Kirkwood Gap Resonant-Angle Phase Portrait (2D)

This 2D companion to the Kirkwood-gap orbit simulator runs the exact same restricted three-body integration — a massless test asteroid under the Sun's and a circularly orbiting Jupiter's gravity, advanced with RK4 — but adds the diagnostic the 3D free-camera view cannot show: a live σ (resonant angle) versus e (eccentricity) phase portrait. Drop the asteroid on a named Jupiter resonance (4:1, 3:1, 5:2 or 2:1) and watch the phase-space trail either curl into a bounded libration island, meaning the orbit is trapped and stable, or sweep all the way across the σ axis while eccentricity climbs, meaning the orbit has entered the chaotic circulating regime that Jack Wisdom identified as the actual mechanism carving the Kirkwood gaps. Drop it at the stable 2.65 AU radius between gaps instead and the phase trail stays a tight, nearly circular dot cluster with negligible eccentricity growth.