A Symplectic Mapping Model for the Study of 2:3 Resonant TransNeptunian Motion
Abstract
A symplectic mapping is constructed for the study of the dynamical evolution of EdgeworthKuiper belt objects near the 2:3 mean motion resonance with Neptune. The mapping is sixdimensional and is a good model for the Poincaré map of the `real' system, that is, the spatial elliptic restricted threebody problem at the 2:3 resonance, with the Sun and Neptune as primaries. The mapping model is based on the averaged Hamiltonian, corrected by a semianalytic method so that it has the basic topological properties of the phase space of the real system both qualitatively and quantitatively. We start with two dimensional motion and then we extend it to three dimensions. Both chaotic and regular motion is observed, depending on the objects' initial inclination and phase. For zero inclination, objects that are phaseprotected from close encounters with Neptune show ordered motion even at eccentricities as large as 0.4 and despite being Neptunecrossers. On the other hand, notphaseprotected objects with eccentricities greater than 0.15 follow chaotic motion that leads to sudden jumps in their eccentricity and are removed from the 2:3 resonance, thus becoming short period comets. As inclination increases, chaotic motion becomes more widespread, but phaseprotection still exists and, as a result, stable motion appears for eccentricities up to e = 0.3 and inclinations as high as i = 15°, a region where plutinos exist.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 October 2002
 Bibcode:
 2002CeMDA..84..135H
 Keywords:

 EdgeworthKuiper belt;
 resonance;
 chaotic motion;
 nonlinear stabilities