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Stable Chaos versus Kirkwood Gaps in the Asteroid Belt: A Comparative Study of Mean Motion Resonances

โœ Scribed by Kleomenis Tsiganis; Harry Varvoglis; John D. Hadjidemetriou


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
797 KB
Volume
159
Category
Article
ISSN
0019-1035

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โœฆ Synopsis


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 โ‰ค 9 in the inner main belt (1.9-3.3 AU) and q โ‰ค 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 outerbelt 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 โˆผ 250 Myr. This slow diffusion picture does not change qualitatively, even if more perturbing planets are included in the model.


๐Ÿ“œ SIMILAR VOLUMES


Comparative Study of Mean-Motion Resonan
โœ M.D. Melita; A. Brunini ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 841 KB

In this work we are interested in the present dynamical structure of the trans-neptunian region. It is known that at moderate to high eccentricities, stable orbits lie close to an exterior-mean-motion resonance with Neptune (NMMR). We study some NMMRs under different points of view. Intrinsic probab