Three Bodies

Three masses, one closed curve — a solution nobody expected to exist. Two bodies under gravity have a closed-form answer: Kepler's ellipse. Three do not, and Poincaré proved in 1890 that none can. So the only way to know what they do is to step them forward and watch.

Eight systems, and what they are for


Figure eight	three equal masses chasing each other along ONE closed curve — found numerically in 1993, proved to exist in 2000
Lagrange triangle	an equilateral triangle rotating rigidly forever — one of only two exact solutions the problem has
Binary and a moon	the hierarchical case: the only reliably stable arrangement three bodies have
Sun and planets	the control — what the n-body problem looks like when it is not a problem
Chaotic trio	the generic case. The choreographies above are the freaks
Light body ×3	one experiment in three frames: stable inside, chaotic between, stable outside

Integrated with velocity Verlet rather than the more accurate Runge–Kutta, because Verlet is symplectic: its energy error oscillates instead of accumulating, so orbits stay closed for as long as you care to watch instead of slowly spiralling.

Try it

🪐 Watch them run — one screen: the orbits going, each body trailing the path it has actually travelled, the eight a click away and your own system a tab away. Move the light body outward step by step and find the boundary between the stable and the chaotic zones yourself.
📖 How it works — the law, the integrator, and why softening matters.

_{Rebuilt from the Systemorph Cloud many-body notebooks as a MeshWeaver node type. The orbits are integrated on every render and animated in the browser as SVG keyframes — no script, no timer, nothing stored that could disagree with the numbers.}