Scattering of Planetesimals by a Planet: Formation of Comet Cloud Candidates

We have investigated the first dynamical stage of comet cloud formation, the scattering of planetesimals by a planet. The orbits of planetesimals were calculated using circular restricted three-body formalism. We obtained the probabilities of the following results of scattering as functions of the orbital parameters of the planets and planetesimals: (1) collision with the planet, (2) escape from the planetary system, and (3) candidacy as a member of the comet cloud (planetesimals with large semimajor axes). We also derived simple empirical formulae for these probabilities that are accurate enough for order-of-magnitude estimation. We found that a planetesimal with an initial eccentricity of e 0.4 can escape from the planetary system or be a candidate for an element of the comet cloud due to scattering by a planet. As the energy range of the comet cloud is narrow, the probability of any planet producing escapers is always much higher than that of producing candidates. Using the probabilities and assuming a distribution of planetesimals, we obtained the efficiencies of collision, escape, and candidacy for a given planet. We applied the results to the solar system and found that, among the four giant planets, Jupiter is the planet most responsible for producing candidate elements of the Oort Cloud, as long as the inclination of planetesimals is constant or proportional to the reduced Hill radius of each planet.