On the origin of chaotic behavior in the [formula omitted] Kirkwood gap

Abstract

We apply to the 2 1 Jovian resonance in the planar elliptic three-body problem a perturbation method we have presented in a previous paper (J. Henrard and A. Lemaitre 1986. Celest. Mech. 39, 213–238). Our aim is to identify those features which lead to the apparition of chaotic layers: crossing of the separatrices of the “circular” problem (slow Hamiltonian chaos), and separatrices of the one degree of freedom system averaged over the libration of the “circular” problem (fast Hamiltonian chaos and secondary resonances). The semianalytical treatment of the 2 1 resonance compares well with results of numerical investigations by C.D. Murray (1986, Iracus 65, 70–82) and J. Wisdom (1987, Icarus 72, 241–275). We find that a large volume of the phase space does not seem to be affected by these chaotic layers and does not show increases in the eccentricity (increases large enough for the asteroid to become a Mars crosser). This picture does not support the theory of the formation of the 2 1 Kirkwood gap by removal of the asteroids through close encounters with Mars.