Elliptical craters and basins on the terrestrial planets

The four largest well-preserved impact basins in the solar system, Borealis, Hellas, and Utopia on Mars, and South Pole–Aitken on the Moon, are all signifi cantly elongated, with aspect ratios >1.2. This population stands in contrast to experimental studies of impact cratering that predict <1% of craters should be elliptical, and the observation that ~5% of the small crater population on the terrestrial planets is elliptical. Here, we develop a simple geometric model to represent elliptical crater formation and apply it to understanding the observed population of elliptical craters and basins. A projectile impacting the surface at an oblique angle leaves an elongated impact footprint. We assume that the crater expands equally in all directions from the scaled footprint until it reaches the mean diameter predicted by scaling relationships, allowing an estimate of the aspect ratio of the fi nal crater. For projectiles that are large relative to the size of the target planet, the curvature of the planetary surface increases the elongation of the projectile footprint for even moderate impact angles, thus increasing the likelihood of elliptical basin formation. The results suggest that Hellas, Utopia, and South Pole–Aitken were formed by impacts inclined at angles less than ~45° from horizontal, with a probability of occurrence of ~0.5. For the Borealis Basin on Mars, the projectile would likely have been decapitated, with the topmost portion of the projectile on a trajectory that did not intersect with the surface of the planet. Andrews-Hanna, J.C., and Zuber, M.T., 2010, Elliptical craters and basins on the terrestrial planets, in Gibson, R.L., and Reimold, W.U., eds., Large Meteorite Impacts and Planetary Evolution IV: Geological Society of America Special Paper 465, p. 1–13, doi: 10.1130/2010.2465(01). For permission to copy, contact [email protected]. ©2010 The Geological Society of America. All rights reserved. INTRODUCTION While the vast majority of impact craters are roughly circular in planform, a small fraction of craters produced both experimentally and observed on planetary surfaces have signifi cantly elongated shapes. Experimental work suggests that these elliptical craters form in only the most oblique impacts, and the critical impact angle for elliptical crater formation (θ c , representing the angle between the projectile trajectory and the horizontal) is 4.7° (Gault and Wedekind, 1978). For a population of projectiles with random trajectories, the probability of an impact occurring at an angle of less than a given angle, θ, is sin (θ) (Gilbert, 1893), irrespective of the gravity of the target planet (Shoemaker, 1962). Thus, the experimentally determined threshold angle for elliptical crater formation would suggest that ~0.7% of craters should be elliptical. However, surveys of the observed population of elliptical craters on Mars, Venus, and the Moon found that roughly 5% of 2 Andrews-Hanna and Zuber the population of small (<150 km diameter) craters are elliptical (Schultz and Lutz-Garihan, 1982; Barlow, 1988; Bottke et al., 2000). Schultz and Lutz-Garihan (1982) proposed that for Mars, this paradox could be resolved if the planet possessed a population of small moons that spiraled inward to strike the surface at low angles. However, using a simple conceptual model of elliptical crater formation to reconcile the frequency of elliptical craters produced experimentally with that observed on the terrestrial planets, Bottke et al. (2000) found that such a scenario is not necessary. They assumed that the tendency of an impact to produce an elliptical crater is related to the ratio between the fi nal crater diameter (D c ) and the projectile diameter (d p ). They considered results from two different experimental studies, investigating impacts into sand (Gault and Wedekind, 1978) and aluminum (Christiansen et al., 1993), with different D c /d p ratios and θ c values. Bottke et al. (2000) used the results from these two studies to generalize an empirical power-law relationship between θ c and D c /d p : θ c = θ 0 (D c /d p ), (1) where θ 0 = 68.1°, and m = −0.648. Utilizing the D c /d p ratio indicated by π-scaling relationships (Holsapple and Schmidt, 1982; Melosh, 1989), this power law successfully explains the 5% abundance of impact craters on the terrestrial planets, and it suggests that θ c will also depend on projectile diameter. At the other end of the size spectrum, the small population of the largest impact basins reveals a further discrepancy between the expected and observed population of elliptical impact craters. Here, we show that four of the six largest well-preserved impact basins in the solar system (Borealis, Hellas, and Utopia on Mars, and South Pole–Aitken on the Moon) all exhibit pronounced elliptical shapes. Of the basins we classify as “giant impact basins,” which are defi ned as a basin diameter greater than half the planetary radius, only Caloris on Mercury and Imbrium on the Moon fall short of our assumed criterion for classifi cation as an elliptical basin. Adopting the 5% abundance of elliptical craters observed in the small crater population, the probability that four of the six giant basins would be elliptical by random chance is 8.5 × 10−5, and thus can be effectively ruled out. We suggest that this paradox can be resolved by considering the effect of the curvature of the planetary surface on the resulting basin shape. For the largest impacts, the surface of the planet curves away from the projectile path, leading to more elongated projectile footprints (the projection of the projectile onto the surface of the planet). This increased elongation of the projectile footprint for a given impact angle increases the probability of elliptical basin formation. We developed a simple geometrical model for elliptical crater formation based on the calculated projectile footprint aspect ratio and the fi nal crater diameter from π-scaling relationships. The model can explain both the critical angle in small-scale laboratory experiments and the observed fraction of elliptical craters in the 1–150-kmdiameter range, and it further offers the expectation that a Hellas-sized impact basin would have a probability of being elliptical of ~0.4. OBSERVED ELLIPTICAL BASINS ON MARS AND THE MOON