DOI: 10.5281/zenodo.5931462
title: EXTREMA: Ballistic capture sets at Mars over an Earth–Mars synodic period from January 1, 2030, to February 20, 2032

description: 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.