Stochastic accretion of the Earth

Chondritic meteorites are thought to be representative of the material that formed the Earth. However, the Earth is depleted in volatile elements in a manner unlike that in any chondrite, and yet these elements retain chondritic isotope ratios. Here we use N-body simulations to show that the Earth did not form from chondrites, but rather by stochastic accretion of many precursor bodies whose variable compositions reflect the temperatures at which they formed. Earth's composition is reproduced when initial temperatures of planetesimal- to embryo-sized bodies are set by disk accretion rates of (1.08±0.17)×10^-7 solar masses/yr, although they may be perturbed by ²⁶Al heating on bodies formed at different times. Our model implies that a heliocentric gradient in composition was present in the protoplanetary disc and that planetesimals formed rapidly within ~1 Myr, in accord with radiometric volatile depletion ages of the Earth.