The configurational integral and the single-particle and pair distributions for a one-dimensional gravitating system are calculated using approximate methods. The Helmholtz free energy and single-particle distributions are in good agreement with the exact analytical results. The pair distribution is new and shows that, in the Vlasov limit, it is approximately the product of two oneparticle distributions. The method may be easily extended to more general systems.
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J. J. Monaghan (1978) studied this question.
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