Giant impacts impactor mass and energy deposited

Giant collisions and the merging of massive bodies, ~ 1027 g, during the late stages of planetary accretion are a straightforward prediction of the standard model (Wetherill, 1990). Probably the Moon was formed by the giant impact of the proto-Earth with an approximately Mars-sized proto-planet. Modelling, both analytical (Vityazev etal., 1990) and numerical (Benz etal., 1986,1987) predicts that impacts between planet-sized bodies must be far from elastic and that most of the energy released must be deposited within the growing planet.

For the Earth-Moon system, the impactor mass mIMP, its velocity uIMP and the "off-centre" or impact parameter &IMP together determined the system's total angular momentum LEM = mIMPfIMP&IMP = 3.5 x 1041 g cm2 s-1, provided that LEM resulted only from the impact (Melosh et al., 1993). The value of each individual quantity is uncertain; nevertheless reasonable estimates are possible. Highresolution numerical modelling of the giant impact suggests a proto-Earth mass at the time of collision of equal to 0.8 to 0.85 Me (Canup, 2004). The escape velocity vESC from such a body is ~ 106 cm s-1 (see Eqn 15.1), and this equals the lowest possible relative velocity of the impactor; vIMP > vESC. For the off-centre parameter &IMP, a value ~ 5 x 108 cm (the centre of the impactor grazes the surface of the proto-Earth) would result in the observed high angular momentum of the post-impact Earth-Moon system. The three values LEM, vIMP and &IMP then give an impactor mass mIMP ~ 1027 g, which exceeds the mass of Mars.

The energy released in such a collision is the sum of the kinetic and gravitational energies and could reach ~ 5 x 1038 erg or ~ 1011 erg g-1 (Melosh et al., 1993). This energy and the mean silicate heat capacity (~ 107 erg g-1 K-1) would give a mean temperature of the proto-Earth of ~ 10 000 K, exceeding the vaporization temperature of any terrestrial matter. Although melting and vaporization are endothermic, and the heat may have been very unevenly distributed, this simple estimate nevertheless illustrates that a giant collision is expected to result in widespread melting and some vaporization.

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