N-Body Gravity

Every body exerts a gravitational pull on every other body simultaneously. Force is calculated using F = Gm₁m₂ / r² — force grows with mass and drops with the square of distance.

For 3 or more bodies, there is no general mathematical solution — the motion is inherently chaotic and unpredictable over long timescales. This is one of physics' oldest unsolved problems.

Discovered in 1993 by mathematician Chenciner, the Figure-8 is a rare, exact periodic solution where 3 equal-mass bodies chase each other in a figure-8 shape. Extraordinarily precise initial conditions are required — slight errors cause it to break apart.

The simulation uses a leapfrog-style Euler integrator with sub-stepping (4 steps per frame) for stability. A softening factor prevents infinite forces when bodies get too close.