Estimation of the Area of the Perpetually Shaded Lunar Surface

We present the results of computer simulation of the shadowing effect for three types of surface: (1) cratered, (2) formed by a random profile with Gaussian statistical height and slope distributions, and (3) a two-scale surface representing a cratered area that is complicated by small-scale random relief. The calculations are based on data on the distribution of lunar craters derived from the diameter/depth ratio and on the assumption of the equilibrium distribution of the crater population in the circumpolar areas of the lunar surface. We determined the characteristics of perpetually shaded areas of the lunar surface: the probability of the constant shadowing of an arbitrary surface point, the fraction of the perpetually shaded area as a function of selenographic latitude, the latitudinal dependence of the perpetually shaded area, and the total area of the perpetually shaded surface. The calculations showed that the presence of structural features of different scale on the lunar surface can considerably increase the estimate of the fraction of the perpetually shaded area compared to existing estimates.