Title: Stable Chaos and Kirkwood Gaps
Author(s): H. Varvoglis, K. Tsiganis, J. Hadjidemetriou (Oral)
ABSTRACT
It is well known since the 19th century that the Kirkwood gaps, observed
in the distribution of orbital periods of the asteroids, correspond to
simple commensurabilities with the orbital period of Jupiter.
Furthermore it is now widely accepted that the main gapdepletion
mechanism is related to the chaotic motion of asteroids, generated in
the vicinity of these resonances, which resulted in an increase of the
asteroids' eccentricities and eventually forced them to suffer close
encounters with the major planets. However, what was not well understood
so far, is why there are gaps only in the observed commensurabilities
and not in others, of comparable order, where chaotic motion is also
dominant, as it is evident in numerical simulations of even the simplest
dynamical models. We suggest that the answer to this question comes from
the fact that Jupiter does not follow a circular trajectory around the
Sun, as assumed in evaluating the commensurabilities. We show that a
resonance, calculated in the circular restricted threebody problem,
does not necessarily entail the existence of a corresponding periodic
trajectory in the elliptic one. As a consequence gaps could not be
formed in the vicinity of most of the resonances of the circular
problem, due to the above fact, unless secular mechanisms (in more
sophisticated dynamical models) act as well. In a resonance where a gap
cannot be formed, there exist semiconfined chaotic trajectories with
small Lyapunov times, for which a secular growth of the eccentricity s
almost undetectable. Therefore, although the trajectory of the asteroid
is chaotic, its orbital elements do not change appreciably for hundreds
of million years. This phenomenon is known as stable chaos.
