[Previous] | [Session 63] | [Next]
A.L. Erickcek (Princeton U, Harvard-Smithsonian CfA), M.J. Holman (Harvard-Smithsonian CfA)
One subpopulation of objects in the Kuiper belt region beyond Neptune is the scattered disk. The orbits of most scattered disk objects have large semi-major axes and correspondingly high eccentricities, permitting intermittent scattering by Neptune. However, one recently discovered body (2000 CR105) has a perihelion distance that is too large for direct scattering by Neptune (Gladman et al 2001). Nevertheless, the orbit of this body is strongly chaotic. Analytic calculations of the widths of mean motion resonances in the extended scattered disk indicate that adjacent resonances overlap at eccentricities near the Neptune-crossing threshold (Holman et al 2001). This overlap may account for the chaos in the orbit of 2000 CR105.
Here, we present an algorithm which automatically locates the stability region associated with a given mean motion resonance. This technique, an extension of that of Malhotra (1996), complements the purely analytic approach by numerically tracing the boundaries of stable regions in phase space containing quasiperiodic orbits near the given mean motion resonance. We demonstrate this technique for a number of mean motion resonances and compare the results to the analytic calculations. In several cases, the stable regions corresponding to adjacent resonances in the extended scattered disk are separated by chaotic zones of comparable width for all eccentricities, even those near the Neptune-crossing threshold. The existence of these chaotic regions confirms the analytical prediction that the outer resonances overlap at these eccentricities and provides further support for the resonance-overlap explanation for the chaotic behavior of 2000 CR105.
This project was conducted as part of the SAO Summer Intern Program, which is supported by the NSF REU (AST-9731923) program.