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 Öpik's theory of close encounters, for an experimental set-up similar to that used by Froeschlé 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 Öpik's theory, as long as the comparison is made on the outcomes of encounters only up to a certain unperturbed distance b_max; several values of the latter are experimented with and it is found that, surprisingly, Öpik's theory seems to be still working reasonably well for values of b_max in excess of several times the Hill's radius of the planet.