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On the planar syzygy solutions of the 3-body problem
Authors:Florin Nicolae Diacu
Institution:(1) Institut für angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 6900 Heidelberg, West Germany
Abstract:Relations between the rectilinear, collinear and syzygy solutions of the N-body problem are first pointed out. It is shown that, along a solution, the set of the non-collinear syzygy configuration instants is formed by isolated points. Then we restrict the study to the planar 3-body problem and prove that for Dirichlet-stable solutions, a non-syzygy solution cannot be as close as possible to a syzygy one. It is also true that, in the case of a syzygy solution, the orbit of one particle crosses the line of the other two and can not be tangent to this line in the transition point. Finally we prove that the set of initial conditions leading to non-collinear syzygy solutions is non-empty and open.
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