Encounter frequency of Halley-like comets with the planets

We present the results of a numerical study on encounter frequencies of fictitious Halley-like comets with the planets in a dynamical model of the solar system, in which we take into account the gravitational forces of the Sun and the planets Venus through Neptune. The change of the orbital elements during a close approach with a planet was carefully monitored with the aid of a thoroughly tested numerical integration method with automatic step size control. We computed the encounter frequencies of the comets' orbits using two different spheres of influence and compared the results. In both cases, it turned out that the encounter frequency of the fictitious Halley-like comets with Jupiter and Saturn is about a factor 10 to 100 higher than for the other planets. Concerning the changes of the semi-major axes and inclinations our results show that an increase and decrease of these elements is equally probable after an encounter.