Chaos 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, Tty.The relation is log (Tc/To)= a + b log (TlyTo)where Tois 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 To.This is the case of interest for the planets in the solar system.