The morphology of the epsilon Eridani dust ring is reproduced by a numerical simulation of dust particles captured into the 5:3 and 3:2 exterior mean-motion resonances with a 0.3 eccentricity 10^-4 solar mass planet at periastron at a semi-major axis of 40 AU. The morphology will differ when the planet is at aphelion, in about 140 years. Moderate eccentricity planets in outer extra-solar systems will cause observable variations in the morphology of associated dusty rings.
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Quillen et al. (2002) studied this question.
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