The zodiacal cloud is our solar system’s largest structure visible to the unaided eye, yet its constituent dust particles’ origins are controversial, with a wide range of proposed divisions between sources in the asteroids and Jupiter Family comets. Furthermore, any contribution from Oort Cloud comets is poorly constrained. The zodiacal cloud gains new meaning with NASA aiming to characterize potentially Earth-like planets around nearby stars. Exoearths will be viewed against the light scattered from extrasolar analogs of our cloud. As the only such dust cloud where the parent bodies can be tracked, our own system is a key to learning how planetary system architecture governs the interplanetary dust’s distribution. We show through radiative transfer modeling that our cloud’s shape and size at the wavelengths of interest for potentially-habitable exoplanets can be measured from Earth orbit by mapping the zodiacal light’s flux and linear polarization across the sky. We demonstrate using a Markov chain Monte Carlo analysis that the division between asteroidal, Jupiter Family, and Oort Cloud dust components with their differing orbital inclinations can be determined by observing with sufficient precision a set of fields distributed along the ecliptic and up to the poles. We quantify how repeated observations at different times of year improve the fidelity of the subtraction of the galactic and extragalactic backgrounds.