3-Body Problem Simulator

The three-body problem is chaotic but not random. Chaos means tiny differences in initial conditions grow exponentially — but refreshing the page changes nothing: same initial positions, same velocities, same dt, same algorithm, same result every time. Deterministic chaos and computational reproducibility are two different things. To actually see the chaos: set perturbation to 0.000001 and watch the dashed twin trajectory. Both trajectories start 10⁻⁶ apart and eventually diverge into completely different paths. That exponential separation is the chaos — the Lyapunov exponent at work. The divergence chart below the orbits plots log₁₀ of that separation over time; a straight rising line means exponential growth.

Two bodies pulling on each other trace simple, endlessly repeating ellipses — that case Newton solved with pen and paper. Add a third body and the neat formula disappears: there is no general equation for where everyone ends up, so the only way forward is to advance the simulation one tiny dt at a time, exactly as this tool does. Click the figure-8 preset to meet one of the rare exceptions — three equal masses forever chasing each other along a single looping path.

People often call the three-body problem 'unsolvable', yet in 1912 Karl Sundman proved a convergent power series in t^1/3 that yields the bodies' positions for all time (barring triple-collision starts). The catch: it converges so slowly that astronomical accuracy would demand on the order of 10^8000000 terms — hopelessly beyond any computer. A formal solution truly exists; stepping the simulation forward, as here, is simply the only usable route.