We examine the eccentricity evolution of a system of two planets locked in a mean motion resonance, in which the outer planet loses energy and angular momentum. The sink of energy and angular momentum could be either a gas or planetesimal disk. We show that the eccentricity of both planetary bodies can grow to large values, particularly if the inner body does not directly exchange energy or angular momentum with the disk. We analytically calculate the eccentricity damping rate in the case of a single planet migrating through a planetesimal disk. We present the results of numerical integrations of two resonant planets showing rapid growth of eccentricity. We also present integrations in which a Jupiter-mass planet is forced to migrate inward through a system of 5-10 roughly Earth mass planets. The migrating planet can eject or accrete the smaller bodies; roughly 5% of the mass (averaged over all the integrations) accretes onto the central star. The results are discussed in the context of the currently known extrasolar planetary systems.
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