Planetary close encounters: Probability distributions of resultant orbital elements and applications to Hidalgo and Chiron

A method is described for computing the probability distributions of the new orbital elements (a, e, i, q, q′) of a minor body which is subject ot close encounters with a planet. By including the frequency of such encounters the rate at which one class of orbit is transposed into a new class (e.g., Mars-crossing asteroids changed into Apollos) can be estimated. By applying this technique to the cases of Hidalgo and Chiron its uses are illustrated, and its limitations due to the two, two-body approximation utilized are pointed out.