Laplace Resonance Simulator

Jupiter's three inner Galilean moons — Io, Europa and Ganymede — are locked in the Laplace resonance: their orbital periods sit in an almost exact 1:2:4 ratio, so gravitational nudges between them repeat at the same orbital phase, orbit after orbit, instead of averaging away. This simulator plays out that lock in real time, tracking the resonant angle φ = λ_Io − 3λ_Europa + 2λ_Ganymede as it librates around 180° rather than drifting freely — the reason the three moons can never all line up with Jupiter simultaneously, and the same mechanism that keeps Io's interior flexing hot enough to drive its volcanoes.