Energies of formation for ejecta blankets of giant impacts
Ejection energy-diameter scaling relations for impact craters are studied by assuming the energy is equal to a constant times the diameter raised to a (different) constant power. These scaling relations are derived from least-squares fits to calculated ejection energies over a range of crater diameters and vary according to ejection angle, ejecta blanket distribution, planetary radius, and the depth-diameter ratio. Extremely broad changes in ejection angle and ejecta blanket distribution result in relatively small changes in the total energy. The way in which the exponent in the scaling relation is dependent on the planetary radius of curvature as well as on the exponent of the power-law depth-diameter scaling relation is described. Two ejection energy-diameter scaling relations, one for simple craters with depth-diameter ratios of approximately 0.2 and the other for large complex craters, are presented. The scaling relations explicitly include target density, surface gravity, and planetary radius.