Circumbinary Planet Stability Zone — 2D

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 2D companion runs the identical restricted three-body RK4 integration as the 3D version, but views it in the frame co-rotating with the binary's mean motion, where the planet's Hill (zero-velocity) forbidden zone can be shaded directly and its Jacobi constant tracked over time. Watch that constant stay essentially frozen for a circular binary, then visibly drift once the binary is given an eccentric orbit — the live numerical signature of the chaotic energy pumping that ejects planets below the Holman & Wiegert (1999) critical radius.