Modelling close encounters with Öpik's theory

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