**Journal of Geophysical Research: Planets**

# Planetary cratering mechanics

## Abstract

The objective of this study was to obtain a quantitative understanding of the cratering process over a broad range of conditions. Our approach was to numerically compute the evolution of impact induced flow fields and calculate the time histories of the key measures of crater geometry (e.g. depth, diameter, lip height) for variations in planetary gravity (0 to 10^{9} cm/s^{2}), material strength (0 to 2400 kbar), and impactor radius (0.05 to 5000 km). These results were used to establish the values of the open parameters in the scaling laws of Holsapple and Schmidt (1987). We describe the impact process in terms of four regimes: (1) penetration, (2) inertial, (3) terminal and (4) relaxation. During the penetration regime, the depth of impactor penetration grows linearly for dimensionless times τ = (*Ut*/*a*) <5.1. Here, *U* is projectile velocity, *t* is time, and *a* is projectile radius. In the inertial regime, τ > 5.1, the crater grows at a slower rate until it is arrested by either strength or gravitational forces. In this regime, the increase of crater depth, *d*, and diameter, *D*, normalized by projectile radius is given by *d/a* = 1.3 (*Ut*/*a*)^{0.36} and *D/a* = 2.0(*Ut*/*a*)^{0.36}. For strength-dominated craters, growth stops at the end of the inertial regime, which occurs at τ = 0.33 (*Y _{eff}*/ρ

*U*

^{2})

^{−0.78}, where

*Y*is the effective planetary crustal strength. The effective strength can be reduced from the ambient strength by fracturing and shear band melting (e.g. formation of pseudo-tachylites). In gravity-dominated craters, growth stops when the gravitational forces dominate over the inertial forces, which occurs at τ = 0.92 (

_{eff}*ga*/

*U*

^{2})

^{−0.61}. In the strength and gravity regimes, the maximum depth of penetration is

*d*= 0.84 (

_{p}/a*Y*/ρ

*U*

^{2})

^{−0.28}and

*d*= 1.2 (

_{p}/a*ga*/

*U*

^{2})

^{−0.22}, respectively. The transition from simple bowl-shaped craters to complex-shaped craters occurs when gravity starts to dominate over strength in the cratering process. The diameter for this transition to occur is given by

*D*= 9.0

_{t}*Y*/ρ

*g*, and thus scales as

*g*

^{−1}for planetary surfaces when strength is not strain-rate dependent. This scaling result agrees with crater-shape data for the terrestrial planets [

*Chapman and McKinnon*, 1986]. We have related some of the calculable, but nonobservable parameters which are of interest (e.g. maximum depth of penetration, depth of excavation, and maximum crater lip height) to the crater diameter. For example, the maximum depth of penetration relative to the maximum crater diameter is 0.6, for strength dominated craters, and 0.28 for gravity dominated craters. These values imply that impactors associated with the large basin impacts penetrated relatively deeply into the planet's surface. This significantly contrasts to earlier hypotheses in which it had been erroneously inferred from structural data that the relative transient crater depth of penetration decreased with increasing diameter. Similarly, the ratio of the maximum depth of excavation relative to the final crater diameter is a constant ≃0.05, for gravity dominated craters, and ≃ 0.09 for strength dominated craters. This result implies that for impact velocities less than 25 km/s, where significant vaporization begins to take place, the excavated material comes from a maximum depth which is less than 0.1 times the crater diameter. In the gravity dominated regime, we find that the apparent final crater diameter is approximately twice the transient crater diameter and that the inner ring diameter is less than the transient crater diameter.