The final stage of terrestrial planet formation consists of several hundred approximately lunar mass bodies accreting into a few terrestrial planets .
This final stage is stochastic , making it hard to predict which parts of the original planetesimal disk contributed to each of our terrestrial planets .
Here we present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of this process .
Although there is a general correlation between a planet ’ s location and the initial semi-major axes of its constituent planetesimals , we concur with previous studies that Venus , Earth , and Mars analogs have overlapping , stochastic feeding zones .
We quantify the feeding zone width , \Delta a , as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet .
The size of a planet ’ s feeding zone in our simulations does not correlate with its final mass or semi-major axis , suggesting there is no systematic trend between a planet ’ s mass and its volatile inventory .
Instead , we find that the feeding zone of any planet more massive than 0.1 M _ { \oplus } is roughly proportional to the radial extent of the initial disk from which it formed : \Delta a \approx 0.25 ( a _ { max } - a _ { min } ) , where a _ { min } and a _ { max } are the inner and outer edge of the initial planetesimal disk .
These wide stochastic feeding zones have significant consequences for the origin of the Moon , since the canonical scenario predicts the Moon should be primarily composed of material from Earth ’ s last major impactor ( Theia ) , yet its isotopic composition is indistinguishable from Earth .
In particular , we find that the feeding zones of Theia analogs are significantly more stochastic than the planetary analogs .
Depending on our assumed initial distribution of oxygen isotopes within the planetesimal disk , we find a \sim 5 % or less probability that the Earth and Theia will form with an isotopic difference equal to or smaller than the Earth and Moon ’ s .
In fact we predict that every planetary mass body should be expected to have a unique isotopic signature .
In addition , we find paucities of massive Theia analogs and high velocity moon-forming collisions , two recently proposed explanations for the Moon ’ s isotopic composition .
Our work suggests that there is still no scenario for the Moon ’ s origin that explains its isotopic composition with a high probability event .