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In order to test planetary accretion and differentiation scenarios, weintegrated a multistage core-mantle differentiation model with N-body accretionsimulations. Impacts between embryos and planetesimals result in magma oceanformation and episodes of core formation. The core formation model combinesrigorous chemical mass balance with metal-silicate element partitioning data.The primary constraint on the combined model is the composition of the Earth'sprimitive mantle, the composition of the Martian mantle, and the mass fractionsof the metallic cores of Earth and Mars. The model is refined by least squaresminimization with up to five fitting parameters that consist of themetal-silicate equilibrium pressure and 1-4 parameters that define the startingcompositions of primitive bodies. This integrated model has been applied to 6Grand Tack simulations. Investigations of a broad parameter space indicatethat: accretion of Earth was heterogeneous, metal-silicate equilibrationpressures increase as accretion progresses and are 60-70% of core-mantleboundary pressures at the time of each impact, and a large fraction (70-100%)of the metal of impactor cores equilibrates with a small fraction of thesilicate mantles of protoplanets during each core formation event. Acceptablefits to the Earth's mantle composition are obtained only when bodies thatoriginated close to the Sun, at <0.9-1.2 AU, are highly reduced and thosebeyond this distance are increasingly oxidized. The FeO content of the Martianmantle depends critically on the heliocentric distance at which theMars-forming embryo originated. Finally, the Earth's core is predicted tocontain 8-9 wt% silicon, 2-4 wt% oxygen and 10-60 ppm hydrogen, whereas theMartian core is predicted to contain low concentrations (<1 wt%) of Si and O.

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Accretion and differentiation of the terrestrial planets with  implications for the compositions of early-formed Solar System bodies and  accretion of water