Abstract
Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m 1,..., m n we denote by N(m 1, ..., m n, k) the number of central configurations' of the n-body problem in ℝk modulus dilatations and rotations. If m n 1,..., m n, k) is finite, then we give a bound of N(m 1,..., m n, k) which only depends of n and k.
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Llibre, J. On the number of central configurations in the N-body problem. Celestial Mech Dyn Astr 50, 89–96 (1990). https://doi.org/10.1007/BF00048988
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DOI: https://doi.org/10.1007/BF00048988