The chronology of the moons of Saturn, especially Titan, has been limited by a lack of strong constraints on the cratering rate, low number statistics for small‐N counts of large‐diameter craters, and uncertainty about whether impactors are mostly heliocentric impactors orbiting the Sun or planetocentric impactors orbiting Saturn itself. Here, I propose to address these three problems. Instead of looking for an absolute cratering rate, I focus on the relative crater densities, calculating scaling relationships between the moons. I update crater analysis methodology by numerically modeling probability density functions of the uncertainty of crater density, enabling me to accurately assess the error of even single‐crater observations. Using these updated statistics, I show how the heliocentric cratering model leads to a dramatic increase in relative crater density for Mimas, Tethys, Dione, Rhea, and Iapetus with distance from Saturn. Under this model, the surface age of Titan is probably older than the cratered plains of Mimas—implying a very low erosion rate and minimal endogenic resurfacing on Titan. I explore possible explanations, concluding that the likeliest explanation is planetocentric cratering, although saturation effects cannot be ruled out. Under the planetocentric model, the relative crater densities of the cratered plains of Mimas, Tethys, Dione, Rhea, and Iapetus are all very close, with the relative crater density at Titan between 1 and 2 orders of magnitude lower. Under planetocentric cratering, the cratering rate on Titan allows for vigorous erosion and endogenic resurfacing.

中文翻译：

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土星主要卫星之间的相对陨石坑缩放：对行星中心陨石坑和泰坦表面年龄的影响

土星，尤其是土卫六卫星的年代，受到火山口率缺乏严格约束的限制，小数字N的数字较少大直径陨石坑的数量，以及撞击器主要是绕太阳运行的日心撞击器还是绕土星自身飞行的平面中心撞击器的不确定性。在这里，我建议解决这三个问题。我没有寻找绝对的陨石坑率，而是关注相对的陨石坑密度，计算了卫星之间的缩放关系。我通过对火山口密度不确定性的概率密度函数进行数值建模来更新火山口分析方法，使我能够准确地评估甚至单个火山口观测值的误差。使用这些更新的统计数据，我展示了以日心为中心的陨石坑模型如何随着距土星的距离而导致Mimas，Tethys，Dione，Rhea和Iapetus的相对陨石坑密度急剧增加。在这种模式下 土卫六的表面年龄可能比密马斯陨石坑的平原还要老，这意味着土卫六上的侵蚀速率非常低，内生表面最少。我探索了可能的解释，认为最可能的解释是平面到中心的缩孔，尽管不能排除饱和效应。在以平面为中心的模型下，Mimas，Tethys，Dione，Rhea和Iapetus火山口平原的相对火山口密度都非常接近，土卫六的相对火山口密度降低了1-2个数量级。在以平面为中心的缩孔作用下，土卫六上的缩孔率可进行剧烈侵蚀和内生表面重铺。尽管不能排除饱和效应。在以平面为中心的模型下，Mimas，Tethys，Dione，Rhea和Iapetus火山口平原的相对火山口密度都非常接近，土卫六的相对火山口密度降低了1-2个数量级。在以平面为中心的缩孔作用下，土卫六上的缩孔速率可进行剧烈侵蚀和内生表面重铺。尽管不能排除饱和效应。在以平面为中心的模型下，Mimas，Tethys，Dione，Rhea和Iapetus火山口平原的相对火山口密度都非常接近，土卫六的相对火山口密度降低了1-2个数量级。在以平面为中心的缩孔作用下，土卫六上的缩孔率可进行剧烈侵蚀和内生表面重铺。