Abstract This paper studies the characteristics of the large natural satellites in the solar system using clustering techniques. A variety of distances such as the Canberra, Arc-Cosine, Jaccard, Euclidean, Lorentzian and Manhattan are used to unravel the relationships between the moons emerging from their attributes. In a first phase, 19 large moons are selected and measured under the light of 9 orbital and physical characteristics. Two visualisation methods, namely the hierarchical clustering and multidimensional scaling, are used to analyse the observed satellite features. The Canberra distance presents a superior performance and leads to the most relevant maps. In a second phase, the influence of adding the hypothetical Satellite X, that is proposed to orbit Planet Nine, is examined. The effect of adding Planet Nine’s moon has a significant impact on the output of the two visualisation techniques. Adding this speculative object leads to a better discrimination of the clusters. Finally, the case of mixing some planets (including Planet Nine) with satellites (consisting of Satellite X) is tested leading to identical conclusions. Indeed, the numerical results reveal that including Planet Nine and its moon decrease the spread of emerging clusters in comparison with the case of their exclusion.

中文翻译：

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太阳系大型天然卫星聚类分析

摘要 本文利用聚类技术研究了太阳系中大型天然卫星的特征。各种距离，例如堪培拉距离、反余弦距离、雅卡德距离、欧几里得距离、洛伦兹距离和曼哈顿距离，都被用来解开从它们的属性中出现的卫星之间的关系。在第一阶段，根据 9 个轨道和物理特性，选择和测量 19 颗大卫星。两种可视化方法，即层次聚类和多维缩放，用于分析观测到的卫星特征。堪培拉距离表现出卓越的性能，并导致最相关的地图。在第二阶段，检查添加假设卫星 X 的影响，该卫星提议绕行星九运行。添加行星九的月亮的效果对两种可视化技术的输出有显着影响。添加这个推测对象可以更好地区分集群。最后，对一些行星（包括行星九）与卫星（由卫星 X 组成）混合的情况进行了测试，得出了相同的结论。事实上，数值结果表明，与排除它们的情况相比，包括第九行星及其卫星在内的新兴星团的传播会减少。