tokens: moon would be able to create the gap. These viscosities are notably lower than those measured by Tiscareno et al. ( 2007 ) and Colwell et al. ( 2009a ) in this region. For , the ratio has a value of 1.2 so the moon might just be able to create the Kuiper gap but for a slightly larger viscosity of, for example, , this ratio has a value of only 0.12 and the moon should definitely create a propeller and not a gap around the entire circumference of the ring. Let us consider the wide Bessel gap as another example. The diameters a spherical ice moon (or hypothetically even a silicate moon) would have to have to open this gap are and , respectively. Even for the lower limit of , the moon would have to have a nonsensical density of to fall below a diameter of . We therefore believe that single solid icy or silicate bodies can be ruled out as an explanation for the observed gaps in the C ring and the Cassini division. Lissauer et al. ( 1981 ) described the rift and gap structure of the Cassini division with a set of five embedded moons. They assumed a dispersion velocity with a spatially constant value of , which for , yields , which is much larger than the viscosities measured by Tiscareno et al. ( 2007 ) and Colwell et al. ( 2009a ), thus our chosen lower limit of . Consequently, the moons they predicted () are significantly larger than the ones we predict (see Table 1 ). Those moons might have been overlooked by Voyager , but would definitely have been detected by the cameras of the Cassini spacecraft. Ruling out the existence of single icy bodies as an explanation for the observed gaps in the C ring and the Cassini division raises the question what process could explain their formation. We believe that a swarm of icy collision shards much smaller than the dimensions presented in Table 1 , but still much larger than the largest ring particles could scatter the ring particles away, creating a gap that despite the existence of this swarm would appear completely void to the cameras of the Cassini spacecraft. However, this hypothesis cannot be tested easily with the model presented in this article and requires additional research. 4. Summary We developed a nonlinear diffusion model for gaps in planetary rings that accounts for gravitational scattering by the embedded moon and for the viscous diffusion of the ring material. This model can be used to estimate the ring’s viscosity from the radial density profile of the gap the moon creates knowing its radial position and mass and the power-law exponent β (). The mass of the moon can be derived by analyzing the wake region (Showalter et al. 1986 ; Seiß et al. 2010 ). We applied the model to the Encke and Keeler gap created by Pan and Daphnis to estimate the rings viscosity. Then, we applied the model to the gaps in the C ring and Cassini division to estimate the masses of moons that would be able to create those gaps. For , we estimate for the Encke gap, which is not an unexpected result, as Tiscareno et
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