Beyond Oligarchy

Physics

Scientific paper

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Scientific paper

We address three questions regarding solar system planets. Whatdetermined their number? Why are their orbits nearly circular andcoplanar? How long did they take to form?We pick up the story of planet formation at the end of oligarchy, whenthe oligarchs'surface mass density matched that of the small bodies they were accreting. Dynamical frictionby the small bodies was no longerable to balance viscous stirring, so the oligarchs' velocitydispersion increased to the extent that their orbits crossed. Anessential assumption of our investigation is that as the big bodiesgot bigger, the small ones got smaller as the result of undergoing acollisional fragmentation cascade. It follows that oligarchy was abrief stage in solar system evolution. What happened next differed inthe inner and outer parts of the planetary system. In the inner part,where the ratio of the escape velocity from the surfaces of theplanets to the escape velocity from their orbits is smaller thanunity, big bodies collided and coalesced once their random velocitiesbecame comparable to their escape velocities. In the outer part, wherethis ratio is larger than unity, the random velocities of some of thebig bodies continued to rise until they were ejected. In both parts,the number density of the big bodies eventually decreased to theextent that gravitational interactions among them no longer producedlarge scale chaos. After that their orbital eccentricities andinclinations were damped by dynamical friction from the remainingsmall bodies.A few implications of the above scenario are worth noting. Impactsamong protoplanets of comparable size were common in the inner planetsystem but not in the outer. Ejections from the outer planet systemincluded several bodies with masses in excess of Earth afteroligarchy.

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