The Area of Cold Traps on the Lunar Surface

We numerically calculate the probability and area of permanent shadowing as a function of the selenographic latitude as well as the total area of the permanently shadowed surface for various hierarchical models of the lunar surface. The permanently shadowed area is shown to rapidly increase with increasing number of hierarchical surface levels. For a two-level model of the lunar relief, where the surface of craters is complicated by a random small-scale relief with a Gaussian distribution of heights and slopes, the area of the doubly shadowed regions of the lunar surface is approximately an order of magnitude smaller than the area of the singly shadowed regions. A comparison of the permanently shadowed area calculated by using averaged statistical relations and data on the actual distribution of craters near the lunar poles shows almost complete agreement.