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The discovery of ring systems around objects of the outer Solar Systemprovides a strong motivation to apply theoretical models in order to betterestimate their physical and orbital parameters, which can constrain scenariosfor their origin. We review the criterion for maintaining apse-alignment acrossa ring and the balance between the energy input rate provided by a close bysatellite and the internal dissipation rate occurring through ring particlecollisions that is required to maintain ring eccentricity, as derived from theequations of motion governing the Lagrangian-displacements of the ring-particleorbits. We use the case of the epsilon-ring of Uranus, to calibrate ourtheoretical discussion and illustrate the basic dynamics governing these typesof ring. In the case of the ring system of (10199) Chariklo, where the evidencethat the rings are eccentric is not conclusive, we apply the theory ofapse-alignment to derive information about the most plausible combination ofvalues of the surface density and eccentricity-gradient, as well as the massesand locations of their postulated but -presentlyundetected-shepherd-satellites. When the balance conditions that we predict areapplied to the ring system of (10199) Chariklo, we are able to estimate theminimum mass of a shepherd satellite required to prevent eccentricity decay, asa function of its orbital location, for two different models of dissipation. Weconclude that the satellite mass required to maintain the m = 1 eccentric modein the ring, would be similar or smaller than that needed to confine the ringsradially.

Apse-alignment in narrow-eccentric ringlets and its implications for the EPSILON-ring of Uranus and the ring system of (10199) Chariklo