Time of Formation of Earth and Mars Constrained by Siderophile Element Geochemistry and the Hafnium-182-Tungsten-182 Isotope System

182Hf-182W chronometry is considered the most powerful tool to determine the formation timescale of the terrestrial planets. However, previous work employed oversimplified accretion and core formation models. The accretion and core formation models presented here for the 182W isotopic evolution in the mantles of the accreting Earth and Mars, can incorporate the core formation conditions constrained by siderophile element geochemistry and can be successfully applied to constrain the formation timescale of Earth and Mars.;Elemental abundance analyses of the Allende meteorite and two martian meteorites lead to new estimates of core-mantle concentration ratios of Si, V, Cr and Mn for Earth and two distinct mantle Hf/W ratios for Mars respectively, and provide better constraints on the models. It is concluded that formation of the proto-Earth (∼87% of its present mass) has to complete rapidly in 10.7 +/- 2.5 Myr after the onset of the Solar System for a late (≥ 52 Myr) Moon-forming giant impact. The mean time of Mars' accretion is determined to be 3.6 +/- 0.1 Myr, meaning that Mars accretes to 95% of its present mass in 10.8 +/- 0.3 Myr after the formation of the Solar System. Therefore, Mars is not a planetary embryo, and Mars and proto-Earth may be formed on a similar timescale if a late Moon-forming giant impact is assumed. In contrast, if the Moon formed early at ∼30 Myr then it takes about 3 times longer to form the proto-Earth compared to Mars.;A stochastic mantle stirring and sampling model was developed to investigate the evolution of W isotope heterogeneities in the mantles of Earth and Mars after accretion and core formation. Our results confirm the mantle stirring rate of ∼ 500 Myr constrained by the long-lived isotope systems in Earth and suggest that the mantle stirring rate in Mars is much slower (∼2 Ga).;A new concept is developed: the core formation memory of a siderophile element. Siderophile elements are shown to have different capabilities in recording core formation history, a very important fact to consider in any core formation modeling.