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 et al., 1990) and numerical (Benz et al., 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 υIMP and the “off-centre” or impact parameter bIMP together determined the system's total angular momentum LEM = mIMPυIMPbIMP = 3.5 × 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. High-resolution numerical modelling of the giant impact suggests a proto-Earth mass at the time of collision of equal to 0.8 to 0.85 M⊕ (Canup, 2004). The escape velocity υESC from such a body is ∼ 106 cm s−1 (see Eqn 15.1), and this equals the lowest possible relative velocity of the impactor; υIMP ≥ υESC. For the off-centre parameter bIMP, a value ∼ 5 × 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.