An Examination of the Relation Between Chaotic Orbits and the Kirkwood Gap at the 2:1 Resonance. II. Escaping Orbit
Abstract
This paper has a very simple motivation: will an integration of especially chaotic orbits within the 2:1 mean motion resonance with Jupiter lead to an escape from this resonance in times less than the solar system' S age? We chose for the very chaotic specimens three orbits with Lyapunov times near 1000 yr, all of which initially lay near secondary resonances, i.e., where the ratios of the libration to apsidal frequencies were small integers. All three clearly escaped from the mean motion resonance (apparently the first instance of this behavior) in slightly less than 10^{9} yr. These integrations allow us to follow escaping orbits in some detail. Because objects can readily move into a secondary resonance, thereby becoming severely chaotic, escape may be far more common than one might at first suppose. A far less chaotic orbit, integrated for above time, remained in the 2:1 resonance. Eccentricities of the three escapers rose above 0.5 (i.e., the value required to cross Mars' orbit) only just prior to escape. Thus we suspect that a depopulation of this resonance to form the wellknown Kirkwood gap is more closely related to dynamical instability than just to collisions with any terrestrial planet.
 Publication:

The Astronomical Journal
 Pub Date:
 September 1996
 DOI:
 10.1086/118095
 Bibcode:
 1996AJ....112.1247F
 Keywords:

 CHAOTIC PHENOMENA;
 SOLAR SYSTEM: GENERAL;
 INSTABILITIES