Hill Sphere: A Planet's Gravitational Reach

Every planet shares the Sun's gravity with everything around it — a moon can only stay bound to its planet inside a finite bubble called the Hill sphere, where the planet's own pull beats the Sun's tidal tug. This simulator runs a real restricted three-body integration: a test moon feels genuine Newtonian gravity from both the Sun and a chosen planet at every timestep (4th-order Runge-Kutta, not a shortcut formula), while the planet follows its own unperturbed orbit. Pick any of the eight planets, move it closer to or farther from the Sun, and release the moon at a chosen fraction of the Hill radius with a chosen speed and direction — then watch it stay bound, precess near the edge, or get torn away entirely, with live readouts of the Hill radius and the moon's real distance from the planet.