Department of Mathematics, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy.
Department of Physics, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy.
Sci Rep. 2021 Nov 22;11(1):22676. doi: 10.1038/s41598-021-02010-x.
Satellite collisions or fragmentations generate a huge number of space debris; over time, the fragments might get dispersed, making it difficult to associate them to the configuration at break-up. In this work, we present a procedure to back-trace the debris, reconnecting them to their original configuration. To this end, we compute the proper elements, namely dynamical quantities which stay nearly constant over time. While the osculating elements might spread and lose connection with the values at break-up, the proper elements, which have been already successfully used to identify asteroid families, retain the dynamical features of the original configuration. We show the efficacy of the procedure, based on a hierarchical implementation of perturbation theory, by analyzing the following four different case studies associated to satellites that underwent a catastrophic event: Ariane 44lp, Atlas V Centaur, CZ-3, Titan IIIc Transtage. The link between (initial and final) osculating and proper elements is evaluated through tools of statistical data analysis. The results show that proper elements allow one to reconnect the fragments to their parent body.
卫星碰撞或碎裂会产生大量的空间碎片；随着时间的推移，碎片可能会分散，难以将它们与解体时的构型联系起来。在这项工作中，我们提出了一种回溯碎片的方法，将它们重新连接到它们的原始构型。为此，我们计算了适当的元素，即随时间变化几乎保持不变的动力学量。虽然轨道元素可能会扩散并与解体时的值失去联系，但适当的元素已经成功地用于识别小行星家族，保留了原始构型的动力学特征。我们通过分析与经历灾难性事件的卫星相关的以下四个不同的案例研究，展示了基于摄动理论的分层实现的程序的有效性：Ariane 44lp、Atlas V Centaur、CZ-3、Titan IIIc Transtage。通过统计数据分析工具评估了（初始和最终）轨道和适当元素之间的联系。结果表明，适当的元素可以将碎片重新连接到它们的母体上。
