Resonances of the Kuiper Belt

Chaos in Mean Motion Resonances of the Kuiper Belt

Authors:

Franklin et al

Abstract:

In this paper on mean motion resonances in the Kuiper belt we consider effects on resonant bodies captured in an earlier migration by determining levels of chaos as a function of eccentricity, e, at the most stable orbital configuration. We find the the maximum observed e's at resonance very closely correspond to orbits with Lyapunov times ~ 1000 orbital periods of Neptune--much the same number as applies in the asteroid belt with Neptune's period replaced by Jupiter's. The fact that this number caps the e's of markedly chaotic but still existing bodies, implies that the great majority of escapes at equal and larger e's have already occurred. Yet escapes must continue at some level if the small population in the outermost belt is to be maintained because typical lifetimes of bodies there are only ~ 1/10 of the solar system's age. A study of stability at resonance also reinforces the claim that the post-migration boundary of the inner Kuiper belt lies near 34 AU and that the primordial, or pre-migration, outer one near 46 AU.