Lunar cratering asymmetries with high lunar orbital obliquity and inclination of the Moon

Accurate estimation of cratering asymmetry on the Moon is crucial for understanding Moon evolution history.Early studies of cratering asymmetry have omitted the contributions of high lunar obliquity and inclination.Here,we include lunar obliquity and inclination as new controlling variables to derive the cratering rate spatial variation as a function of longitude and latitude.With examining the influence of lunar obliquity and inclination on the asteroids population encountered by the Moon,we then have derived general formulas of the cratering rate spatial variation based on the crater scaling law.Our formulas with addition of lunar obliquity and inclination can reproduce the lunar cratering rate asymmetry at the current Earth-Moon distance and predict the apex/ant-apex ratio and the pole/equator ratio of this lunar cratering rate to be 1.36 and 0.87,respectively.The apex/ant-apex ratio is decreasing as the obliquity and inclination increasing.Combining with the evolution of lunar obliquity and inclination,our model shows that the apex/ant-apex ratio does not monotonically decrease with Earth-Moon distance and hence the influences of obliquity and inclination are not negligible on evolution of apex/ant-apex ratio.This model is generalizable to other planets and moons,especially for different spin-orbit resonances.