http://groups.csail.mit.edu/mac/users/wisdom/kirkwood.pdf

Chaotic behavior and the origin of the 3/1 Kirkwood gap

A perturbative treatment of motion near the 3/1 commensurability

https://www.boulder.swri.edu/~davidn/papers/morbidelli.1999.pdf

Numerous Weak Resonances Drive Asteroids toward Terrestrial Planets Orbits

Urey Prize Lecture - Chaotic dynamics in the solar system

We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, Tc, is a function of the Lyapunov time, T ly. The relation is log(T c /T o) = a + b log(T ly /T o) where T o is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a “zero velocity curve”. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T o. This is the case of interest for the planets in the solar system.

/pdf/chaos-in-the-solar-system-2dyqcnceja.pdf

Chaos in the solar system

A Study of Commensurable Motion in the Asteroid Belt

The motion at the 3/2 Hilda resonance and the motion at the 2/1 Hecuba resonance are compared in an effort to explain the differences between the two motions. The comparison suggests the hypothesis that, in the Hilda case, the existence of invariant curves makes motion resonance with Jupiter possible over a wide range of eccentricities while, in the Hecuba case, these curves exist only for large eccentricities. (IAA)

R. B. Giffen

Papers

A Study of Commensurable Motion in the Asteroid Belt

A study of commensurable motion in the asteroid belt.