Collisional Processes of Planetesimals with a Protoplanet under the Gravity of the Proto-Sun

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Abstract
We investigate collisional processes of planetesimals with a protoplanet, assuming that the mass of the protoplanet is much larger than that of a planetesimal and the motion of the planetesimal is limited in the two-dimensional ecliptic plane. Then, we can describe the orbit by a solution to the plane circular Restricted Three-Body problem. Integrating numerically the equations of motion of the plane circular RTB problem for numerous sets of initial osculating orbital elements, we obtain the overall features of the encounters between the Keplerian particles. In this paper we will represent only the cases e=0 and 4h, where e is the eccentricity of the planetesimal far from the protoplanet and h is the normalized Hill radius of the protoplanet. We find that the collisional rate of Keplerian particles is enhanced by a factor of about 2.3 (e=0) or 1.4 (e=4h) compared with that of particles in a free space, as long as we are concerned with the two-dimensional motion of particles.