Kirkwood Gap Eccentricity Pumping

The Kirkwood gaps are conspicuous empty lanes in the asteroid belt at semi-major axes that put an asteroid in a low-order mean-motion resonance with Jupiter — 4:1, 3:1, 5:2 and 2:1. This simulator numerically integrates a single test asteroid under the gravity of the Sun and a circularly orbiting Jupiter (the restricted three-body problem) and tracks its osculating semi-major axis, eccentricity and resonant angle in real time. Drop the asteroid exactly on a resonance and its resonant angle circulates while its eccentricity random-walks upward — the chaotic mechanism, discovered by Jack Wisdom in the early 1980s, that clears the gap over geological time. Drop it between resonances instead and the orbit stays quietly near-circular.