Hypervelocity Impacts
When an asteroid strikes a planet at tens of kilometers per second, the kinetic energy exceeds the binding energy of both impactor and target by orders of magnitude. The impactor does not simply push into the surface like a bullet — it generates a shock wave that vaporizes, melts, and excavates material in a hemispherical explosion. The resulting crater is always much larger than the impactor itself, typically 10 to 20 times the impactor diameter.
Pi-Scaling Framework
Crater scaling laws use dimensionless ratios (pi-groups) to relate crater size to impact parameters across many orders of magnitude — from centimeter-scale laboratory shots to 200-km basins. The transient crater diameter scales as D proportional to d^0.78 times v^0.44, meaning velocity matters almost as much as impactor size. Gravity limits final crater size, which is why the Moon's low gravity allows proportionally larger craters.
Simple vs Complex Craters
Below a critical diameter (about 2-4 km on Earth, 15-20 km on the Moon), craters are simple bowls with depth-to-diameter ratios near 0.2. Above this threshold, the crater floor rebounds upward to form a central peak while the steep walls collapse into terraces. The largest impacts create multi-ring basins like the South Pole-Aitken basin on the Moon (2,500 km diameter).
Catastrophic Impacts in Earth History
Impact cratering has shaped the course of life on Earth. The Chicxulub impact 66 million years ago caused the Cretaceous-Paleogene mass extinction, eliminating 75% of all species. Earlier, the Vredefort impact (2 Gya, 300 km crater) and Sudbury impact (1.85 Gya, 250 km crater) left geological scars still visible today. Understanding crater scaling helps assess the hazard from near-Earth asteroids.