Three-Body Problem

Gravitational chaos — sensitive dependence on initial conditions

Configuration

Three-Body Problem:
No general closed-form solution (Poincaré, 1890). Only ~20 periodic families known (Chenciner-Montgomery 2000: figure-8).

The shadow system (dashed) starts with a tiny perturbation ε — watch trajectories diverge exponentially.

Lyapunov time: characteristic timescale for exponential separation. Solar system: ~5 Myr.
Time: 0
Separation:
Energy drift: