Centroid migration on an impacted granular slope due to asymmetric ejecta deposition and landsliding

For a fundamental understanding of terrain relaxation occurring on sloped surfaces of terrestrial bodies, we analyze the crater shape produced by an impact on an inclined granular (dry-sand) layer. Owing to asymmetric ejecta deposition followed by landsliding, the slope of the impacted inclined surface can be relaxed. Using the experimental results of a solid projectile impact on an inclined dry-sand layer, we measure the distance of centroid migration induced by asymmetric cratering. We find that the centroid migration distance $x_\mathrm{mig}$ normalized to the crater minor-axis diameter $D_\mathrm{cy}$ can be expressed as a function of the initial inclination of the target $\tan\theta$, the effective friction coefficient $\mu$, and two parameters $K$ and $c$ that characterize the asymmetric ejecta deposition and oblique impact effect: $x_\mathrm{mig}/D_\mathrm{cy}=K \tan\theta/(1-(\tan\theta/\mu)^2)+c$, where $K=0.6$, $\mu=0.8$, and $c=-0.1$ to $0.3$. This result is consistent with a previous study that considered the effect of asymmetric ejecta deposition. The obtained results provide fundamental information for analyzing the degradation of sloped terrain on planetary surfaces, such as crater-shape degradation due to the accumulation of micro-impacts.