Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997a%26a...319..290w&link_type=abstract
Astronomy and Astrophysics, v.319, p.290-304
Astronomy and Astrophysics
Astrophysics
20
Chaos, Celestial Mechanics, Minor Planets
Scientific paper
Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted three-body problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincar e surfaces of section with a mass ratio of 10^-3^ (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the `evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.
Cabo Winter Othon
Murray Carl D.
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