Statistical Behavior of Planetesimals in the Primitive Solar System

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Abstract
A probability distribution function P(v, r', z, t) for a planetesimal which is moving in the gaseous nebula under the solar gravity and frequently undergoing gravitational encounters with others of different masses is obtained by solving the Fokker-Planck equation. It is found not to be a Maxwellian but a nonsteady general Gaussian distribution, owing to the fact that the planetesimals are in systematic circular motions around the sun. The magnitude of the random motion is determined by the balance of two effects, one due to mutual encounters and the other due to a gas drag force, and found to be much smaller than the systematic motion owing to the effective gas drag force, and found to be much smaller than the systematic motion owing to the effective gas drag force. The eccentricities and inclinations are typically 10-3 in the order of magnitude. The growth of planetesimals due to the direct collisions is also investigated. It is found numerically that the mass distribution n(m) is nearly proportional to m-1,48 and about 40% of the planetesimals by mass are in the form of bodies with more than one thousand times their initial mass in 104 years in the Earth's region, and in 105 years in the Jupiter's region.

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