Statistical Treatment of Weakly Interacting Particles in a Newtonian Potential

Abstract

A distribution function has been obtained for a two-dimensional system of weakly interacting particles which execute bound periodic motion in a Newtonian potential. The failure of the familiar formulas of statistical mechanics to yield bound distributions for such potentials has been avoided by first restricting the available phase space to that corresponding to periodic motion of independent particles, and then determining the most probable distribution of bound orbits. The effect of weak interaction is considered, then, with the aid of the principle of least action. As an illustration, the distribution of mass has been computed for a many-particle system having the same energy and momentum per unit mass as the nine planets, and compared with the actual distribution of planetary mass.