Froude number scaling unifies impact trajectories into granular media across gravitational conditions

The interactions of solid objects with granular media is countered by a resistance force that stems from frictional forces between the grains and the media's resistance to inertia imposed by the intruder. Earlier theories of granular intrusion have suggested an additive contribution of these two families of forces and had tremendous success in predicting resistive forces on arbitrary shaped objects. However, it remains unclear how these forces are influenced by gravitational conditions. We examine the role of gravity on surface impact behavior into cohesionless granular media using hundreds of soft-sphere discrete element simulations, we demonstrate that the outcome of impacts remain qualitatively similar under varying gravitational conditions if initial velocities are scaled with the Froude number, suggesting an underlying law. Using theoretical arguments, we provide reasoning for the observed universality and show that there is a hidden dependency in resistive forces into granular media on Froude number. Following the theoretical framework, we show that Froude number scaling precisely collapses impact trajectories across gravitational conditions, setting the foundation for explorations in granular behavior beyond Earth.