PLANETARY CRATERING MECHANICS

The objective of this study was to obtain a quantitative understanding of the cratering process over a broad range of conditions. Our approa ch was to numerically compute the evolution of impact induced flow fie lds and calculate the time histories of the key measures of crater geo metry (e.g. depth, diameter, lip height) for variations in planetary g ravity (0 to 10(9) cm/s2), material strength (0 to 2400 kbar), and imp actor radius (0.05 to 5000 km). These results were used to establish t he values of the open parameters in the scaling laws of Holsapple and Schmidt (1987). We describe the impact process in terms of four regime s: (1) penetration, (2) inertial, (3) terminal and (4) relaxation. Dur ing the penetration regime, the depth of impactor penetration grows li nearly for dimensionless times tau = (Ut/a) <5.1. Here, U is projectil e velocity, t is time, and a is projectile radius. In the inertial reg ime, tau > 5.1, the crater grows at a slower rate until it is arrested by either strength or gravitational forces. In this regime, the incre ase of crater depth, d, and diameter, D, normalized by projectile radi us is given by d/a = 1.3 (Ut/a)0.36 and D/a = 2.0(Ut/a)0.36. For stren gth-dominated craters, growth stops at the end of the inertial regime, which occurs at tau = 0.33 (Y(eff)/rhoU2)-0.78, where Y(eff) is the e ffective planetary crustal strength. The effective strength can be red uced from the ambient strength by fracturing and shear band melting (e .g. formation of pseudo-tachylites). In gravity-dominated craters, gro wth stops when the gravitational forces dominate over the inertial for ces, which occurs at tau = 0.92 (ga/U2)-0.61. In the strength and grav ity regimes, the maximum depth of penetration is d(p)/a = 0.84 (Y/rho U2)-0.29 and d(p)/a = 1.2 (ga/U2)-0.22, respectively. The transition f rom simple bowl-shaped craters to complex-shaped craters occurs when g ravity starts to dominate over strength in the cratering process. The diameter for this transition to occur is given by D(t) = 9.0 Y/rhog, a nd thus scales as g-1 for planetary surfaces when strength is not stra in-rate dependent. This scaling result agrees with crater-shape data f or the terrestrial planets [Chapman and McKinnon, 1986]. We have relat ed some of the calculable, but nouobservable parameters which are of i nterest (e.g. maximum depth of penetration, depth of excavation, and m aximum crater lip height) to the crater diameter. For example, the max imum depth of penetration relative to the maximum crater diameter is 0 .6, for strength dominated craters, and 0.28 for gravity dominated cra ters. These values imply that impactors associated with the large basi n impacts penetrated relatively deeply into the planet's surface. This significantly contrasts to earlier hypotheses in which it had been er roneously inferred from structural data that the relative transient cr ater depth of penetration decreased with increasing diameter. Similarl y, the ratio of the maximum depth of excavation relative to the final crater diameter is a constant congruent-to 0.05, for gravity dominated craters, and congruent-to 0.09 for strength dominated craters. This r esult implies that for impact velocities less than 25 km/s, where sign ificant vaporization begins to take place, the excavated material come s from a maximum depth which is less than 0.1 times the crater diamete r. In the gravity dominated regime, we find that the apparent final cr ater diameter is approximately twice the transient crater diameter and that the inner ring diameter is less than the transient crater diamet er.