  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.
