Statistical theory of interiorexterior
transition and collision probabilities for minor bodies in the
solar system
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
transition between the interior and exterior Hill's regions, temporary
capture, and collision. The invariant manifold structures of the
collinear libration points for the planar, circular
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. The stable and unstable invariant manifold
tubes associated to libration point orbits are the phase space
structures that provide a conduit for particles travelling to and from
the secondary body (e.g., Jupiter). Using the structures around
libration points, a statistical theory of the probability of
interiorexterior transition and the probability of
collision with the secondary body can be developed. Comparisons
with observations of Jupiter family comets are made.
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