Abstract
The near-polar-position rings whose possible existence and character around Neptune are presently considered correspond to the equilibrium configuration of a test-particle orbital plane in the gravitational potential of Neptune and Triton. At these equilibria, of which two whose invariable-plane nodal line is approximately perpendicular to the nodal line of Triton on the same plane are dynamically stable, the orbit of the test particle maintains a fixed orientation with respect to the invariable plane and the node of triton on that plane. The stable equilibria are noted to correspond to a maximum of the total energy for a given semimajor axis; their stability is found to remain unperturbed despite collisions among particles.
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