EXTREMA: Ballistic capture sets at Mars over an Earth–Mars synodic period from January 1, 2030, to February 20, 2032

EXTREMA (short for Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy) enables self-driving spacecraft, challenging the current paradigm under which spacecraft are piloted in the interplanetary space. Deep-space guidance, navigation, and control applied in a complex scenario is the subject of EXTREMA, which wants to engineer ballistic capture in a totally autonomous fashion. EXTREMA is erected on three pillars. Pillar 1 is on autonomous navigation. Pillar 2 involves autonomous guidance and control. Pillar 3 deals with autonomous ballistic capture, the focus of this work. The project has been awarded a European Research Council (ERC) Consolidator Grant in 2019. In Pillar 3 it is investigated how a spacecraft can attain ballistic capture in autonomy. Ballistic capture is an event that occurs in extremely-rare occasions, and requires acquiring a proper state (position, velocity) far away from the target planet [1]. Massive numerical simulations are required to find the specific conditions that support capture [2]. On average, 1 out of 10,000 conditions explored by the algorithm grants capture [3]. The union of these points defines the capture set, which in turn is used to find the capture corridors: these are streams of orbits that can be targeted far away from the planet and that guarantee ballistic capture. The data set contains the initial conditions of weakly-stable, unstable, crash, moon-crash, and capture sets at Mars with initial epochs uniformly distributed from 01 JAN 2030 12:00:00.000 (UTC) to 20 FEB 2032 10:32:39.144 (UTC), covering a complete Earth–Mars synodic period of approximately 780 days. The grid of initial conditions is built to maximize the capture ratio for Mars (see Figure 10 in [3]). Initial conditions are propagated in high-fidelity. The equations of motion of the restricted n-body problem are considered. The gravitational attractions of the Sun, Mercury, Venus, Earth (B*), Mars (central body), Jupiter (B), Saturn (B), Uranus (B), and Neptune (B) are taken into account. Additionally, solar radiation pressure, Mars’ non-spherical gravity, and relativistic corrections [4] (Schwarzschild solution, geodesic precession, and Lense-Thirring precession) are also included in the model. For additional information about the EXTREMA project visit the page extrema.polimi.it. <strong>References</strong><br> [1] F. Topputo and E. Belbruno,'Earth–Mars transfers with ballistic capture', Celestial Mechanics and Dynamical Astronomy, Vol. 121, No. 4, 2015, pp. 329–346. DOI: 10.1007/s10569-015-9605-8.<br> [2] F. Topputo and E. Belbruno, 'Computation of weak stability boundaries: Sun–Jupiter system', Celestial Mechanics and Dynamical Astronomy, Vol. 105, No. 1-3, 2009, pp. 3–17. DOI: 10.1007/s10569-009-9222-5<br> [3] Z.-F. Luo and F. Topputo, 'Analysis of ballistic capture in Sun–planet models', Advances in Space Research, Vol. 56, No. 6, 2015, pp. 1030–1041. DOI: 10.1016/j.asr.2015.05.042<br> [4] C. Huang, J. C. Ries, B. D. Tapley, and M. M.Watkins, 'Relativistic effects for near-earth satellite orbit determination', Celestial Mechanics and Dynamical Astronomy, Vol. 48, No. 2, 1990, pp. 167–185. DOI: 10.1007/BF00049512 * Here B stands for barycenter.EXTREMA（全称为*Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy*，即面向自主深空探测任务的天体动力学极端稀有事件构建）可赋能自主运行航天器，挑战当前行星际空间需人工操控航天器的主流范式。该数据集的核心研究主题为复杂场景下的深空制导、导航与控制，目标是以完全自主的方式实现弹道捕获（ballistic capture）。EXTREMA项目依托三大支柱展开：支柱1聚焦自主导航，支柱2涵盖自主制导与控制，支柱3则针对自主弹道捕获开展研究，亦是本工作的核心关注点。该项目于2019年获得欧洲研究理事会（European Research Council, ERC）的巩固型研究基金资助。 在支柱3中，研究团队探讨航天器如何自主实现弹道捕获。弹道捕获是一种极为罕见的事件，需要在远离目标行星的位置获取恰当的状态（位置、速度）[1]。为找到支持捕获的特定条件，需开展大规模数值模拟[2]。平均而言，算法探索的每10000个初始条件中，仅有1个可实现捕获[3]。上述条件的集合构成捕获集，借此可进一步推导捕获走廊：即一系列可从行星远距离瞄准并确保实现弹道捕获的轨道流。 本数据集包含火星轨道下的弱稳定、不稳定、坠毁、月球坠毁以及捕获集的初始条件，初始历元均匀分布于2030年1月1日12:00:00.000（协调世界时，UTC）至2032年2月20日10:32:39.144（UTC）之间，覆盖约780天的完整地火会合周期。初始条件网格的构建旨在最大化火星捕获率（详见文献[3]中的图10）。初始条件采用高保真度传播方式：所采用的运动方程为限制性n体问题（restricted n-body problem），计入太阳、水星、金星、地球（B*）、火星（中心天体）、木星（B）、土星（B）、天王星（B）以及海王星（B）的引力作用。此外，模型还纳入了太阳辐射压、火星非球形引力场以及相对论修正[4]（包括史瓦西解、测地线进动以及兰斯-蒂林进动）。注：此处B代表质心（barycenter）。 如需了解EXTREMA项目的更多信息，请访问官网extrema.polimi.it。 <strong>参考文献</strong><br> [1] F. Topputo与E. Belbruno, 《Earth–Mars transfers with ballistic capture》, 《Celestial Mechanics and Dynamical Astronomy》, 第121卷第4期, 2015年, 第329–346页. DOI: 10.1007/s10569-015-9605-8.<br> [2] F. Topputo与E. Belbruno, 《Computation of weak stability boundaries: Sun–Jupiter system》, 《Celestial Mechanics and Dynamical Astronomy》, 第105卷第1-3期, 2009年, 第3–17页. DOI: 10.1007/s10569-009-9222-5<br> [3] Z.-F. Luo与F. Topputo, 《Analysis of ballistic capture in Sun–planet models》, 《Advances in Space Research》, 第56卷第6期, 2015年, 第1030–1041页. DOI: 10.1016/j.asr.2015.05.042<br> [4] C. Huang、J. C. Ries、B. D. Tapley与M. M. Watkins, 《Relativistic effects for near-earth satellite orbit determination》, 《Celestial Mechanics and Dynamical Astronomy》, 第48卷第2期, 1990年, 第167–185页. DOI: 10.1007/BF00049512 * 此处B代表质心。