Orbital evolution of protoplanets embedded in a swarm of planetesimals

Computer Science

Scientific paper

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Computerized Simulation, Many Body Problem, Orbit Calculation, Orbital Elements, Orbital Mechanics, Perturbation, Planetary Evolution, Protoplanets, Circular Orbits, Eccentricity, Scattering

Scientific paper

Orbital evolution of protoplanets embedded in a swarm of planetesimals has been investigated to study the late state 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 5 rH, where rH is the Hill radius of the two protoplanets. If it is smaller than about 5 rH, 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 5 rH, when the protoplanet-protoplanet scattering is no longer effective. As protoplanets grow, their orbital separation measured by the Hill radius becomes small since rH varies as M1/3, 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 orbit separation larger than about 5 rH without orbit crossing. Based on these results, we describe a scenario for the late state of planetary formation.

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