Prevailing models for the formation of the Moon invoke a giant impact between a planetary embryo and the proto-Earth (Canup, 2004; Cuk et al., 2016). Despite similarities in the isotopic and chemical abundances of refractory elements compared to Earth's mantle, the Moon is depleted in volatiles (Wolf and Anders, 1980). Current models favour devolatilisation via incomplete condensation of the proto-Moon in an Earth-Moon debris-disk (Charnoz and Michaut, 2015; Canup et al., 2015; Lock et al., 2018). However the physics of this protolunar disk is poorly understood and thermal escape of gas is inhibited by the Earth's strong gravitational field (Nakajima and Stevenson, 2014). Here we investigate a simple process, wherein the Earth's tidal pull promotes intense hydrodynamic escape from the liquid surface of a molten proto-Moon assembling at 3-6 Earth radii. Such tidally-driven atmospheric escape persisting for less than 1 Kyr at temperatures similar to 1600 1700 K reproduces the measured lunar depletion in K and Na, assuming the escape starts just above the liquid surface. These results are also in accord with timescales for the rapid solidification of a plagioclase lid at the surface of a lunar magma ocean (Elkins-Tanton et al., 2011). We find that hydrodynamic escape, both in an adiabatic or isothermal regime, with or without condensation, induces advective transport of gas away from the lunar surface, causing a decrease in the partial pressures of gas species (P-s) with respect to their equilibrium values (P-sat). The observed enrichment in heavy stable isotopes of Zn and K (Paniello et al., 2012; Wang and Jacobsen, 2016) constrain P-s/P-sat > 0.99, favouring a scenario in which volatile loss occurred at low hydrodynamic wind velocities (<1% of the sound velocity) and thus low temperatures. We conclude that tidally-driven atmospheric escape is an unavoidable consequence of the Moon's assembly under the gravitational influence of the Earth, and provides new pathways toward understanding lunar formation.

High-precision magnesium (Mg) isotope data obtained using a large geometry high resolution MC-ICPMS are reported for 9 carbonaceous and ordinary chondrites, 9 eucrites and diogenites generally considered to originate from Asteroid 4 Vesta, together with 4 martian meteorites, and a variety of terrestrial and lunar materials. The variation in Mg isotopic composition found for mafic and ultramafic rocks, mafic minerals and chondrites is smaller than reported previously. The range of delta Mg-26 and delta Mg-25 of 0.6 parts per thousand and 0.3 parts per thousand defines a single mass-dependent fractionation line consistent with a homogeneous mix of nucleosynthetic components. Data for the Earth, Mars and Vesta display no systematic Mg isotopic differences despite large variations in the level of depletion in moderately volatile elements. Lunar mare basalts exhibit a significant range in delta Mg-26 (-0.53 parts per thousand to +0.05 parts per thousand) and delta Mg-25 (-0.27 parts per thousand to +0.02 parts per thousand) attributable to magmatic differentiation in the lunar magma ocean (LMO). Lunar basalts derived from early segregated cumulates and thought to be the most primitive are on average slightly similar to 0.17 parts per thousand (delta Mg-26) heavy relative to basalts from the Earth, Mars and Vesta. However, the difference is not well-resolved. More strikingly, all differentiated planets and planetesimals, as sampled, have Mg that is on average isotopically heavy compared with most chondrites analyzed thus far. Chondrules and CAIs also are generally heavy in terms of Mg, so this might reflect sorting of material in the proto-planetary disk. Such an explanation would be similar to one previously proposed (Hewins R. H. and Herzberg C. T. (1996) Earth Planet. Sci. Lett. 144, 1-7.) to explain the non-chondritic Si/Mg of the Earth. In this model chondrule-like objects separate from volatile rich planetary dust by accumulation in stagnant regions between eddies in the solar nebula. Small (similar to 1 km) planetesimals formed by accumulation of such molten material then develop into planetary embryos and thence to larger terrestrial planets by combinations of runaway growth and collisions. As such accumulation of molten chondrule-like droplets provides an explanation that obviates some of the dynamic difficulties associated with the onset of planetary accretion. The non-chondritic Mg isotopic composition of the Earth is consistent with data for Li and has important implications for Earth's bulk composition and putative hidden reservoirs. (C) 2007 Published by Elsevier B.V.