ORBITAL EVOLUTION OF PROTOPLANETS EMBEDDED IN A SWARM OF PLANETESIMALS

Orbital evolution of protoplanets embedded in a swarm of planetesimals has been investigated to study the late stage of planetary formation when protoplanets suffer perturbations among themselves and dynamical friction by surrounding planetesimals. We investigated the orbital evolution through direct three-dimensional N-body simulations. We found that the orbital separation between two protoplanets on circular orbits cannot be smaller than about 5r(H), where r(H) is the Hill radius of the two protoplanets. If it is smaller than about 5r(H), two protoplanets approach closely and experience close encounters. This protoplanet-protoplanet scattering increases their eccentricities and expands their orbital separation. Dynamical friction by planetesimals does not work effectively during such an impulsive scattering. After the scattering, dynamical friction damps the gained eccentricities gradually and makes their orbits nearly circular again, keeping the expanded orbital separation. This repulsion of two nearly circular orbits continues until their separation becomes larger than about 5r(H), when the protoplanet-protoplanet scattering is no longer effective. As protoplanets grow, their orbital separation measured by the Hill radius becomes small since r(H) proportional to M(1/3), where M is the mass of the protoplanet. They repeat the repulsion while growing. In conclusion, two protoplanets grow keeping their orbits nearly circular and their orbital separation larger than about 5r(H) without orbit crossing. Based on these results, we describe a scenario for the late stage of planetary formation. (C) 1995 Academic Press, Inc.