A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets

Understand

We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets.

• Given the planets' masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered.
• Chaos occurs where mean motion resonances overlap, as in Wisdom (1980)'s pioneering work.
• But whereas Wisdom considered only nearly circular planets, and hence examined only first order resonances, we extend his results to arbitrarily eccentric planets (up to crossing orbits) by examining resonances of all orders.