Collisional theory of non-identical particles in a gravitational field

Statistics – Computation

Scientific paper

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Computational Astrophysics, Elastic Scattering, Gravitational Fields, Particle Collisions, Particle Size Distribution, Statistical Distributions, Equations Of Motion, Particle Mass, Radii, Velocity Distribution

Scientific paper

The statistical theory of partially elastic collisions and gravitational encounters is generalized for nonidentical particles having different masses, internal densities, radii, elastic parameters or other properties. In those cases which are numerically studied, the differences in elasticity do not produce significant effects: essentially the same distribution of orbits is found if the mean value of the restitution coefficients is used for all the particles. Differences in the internal density lead to the equipartition of energy in the random motion, although this approximation is rather rough and affords for the lightest particles an overestimated energy. Mass differences which correspond to a dispersion of radii produce a complicated behavior. The equipartition of the energy is occasionally possible, but if the mass differences are large, the velocity dispersion can be inversely proportional to the radius.

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