Application Of A Statistical Accretion Model To Predict Undetected Moons Around Uranus In The Vicinity Of Mab

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In 2006, Showalter and Lissauer announced the discovery of the mu-ring around Uranus and a accompanying small moon Mab (Showalter and Lissauer, 2006). They derived the orbital position of Mab from both Voyager flyby (1986) and HST (2003-2006) data and showed that it is poorly understood. The observed positions were compared against an orbital model that includes gravitational flattening of Uranus. Although this model works well for nine other Uranian moons, for Mab the fitting errors of the observed orbital motion are six times larger. This indicates that we are currently overlooking an essential part of the dynamics that determine the orbit of Mab. Known moons in the Uranian system do not perturb Mab sufficiently to account for the fitting anomalies. Are there undetected bodies in the Uranian system that affect Mab's orbit?
In a previous study (Kumar et al., 2010), we applied a statistical accretion model (SAM) (Laskar, 2000) to determine the presence of undetected moons in the vicinity of Mab. We used a modified SAM, including different aggregation criteria and employing conservation of total angular momentum (Mena and Benet, 2010). This model has been primarily used to simulate the evolution of the solar system, in the secular limit.
The results of our initial simulations indicated that the environment around Mab is efficiently cleared such that only three to four large bodies remain when the simulations terminate (when the disc is collision-free). Observational constraints however imply that there must be more bodies in the neighbourhood of Mab. Hence, the suggestion is that the environment around Mab might not be collision-free.
We revisit the previously obtained results and analyze configurations of additional moons near Mab for systems that still contain collision geometries. Based on this new analysis, we indicate the likely configuration of undetected bodies in the neighbourhood of Mab.

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