  The leading face of Saturn's moon Iapetus, Cassini Regio, has an albedo only
one tenth that on its trailing side. The origin of this enigmatic dichotomy has
been debated for over forty years, but with new data, a clearer picture is
emerging. Motivated by Cassini radar and imaging observations, we investigate
Soter's model of dark exogenous dust striking an originally brighter Iapetus by
modeling the dynamics of the dark dust from the ring of the exterior retrograde
satellite Phoebe under the relevant perturbations. In particular, we study the
particles' probabilities of striking Iapetus, as well as their expected spatial
distribution on the Iapetian surface. We find that, of the long-lived particles
(greater than about 5 microns), most particle sizes (greater than about 10
microns) are virtually certain to strike Iapetus, and their calculated
distribution on the surface matches up well with Cassini Regio's extent in its
longitudinal span. The satellite's polar regions are observed to be bright,
presumably because ice is deposited there. Thus, in the latitudinal direction
we estimate polar dust deposition rates to help constrain models of thermal
migration invoked to explain the bright poles (Spencer & Denk 2010). We also
analyze dust originating from other irregular outer moons, determining that a
significant fraction of that material will eventually coat Iapetus--perhaps
explaining why the spectrum of Iapetus' dark material differs somewhat from
that of Phoebe. Finally we track the dust particles that do not strike Iapetus,
and find that most land on Titan, with a smaller fraction hitting Hyperion. As
has been previously conjectured, such exogenous dust, coupled with Hyperion's
chaotic rotation, could produce Hyperion's roughly isotropic, moderate-albedo
surface.
