Circumbinary Planet Stability Zone

A planet orbiting both stars of a binary pair — a "P-type" or circumbinary orbit, like the real Kepler-16b — only survives if it starts far enough out. This simulator numerically integrates a massless planet under the true time-varying gravity of two mutually orbiting stars (a restricted three-body problem, solved with 4th-order Runge–Kutta) and compares the outcome live against the Holman & Wiegert (1999) empirical critical-radius formula, the same relation astronomers use to check whether a discovered circumbinary planet's orbit is dynamically stable. Set the binary's mass ratio and eccentricity, launch the planet at any starting radius, and watch it either settle into a bounded quasi-periodic orbit or get chaotically pumped into ejection as close encounters with the stars grow.