Solution
= Solution
In a gravity-dominated excavation model, displaced <mass> scales as $\rho D^3$ and lifting it through a distance of order $D$ costs order $\rho gD^4$. If a comparable fraction of impact <energy> supplies this <work> across similar impacts, $\boxed{D\propto E_{\mathrm{impact}}^{1/4}}$. This is a scaling justification, not a universal crater law: strength-dominated small craters or varying coupling efficiencies can have different <Exponent>[exponents].