Analytical estimates of melt volumes produced by a given projectile and contained in a given impact crater are derived as a function of impact velocity, impact angle, planetary gravity, target and projectile densities, and specific internal energy of melting. Applications to impact events and impact craters on the Earth, Moon, and Mars are demonstrated and discussed. The most probable oblique impact (45°) produces ∼1.6 times less melt volume than a vertical impact, and ∼1.6 and 3.7 times more melt volume than impacts with 30° and 15° trajectories, respectively. The melt volume for a particular crater diameter increases with planetary gravity, so a crater on Earth should have more melt than similar-size craters on Mars and the Moon. 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 significantly larger than on Mars. Higher surface temperatures and geothermal gradients increase melt production, as do lower energies of melting. Collectively, the results imply thinner central melt sheets and a smaller proportion of melt particles in impact breccias on the Moon and Mars than on Earth. These effects are illustrated in a comparison of the Chicxulub crater on Earth, linked to the Cretaceous–Tertiary mass extinction, Gusev crater on Mars, where the Mars Exploration Rover Spirit landed, and Tsiolkovsky crater on the Moon. The results are comparable to those obtained from field and spacecraft observations, other analytical expressions, and hydrocode simulations.
