Scaling laws for doublet craters formed by low-velocity impacts of unequal-mass spheres into a granular bed

Abstract

Understanding the formation mechanism of doublet craters is an important challenge for advancing knowledge in astronomy and granular physics. In this study, we investigated craters formed by low-velocity impacts of two steel spheres with different masses into a granular bed. Even when the masses were different, a figure-eight-shaped doublet crater and a central ridge were observed, similar to the case with equal masses. However, the resulting shape became asymmetric even without a time delay between impacts. The total length of the doublet crater increased depending on the spacing between the two spheres and the ratio of their impact energies. These results followed a theoretical model based on a scaling law, where the crater diameter is proportional to the one-fourth power of the impact energy. A model was also developed to describe the crater overlap, which increases as the spheres become closer. It was also shown that the crater diameters vary with the time difference, and that the second impact tends to form a larger crater due to fluidization induced by the first.