[Abridged] We present an extensive suite of terrestrial planet formationsimulations that allows quantitative analysis of the stochastic late stages ofplanet formation. We quantify the feeding zone width, Delta a, as themass-weighted standard deviation of the initial semi-major axes of theplanetary embryos and planetesimals that make up the final planet. The size ofa planet's feeding zone in our simulations does not correlate with its finalmass or semi-major axis, suggesting there is no systematic trend between aplanet's mass and its volatile inventory. Instead, we find that the feedingzone of any planet more massive than 0.1M_Earth is roughly proportional to theradial extent of the initial disk from which it formed: Deltaa~0.25(a_max-a_min), where a_min and a_max are the inner and outer edge of theinitial planetesimal disk. These wide stochastic feeding zones have significantconsequences for the origin of the Moon, since the canonical scenario predictsthe Moon should be primarily composed of material from Earth's last majorimpactor (Theia), yet its isotopic composition is indistinguishable from Earth.In particular, we find that the feeding zones of Theia analogs aresignificantly more stochastic than the planetary analogs. Depending on ourassumed initial distribution of oxygen isotopes within the planetesimal disk,we find a ~5% or less probability that the Earth and Theia will form with anisotopic difference equal to or smaller than the Earth and Moon's. In fact wepredict that every planetary mass body should be expected to have a uniqueisotopic signature. In addition, we find paucities of massive Theia analogs andhigh velocity moon-forming collisions, two recently proposed explanations forthe Moon's isotopic composition. Our work suggests that there is still noscenario for the Moon's origin that explains its isotopic composition with ahigh probability event.
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