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Some of the small inner moons of Uranus have very closely-spaced orbits.Multiple numerical studies have found that the moons Cressida and Desdemona,within the Portia sub-group, are likely to collide in less than 100 Myr. Thesubsequent discovery of three new moons (Cupid, Perdita, and Mab) made thesystem even more crowded. In particular, it has been suggested that the Belindagroup (Cupid, Belinda, and Perdita) will become unstable in as little as 10$^5$years. Here we revisit the issue of the stability of the inner moons of Uranususing updated orbital elements and considering tidal dissipation. We find thatthe Belinda group can be stable on $10^8$-year timescales due to an orbitalresonance between Belinda and Perdita. We find that tidal evolution cannot formthe Belinda-Perdita resonance, but convergent migration could contribute to thelong-term instability of the Portia group. We propose that Belinda capturedPerdita into the resonance during the last episode of disruption andre-accretion among the inner moons, possibly hundreds of Myr ago.

Cupid Is Not Doomed Yet: On the Stability of the Inner Moons of Uranus