On the origin of chaotic behavior in the 2/1 Kirkwood Gap

The Henrard and Lemaitre (1986) perturbation method is presently applied to the 2/1 Jovian resonance, in the planar elliptic three-body problem, in order to identify those features leading to the generation of chaotic layers. These features are (1) the crossing of the separatrices of the circular problem and (2) separatrices of the one-DOF system, averaged over the circular problem's libration. The 2/1 resonance's semianalytical treatment compares favorably with the numerical results of Murray (1986) and Wisdom (1987); a large volume of the phase space appears unaffected by these chaotic layers, and exhibits no eccentricity increases sufficient to render the asteroid's orbit a Mars-crosser. The theory of 2/1 Kirkwood gap formation through asteroid removal by Martian encounters is not supported by these results. 28 refs