de Almeida Junior Allan Kardec, de Almeida Prado Antonio Fernando Bertachini
INPE: National Institute for Space Research, São José dos Campos, SP, Brazil.
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow, Russian Federation.
Sci Rep. 2022 Mar 9;12(1):4148. doi: 10.1038/s41598-022-08046-x.
Important properties of the dynamics of a spacecraft can be obtained from the Circular Restricted Three Body Problem and the Bi-Circular Bi-planar Four Body Problem. In this work, both systems are compared under the perspective of the costs involved in a transfer between the smaller primaries. An analytical approach shows several properties of the perturbation due to the gravity of the Sun and the motion of the smaller primaries around it over a spacecraft in the region of interest, like its behavior at and around the barycenter or at any point in a circle around the Sun. The costs involved in transfers between the smaller primaries are numerically evaluated and analyzed using the newly developed Theory of Functional Connections. The results show that the influence of this perturbation over the costs is significant for systems like the Sun-Earth-Moon or Sun-Mars-Phobos. On the other hand, it is also shown that this influence may be negligible for other very different systems, like the Sun-Saturn-Titan or Sun-Ida-Dactyl. Maps of perturbation are drawn in the region of interest, which can be used for mission designers. Finally, a new approach to describe the influence of the Sun over the tides of the smaller primaries is proposed under the Four Body Problem model.
航天器动力学的重要特性可从圆型限制性三体问题和双圆双平面四体问题中获得。在这项工作中，从较小主天体之间转移所涉及的成本角度对这两个系统进行了比较。一种分析方法展示了由于太阳引力以及较小主天体围绕太阳在感兴趣区域内航天器周围的运动所产生的摄动的若干特性，比如其在质心处及附近或围绕太阳的圆上任意一点的行为。使用新开发的函数连接理论对较小主天体之间转移所涉及的成本进行了数值评估和分析。结果表明这种摄动对成本的影响对于太阳 - 地球 - 月球或太阳 - 火星 - 火卫一等系统而言是显著的。另一方面，也表明对于其他非常不同的系统，如太阳 - 土星 - 土卫六或太阳 - 艾达 - 达克泰尔，这种影响可能可以忽略不计。在感兴趣区域绘制了摄动图，可供任务设计者使用。最后，在四体问题模型下提出了一种描述太阳对较小主天体潮汐影响的新方法。
