An Examination of the Relation Between Chaotic Orbits and the Kirkwood Gap at the 2:1 Resonance. II. Escaping Orbit

Details An Examination of the Relation Between Chaotic Orbits and the Kirkwood Gap at the 2:1 Resonance. II. Escaping Orbit An Examination of the Relation Between Chaotic Orbits and the Kirkwood Gap at the 2:1 Resonance. II. Escaping Orbit

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aj....112.1247f&link_type=abstract

Astronomical Journal v.112, p.1247

Astronomy and Astrophysics

Astronomy

2

Chaotic Phenomena, Solar System: General, Instabilities

Scientific paper

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 109 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 well-known Kirkwood gap is more closely related to dynamical instability than just to collisions with any terrestrial planet.

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