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Method of pairwise separations and its astronomical applications




The distribution f(l) of pairwise separations is used for studying geometric and energy-related characteristics of interacting particle systems. We present some formulae for calculating the distribution f(l) for finite regular spherical sets. We also study local properties of fractal systems and show that for small (compared to the system size) separations l one can use the asymptotic approximation f(l) ∝lD− 1 (where D is the fractal dimension). The distribution f(l) can also be used for calculating binding energies of systems having arbitrary shapes and arbitrary interaction potentials.