Lunar surface roughness from crater statistics

Statistical data have been compiled on the size distribution of craters in the range of sizes visible on lunar maps and photographs. These data are extrapolated to the smaller sizes to make an estimate of the relative frequency of smaller craters. It is found that cumulative crater size distribution in the visible range of sizes may be approximated by the law N = AD−B where N is the number of craters having diameter greater than D, and A and B are constants. The coefficient A depends upon the total number of craters per unit area, varying from about 1400 for the maria to 30,000 for the highland regions when D is measured in kilometers and N is in craters per 106 km2. However, it is found that the exponent B is reasonably independent of location on the lunar surface, having a value of about 1.6. Extrapolation using this expression shows that not more than 0.2 per cent of the surface of the maria is covered by craters in the diameter range 1 to 100 meters, and that even in the highlands, this size range covers less than 6.4 per cent of the area. Thus it would appear that mobility of vehicles is not likely to be jeopardized by these craters.