Investigating The Effects Of Additional Shepherding Moons On The Motion Of Mab

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In 2006, Showalter and Lissauer announced the discovery of an outer ring system around Uranus, composed of the nu-ring and the mu-ring. Their discovery was made using Hubble Space Telescope (HST) observations and was followed up using the Keck observatory. A small moon Mab, centered in the mu-ring, was also detected (Showalter and Lissauer, 2006). Current hypothesis is that Mab serves as the source of the material for the mu-ring.
Showalter and Lissauer (2006) show that the orbit of Mab is poorly understood. They derived its orbital position from both Voyager flyby data (1986) and HST data (2003-2006). They compared the observed positions with an orbital model that includes gravitational flattening of Uranus. Although this model works well for nine other Uranian moons, for Mab the fitting errors are six times larger. This indicates that we are currently overlooking an essential part of the dynamics that determine the orbit of Mab. Is there an unknown body in the Uranian system that affects Mab's orbit?
In this study, we considered the effects of additional, hypothetical shepherding moons in the vicinity of Mab on its motion. We analyzed different configurations and assessed whether these additional moons can induce the observed motion of Mab. In doing so, we assessed the likely masses of these moons and their separation distances with respect to Mab.

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