Hill Sphere: A Planet's Gravitational Reach (2D)

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 2D top-down companion runs the same real restricted three-body integration as the 3D version: 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 in the plane. 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 a live inset showing the planet's own position around the Sun for context.