Speculative histories of the Uranian satellite system

The hypothetical histories presently considered for the Uranian satellite system are very sensitive to the assumed satellite masses, within the errors of their determinations, as well as to the Uranian tidal effective dissipation function. A determination is made of the resonances that could have been encountered in these histories, and of the orbital eccentricity constraints that would have led to certain capture. It is found that if the mass of Miranda were of the upper extreme value, it would have been locked in a long-term 2/1 orbital resonance with Ariel to form a Laplacelike, three-body resonance that encompassed Umbriel.