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We study in this paper the capture of a massless particle into an isolated,first order Corotation Eccentric Resonance (CER), in the framework of thePlanar, Eccentric and Restricted Three-Body problem near a m+1:m mean motioncommensurability (m integer). While capture into Lindblad Eccentric Resonances(where the perturber's orbit is circular) has been investigated years ago,capture into CER (where the perturber's orbit is elliptic) has not yet beeninvestigated in detail. Here, we derive the generic equations of motion near aCER in the general case where both the perturber and the test particle migrate.We derive the probability of capture in that context, and we examine moreclosely two particular cases: (i) if only the perturber is migrating, captureis possible only if the migration is outward from the primary. Notably, theprobability of capture is independent of the way the perturber migratesoutward; (ii) if only the test particle is migrating, then capture is possibleonly if the algebraic value of its migration rate is a decreasing function oforbital radius. In this case, the probability of capture is proportional to theradial gradient of migration. These results differ from the capture intoLindblad Eccentric Resonance (LER), where it is necessary that the orbits ofthe perturber and the test particle converge for capture to be possible.Possible applications for planetary satellites are discussed.

Derivation of Capture Probabilities for the Corotation Eccentric Mean Motion Resonances