The distribution of energy perturbations at close
planetary encounters
G.B. Valsecchi
Istituto di Astrofisica Spaziale - Roma, Italy
Opik's theory of close encounters allows to deduce an analytic
expression for the distribution of energy perturbations at close
encounters between small bodies and planets. The derivation of
this expression highlights a simple geometric structure in the
b-plane, the plane containing the planet and perpendicular to
the unperturbed planetocentric velocity vector. We test the
validity of the analytic energy perturbation distribution against
the results of numerical integrations in the restricted circular
three-dimensional three-body problem, and explore the ranges of
masses and encounter circumstances for which it works
satisfactorily.