  The solar system's Zodiacal Cloud is visible to the unaided eye, yet the
origin of its constituent dust particles is not well understood, with a wide
range of proposed divisions between sources in the asteroid belt and Jupiter
Family comets. The amount of dust contributed by Oort Cloud comets is
uncertain. Knowledge of the Zodiacal Cloud's structure and origins would help
with NASA's aim of characterizing potentially Earth-like planets around nearby
stars, since the exo-Earths must be studied against the light scattered from
extrasolar analogs of our cloud. As the only example where the parent bodies
can be tracked, our own cloud is critical for learning how planetary system
architecture governs the interplanetary dust's distribution. Our cloud has been
relatively little-studied in the near-ultraviolet, a wavelength range that is
important for identifying potentially-habitable planets since it contains the
broad Hartley absorption band of ozone. We show through radiative transfer
modeling that our cloud's shape and size at near-UV wavelengths can be measured
from Earth orbit by mapping the zodiacal light's flux and linear polarization
across the sky. We quantify how well the cloud's geometric and optical
properties can be retrieved from a set of simulated disk observations, using a
Markov chain Monte Carlo analysis. The results demonstrate that observations
with sufficient precision, covering a set of fields distributed along the
ecliptic and up to the poles, can be used to determine the division between
asteroidal, Jupiter Family, and Oort Cloud dust components, primarily via their
differing orbital inclination distributions. We find that the observations must
be repeated over a time span of several months in order to disentangle the
zodiacal light from the Galactic background using the Milky Way's rotation
across the sky.
