A Statistical Theory of Transition and Collision Probabilities
Shane D. Ross
Control and Dynamical Systems, California Institute of Technology
MC 10781, Pasadena, CA 91125, USA. Email: shane@cds.caltech.edu
ABSTRACT
The dynamics of comets and other solar system objects which have a threebody
energy close to that of the collinear libration points are known to exhibit a complicated
array of behaviors such as rapid transition between the interior and exterior Hillls
regions, temporary capture, and collision. The invariant manifold structures of the
collinear libration points for the restricted threebody problem, which exist for a
range of energies, provide the framework for understanding these complex dynamical
phenomena from a geometric point of view. In particular, the stable and unstable
invariant manifold tubes associated to libration point orbits are the phase space
structures that provide a conduit for orbits travelling to and from the smaller primary
body (e.g., Jupiter). Using the structures around libration points, a statistical
theory for the probability of transition between the interior and exterior Hill's regions
and collision with the smaller primary body can be developed. Comparisons with
observations of Jupiter family comets are made.
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