Mathematics – Logic
Scientific paper
Oct 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002icar..159..284t&link_type=abstract
Icarus, Volume 159, Issue 2, p. 284-299.
Mathematics
Logic
12
Scientific paper
We have shown, in previous publications, that stable chaos is associated with medium/high-order mean motion resonances with Jupiter, for which there exist no resonant periodic orbits in the framework of the elliptic restricted three-body problem. This topological ``defect'' results in the absence of the most efficient mechanism of eccentricity transport (i.e., large-amplitude modulation on a short time scale) in three-body models. Thus, chaotic diffusion of the orbital elements can be quite slow, while there can also exist a nonnegligible set of chaotic orbits which are semiconfined (stable chaos) by ``quasi-barriers'' in the phase space. In the present paper we extend our study to all mean motion resonances of order q<=9 in the inner main belt (1.9-3.3 AU) and q<=7 in the outer belt (3.3-3.9 AU). We find that, out of the 34 resonances studied, only 8 possess resonant periodic orbits that are continued from the circular to the elliptic three-body problem (regular families), namely, the 2/1, 3/1, 4/1, and 5/2 in the inner belt and the 7/4, 5/3, 11/7, and 3/2 in the outer belt. Numerical results indicate that the 7/3 resonance also carries periodic orbits but, unlike the aforementioned resonances, 7/3-periodic orbits belong to an irregular family. Note that the five inner-belt resonances that carry periodic orbits correspond to the location of the main Kirkwood gaps, while the three outer-belt resonances correspond to gaps in the distribution of outer-belt asteroids noted by Holman and Murray (1996, Astron. J.112, 1278-1293), except for the 3/2 case where the Hildas reside. Fast, intermittent eccentricity increase is found in resonances possessing periodic orbits. In the remaining resonances the time-averaged elements of chaotic orbits are, in general, quite stable, at least for times t~250 Myr. This slow diffusion picture does not change qualitatively, even if more perturbing planets are included in the model.
Hadjidemetriou John D.
Tsiganis Kleomenis
Varvoglis Harry
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