Point source solutions and coupling parameters in cratering mechanics

Many phenomena of interest in impact cratering occur on a time and distance scale large compared to those of the impactor. As a consequence, the details of the impactor may be of little consequence, and the effects of the impactor can be replaced by an equivalent point source of energy and momentum. This point source assumption is developed and proved to define a single scalar “coupling parameter” measure, C ∝ αUμδν of the impactor radius α, velocity U, and density δ. Idealized examples are given where this measure can range from the cube root of the impactor kinetic energy, with μ = 2/3, to cases where it is the cube root of its momentum with μ = 1/3. For real materials the correct choice of μ depends on the material of the target. Materials with little dissipation have the exponent μ ≃ 0.6; while materials with large dissipation have μ ≃ 0.4. The assumption of such a measure is shown to lead to a unified theory of crater scaling in terms of the exponent μ. Results are given for crater size, ejecta distributions, growth histories, time of formation, melt volume, and shock decay. The results are compared to experiments and code calculations. (Craters, impacts, scaling, point source, self-similar, coupling parameter).