  Crater count equilibrium occurs when new craters form at the same rate that
old craters are erased, such that the total number of observable impacts
remains constant. Despite substantial efforts to understand this process, there
remain many unsolved problems. Here, we propose an analytical model that
describes how a heavily cratered surface reaches a state of crater count
equilibrium. The proposed model formulates three physical processes
contributing to crater count equilibrium: cookie-cutting (simple, geometric
overlap), ejecta-blanketing, and sandblasting (diffusive erosion). These three
processes are modeled using a degradation parameter that describes the
efficiency for a new crater to erase old craters. The flexibility of our newly
developed model allows us to represent the processes that underlie crater count
equilibrium problems. The results show that when the slope of the production
function is steeper than that of the equilibrium state, the power law of the
equilibrium slope is independent of that of the production function slope. We
apply our model to the cratering conditions in the Sinus Medii region and at
the Apollo 15 landing site on the Moon and demonstrate that a consistent
degradation parameterization can successfully be determined based on the
empirical results of these regions. Further developments of this model will
enable us to better understand the surface evolution of airless bodies due to
impact bombardment.
