MODELING CLOSE ENCOUNTERS WITH OPIKS THEORY

The results obtained by numerical integration of the equations of moti on of fictitious comets, in the restricted circular three-dimensional three-body problem, are compared with those obtained with Opik's theor y of close encounters, for an experimental set-up similar to that used by Froeschle and Rickman (1980-1981) to model both the infeed of come ts from the trans-jovian region into the Jupiter family and their subs equent orbital evolution within the family. The distributions of pertu rbations in orbital energy E, eccentricity e and inclination i are wel l reproduced by Opik's theory, as long as the comparison is made on th e outcomes only up to a certain unperturbed distance b(max); several v alues of the latter are experimented with and it is found that, surpri singly, Opik's theory seems to be still working reasonably well for th e values of b(max) in excess of several times the Hill's radius of the planet. (C) 1998 Elsevier Science Ltd. All rights reserved.