Transport of Mars-Crossing Asteroids from the Quasi-Hilda Region

We employ set oriented methods in combination with graph partitioning algorithms to identify key dynamical regions in the Sun-Jupiter-particle three-body system. Transport rates from a region near the $3:2$ Hilda resonance into the realm of orbits crossing Mars’ orbit are computed. In contrast to common numerical approaches, our technique does not depend on single long term simulations of the underlying model. Thus, our statistical results are particularly reliable since they are not affected by a dynamical behavior which is almost nonergodic (i.e., dominated by strongly almost invariant sets).

Figure 1

The mixed phase space structure of the PCRTBP is shown on this SOS. KAM (Kolmogorov-Arnold-Moser) tori and the chaotic sea are visible. The bright line corresponds to a line of constant periapse. In this case the periapse is equal to the semimajor axis of Mars’ orbit around the Sun.

Figure 2

A decomposition of a Poincaré SOS into three almost-invariant sets is shown for the mixed regular and chaotic phase space of the restricted three-body problem. The quasi-Hilda region and Mars-crossing line are labeled.

Figure 3

Decomposition of the SOS including the quasi-Hilda region $R$ and the region beyond the Mars-crossing line $Q$ as used for the transport computation.

Figure 4

Transition probability for a particle from the quasi-Hilda region to the Mars-crossing region as a function of the number of iterates of the return map.