IMPACT MELT VOLUMES IN OBLIQUE IMPACTS ON THE EARTH, MOON, AND MARS

Existing analytical expressions for calculating impact melt volume assume a vertical impact trajectory and, thus, do not allow the community to investigate or predict melt volumes produced by oblique impacts. This shortcoming needs to be overcome, because the most probable impact trajectories have angles of 45º with the surface (G. K. Gilbert 1893; E. M. Shoemaker 1962) and impact events with even shallower inclinations are possible. Recently time-intensive computer codes have been developed that allow three-dimensional simulations of impact events. They have shown that the amount of melt produced by impacts at various impact angles on Earth decreases with impact angle. We use that type of result to render a new easy-to-use analytical expression for calculating impact melt volumes applicable to a broad range of planetary conditions.

Our analytical expression is derived for melt volumes produced by oblique impacts as a function of gravity, impact velocity, impact angle, and density of impact projectiles and target surfaces on the Earth, Moon, and Mars. The most probable oblique impact (45º) produces ~1.6 times less melt volume than a vertical impact, and ~1.6 to 3.7 times more melt than impacts with 30º and 15º trajectories, respectively. The melt volume for a particular crater diameter increases with gravity and impact velocity, so a crater on Earth will have more melt than similar-size craters on Mars and the Moon. For example, the formation of a transient crater with a particular diameter on Earth generates 2 to 3 times more melt than on Mars and 4 to 5 times more melt than on the Moon. The direction of the trend is similar when comparing structures with the same final crater diameters: assuming a 45º trajectory the 180 km diameter Chicxulub impact crater produced at the K-T boundary on Earth contains ~7,800 km³ of melt (and up to 12,000 km³ for a vertical impact), while the 180 km diameter Tsiolkovsky crater on the Moon contains only ~6,900 km³ of melt. However, the melt volume for a particular projectile diameter does not depend on gravity, but has a strong dependence on impact velocity, so the melt generated by a given projectile on the Moon is ~2 times greater than that on Mars. Collectively, these results imply thinner central melt sheets and smaller proportion of melt particles in impact breccias on the Moon and Mars than on Earth.