Numerical simulations of collisions in Keplerian systems

Astronomy and Astrophysics – Astrophysics

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Computerized Simulation, Cosmology, Particle Collisions, Particle Motion, Optical Thickness, Orbital Elements, Rarefied Gases, Systems Analysis

Scientific paper

Computer simulations which were carried out for Keplerian collisional systems of 250 frictionless particles with a ratio of particle radius to mean semi-major axis of 0.001 confirm the theoretically predicted evolution very well until the thickness of the system is a few times the particle radius and the mass-point approximation becomes invalidated. Before this happens, the collisional contraction of denser regions can be observed. The local dispersions of the perihelia and ascending nodes diminish if the local mean orbit is not too close to a circle with zero inclination. When the mass-point approximation ceases to be valid, the system begins to expand, but with the parameter values of the standard system this process is much slower than the simultaneously observed evolution toward grazing collisions which do not affect the orbital elements. If the ratio of particle radius to semi-major axis is larger, the expansion becomes faster and the contraction ceases earlier. In late evolutionary phases the thickness of the system remains essentially constant. At the end of the longest simulation (70,000 impacts) the centers of the particles were in a layer of thickness twice the radius of the particles.

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