Impact flows and crater scaling on the moon

The axisymmetric distribution of stress, internal energy and particle velocity resulting from the impact of an iron meteoroid with a gabbroic anorthosite lunar crust has been calculated for the regime in which shock-induced melting and vaporization takes place. Comparison of impact flow fields, with phase changes in silicates taken into account, with earlier results demonstrate that in the phase change case when the 15-km/s projectile has penetrated some two projectile radii into the moon, the peak stress in the flow is ～0.66 Mbar at a depth of 66 km, and the stress has decayed to ～66 kbar at a depth of 47 km. Rapid attenuation occurs because of the high rarefaction velocity of the high-pressure phases associated with a 35% (zero-pressure) density increase. This feature of the phase-change flow tends to strongly concentrate the maximum shock pressures along the meteoroid trajectory (axis) and makes the conical zone along which high internal energy deposition occurs, both shallow and narrow. Examination of the gravitational energies required to excavate larger craters on the moon indicates the importance of gravity forces acting during the excavation of craters having radii in the range greater than ～2 – ～140 km. It is observed that the “hydrodynamic” energy vs. crater radius relation approaches those for various “gravitational” energy vs. radius relations at the radii values corresponding to the larger mare basins. Cratering energy values in the range of (1.0 – 9.4) · 10³² erg are inferred on this basis for the Imbrium crater. Using these values and the criteria that all rocks exposed to ～100 kbar or greater shock pressures are included in the ejecta (some of which falls back) implies that the maximum depth of sampling expected to be represented within the Apollo collection lies in the range 148–328 km.