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Astron. Astrophys. 328, 399-408 (1997)

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Resonance and chaos

II. Exterior resonances and asymmetric libration

O.C. Winter 1, 2 and C.D. Murray 2

1 Grupo de Dinâmica Orbital e Planetologia, Campus Guaratinguetá, UNESP, CP 205, CEP 12500-000, Guaratinguetá, São Paulo, Brazil
2 Astronomy Unit, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, UK

Received 23 September 1996 / Accepted 18 December 1996


The motion of a test particle in the vicinity of exterior resonances is examined in the context of the planar, circular, restricted three-body problem. The existence of asymmetric periodic orbits associated with the [FORMULA] resonances (where [FORMULA]) is confirmed; there is also evidence of asymmetric resonances associated with larger values of n. A detailed examination of the evolution of the family of orbits associated with the 1:2 resonance shows the sequence that leads to asymmetric libration. On the basis of numerical studies of the phase space it is concluded that the existence of asymmetric libration means that the region exterior to the perturbing mass is more chaotic than the interior region. The apparent absence of `particles' in [FORMULA] resonances in the solar system may reflect this inherent bias.

Key words: chaos – dynamics – asteroids


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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998