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Astron. Astrophys. 320, 672-680 (1997)

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Chaotic diffusion in the 2/1 asteroidal resonance

An application of the frequency map analysis

D. Nesvorný * and S. Ferraz-Mello

Instituto Astronômico e Geofísico, Universidade de São Paulo, Caixa Postal 9638, CEP 04301, São Paulo, Brasil

Received 29 August 1996 / Accepted 19 September 1996


We have applied the frequency map analysis of Laskar (1993) to the following dynamical models of the 2/1 asteroidal mean-motion resonance: the planar restricted three-body model and the planar restricted four-body model with Saturn. It allowed us to reproduce the chaotic region, which is formed by the overlap of secondary resonances in low eccentricities. We have examined the chaos generated by high-order secondary resonances in moderate eccentricities and concluded that, in the three-body planar model, most of the area remains regular even in the model with Jupiter's eccentricity equal to 0.061. But, when the basic secular frequencies of Jupiter's orbit were taken into account, the moderate-eccentricity region turned chaotic and a slow chaotic diffusion appeared. The diffusion was found to be more significant in the full, planar four-body model. Asteroids exhibited random excursions in the phase space and we studied this possible mechanism of resonance emptying in several 10-Myr integrations.

Key words: minor planets – celestial mechanics – chaos

* e-mail address: david@vax.iagusp.usp.br

Send offprint requests to: D. Nesvorný

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998