We present a study on the relationship between the ratio of the depth of a crater to its diameter and the diameter for lunar craters both on the maria and on the highlands. We consider craters younger than 1.1 billion years in age, i.e. of Copernican period. The aim of this work is to improve our understanding of such relationships based on our new estimates of the craters’s depth and diameter. Previous studies considered similar relationships for much older craters (up to 3.2 billion years). We calculated the depths of craters with diameters from 10 to 100 km based on the altitude profiles derived from data obtained by the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter (LRO). The obtained ratios h/D of the depths h of the craters to their diameters D can differ by up to a factor of two for craters with almost the same values of diameters. The linear and power approximations (regressions) of the dependence of h/D on D were made for simple and complex Copernican craters selected from the data from Mazrouei et al. (Science 363:253–255, 2019) and Losiak et al. (Lunar Impact Crater Database, 2015). For the separation of highland craters into two groups based only on their dependences of h/D on D, at D < 18 km these are mostly simple craters, although some complex craters can have diameters D ≥ 16 km. Depths of mare craters with D ≤ 14 km are greater than 0.15D. Following Pike’s (Lunar Planet Sci XII:845–847, 1981) classification, we group mare craters of D < 15 km as simple craters. Mare craters with 15 < D < 18 km fit both approximation curves for simple and complex craters. Depths of mare craters with D > 18 km are in a better agreement with the approximation curve of h/D versus D for complex craters than for simple craters. At the same diameter, mare craters are deeper than highland craters at a diameter smaller than 30–40 km. For greater diameters, highland craters are deeper. The values of h/D for our approximation curves are mainly smaller than the values of the curve by Pike (in: Roddy, Pepin, Merrill (eds) Impact and explosion cratering: planetary and terrestrial implications, University of Arizona Press, Tucson, 1977) at D < 15 km. Only for mare craters at D < 11 km, our approximation curve is a little higher than the curve by Pike (1977). For our power approximations, the values of h/D obtained for complex craters are greater than those obtained by Pike (1981) at D > 53 km for highland craters, and at D < 80 km for mare craters.

我们对月海和高地上的陨石坑深度与其直径之比与月球陨石坑直径之间的关系进行了研究。我们认为陨石坑的年龄小于 11 亿年，即哥白尼时期的陨石坑。这项工作的目的是根据我们对陨石坑深度和直径的新估计，增进我们对这种关系的理解。之前的研究考虑了更古老的陨石坑（长达 32 亿年）的类似关系。我们根据月球勘测轨道飞行器（LRO）上的月球轨道飞行器激光高度计（LOLA）获得的数据得出的高度剖面，计算了直径为10至100公里的陨石坑的深度。对于具有几乎相同直径值的凹坑，所获得的凹坑深度h与其直径D的比率h / D可以相差高达两倍。h/D对D的依赖性的线性和幂近似（回归）是针对从 Mazrouei 等人的数据中选择的简单和复杂的哥白尼陨石坑进行的。 （科学 363：253–255，2019）和 Losiak 等人。 （月球撞击坑数据库，2015 年）。仅根据h/D对D的依赖关系将高地陨石坑分为两组，在D  < 18 km 时，这些陨石坑大多是简单陨石坑，尽管一些复杂陨石坑的直径D  ≥ 16 km。D ≤ 14 km的母马陨石坑深度 大于 0.15 D。根据派克（Lunar Planet Sci XII：845–847，1981）的分类，我们将D  < 15 km 的母陨石坑分组为简单陨石坑。 15 <  D  < 18 km 的马雷陨石坑符合简单和复杂陨石坑的近似曲线。D > 18 km的母海陨石坑的深度与复杂陨石坑的h/D与D的近似曲线比简单陨石坑的深度 更加吻合。在相同直径下，海马陨石坑比直径小于30-40公里的高地陨石坑更深。对于更大的直径，高地陨石坑更深。我们的近似曲线的h/D值主要小于 Pike 的曲线值（见：Roddy、Pepin、Merrill（编）《撞击和爆炸坑：行星和地球的影响》，亚利桑那大学出版社，图森，1977 年） ）在D  < 15 公里。仅对于D < 11 km的母马陨石坑 ，我们的近似曲线略高于 Pike (1977) 的曲线。对于我们的幂近似值， h/D的值对于复杂陨石坑，获得的结果大于 Pike (1981) 在D  > 53 km 处的高地陨石坑和在D  < 80 km 处的海马陨石坑处获得的结果。