Abstract
The necessary conditions for planetary arc confinement are investigated, concentrating on the limiting case where the arc is marginally confined. It is shown that periodic perturbations due to a discrete Lindblad resonance can induce a secular change of Jacobian energy as well as orbital eccentricity. If the particles are subject to the perturbation of only one inner (outer) Lindblad resonance, the Lindblad resonance's location must be exterior (interior) to that of the corotation resonance if the perturbations are to lead to confinement. The trajectories of particles that are subject to inelastic collisions and pertubations due to corotation and Lindblad resonances are computed, showing that the confinement mechanism can indeed operate provided the perturbation due to the Lindblad resonance is sufficiently strong to balance viscous effects. The possibility that internal nonradial oscillations of Neptune may provide the necessary perturbations for arc confinement is considered.
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