Stability of Uranus' Inner Satellites with Updated Masses for Cordelia, Ophelia, and Cressida.

The inner satellites of Uranus, most of which were discovered during the Voyager 2 mission in 1986, form a remarkably distinct system when compared to other known satellite groups in the Solar System. These moons are characterized by their small sizes, low reflectivity, and nearly circular orbits that lie very close to Uranus’s equatorial plane. These features give rise to a complex and highly sensitive orbital configuration, often described as a chaotic “orbital dance” due to the intense gravitational interactions among them. Many are packed so closely together that even small perturbations can trigger orbital instabilities on relatively short timescales.

The lack of well-constrained mass values, combined with the fact that several of these moons participate in chains of mean-motion or secular resonances, makes the system particularly intriguing from a dynamical standpoint.

In this work, we carried out a series of numerical simulations considering Uranus as the central body and incorporating all 13 known inner satellites. The main goal was to investigate the orbital stability of the system in light of the recently updated mass values for Cordelia, Ophelia, and Cressida (French et al., 2024). Additionally, we included revised values of Uranus’s gravitational zonal harmonics J₂, J₄, and J₆ (Jacobson et al., 2025) in order to assess their impact on the long-term dynamical behavior of the system.

To diagnose potential changes in orbital stability resulting from these updates, we employed the frequency analysis method (Laskar, 1990), which enables us to quantify orbital diffusion and, consequently, to infer the degree of stability or instability over extended timescales. Preliminary results indicate that the satellites Desdemona, Juliet, Cressida, Bianca, Portia, and Rosalind are particularly sensitive to the changes in mass parameters and gravitational coefficients, exhibiting significant levels of orbital diffusion. Furthermore, we found that the libration amplitude of the resonant angle associated with the mean-motion resonance between Belinda and Perdita decreases considerably with the newly adopted parameters, suggesting a possible transition toward a more stable regime of dynamical coupling between these two moons.

Fig 1: Diffusion values as a function of Mab's orbital period, calculated for standard mass values and for the case in which updated mass values of Cordelia, Ophelia, and Cressida are added to the system.