps a delicate periodic orbit from spiralling apart through numerical drift over many loops.
- Runs 100% in your browser — simulations are computed locally on your device.
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