A flow-informed strategy for ballistic capture trajectory design

Abstract

In interplanetary mission design, ballistic capture is the phenomenon by which a spacecraft approaches its target body, and performs a number of revolutions around it, without requiring manoeuvres in between. For a spacecraft to be captured, its gravitational interaction with at least two celestial bodies has to be taken into account. Because of their fail-safe nature (eliminating the possibility of single point failures), their fuel efficiency and their wider launch windows, ballistic capture trajectories are of particular scientific and engineering interest. Capture orbits are characterized by a specific qualitative dynamics, defining almost-invariant regions in a given space, guiding transport phenomena; the introduction of structures, defining and bounding such domains, naturally follows. Traditionally, the set of initial conditions leading to capture, the Capture Set, has been computed by sampling the domain of interest, and hence analysing the forward and backward behaviour of the orbit associated to each sample. The main limitations of this approach reside in its large computational cost and, even for a dense grid, in the non-smooth approximation of the aforementioned boundary regions; the theory of Lagrangian Coherent Structures (LCS) has the potential of overcoming both limitations, allowing at the same time for a more insightful description of the phenomenon. In fact, Lagrangian Coherent Structures identify transport barriers in dynamical systems, separating regions with qualitatively different dynamics. The development of heuristics applicable to ballistic capture trajectory design and informed by such theory (i.e. flow-informed) appears desirable. In this research, different flow-informed approaches are presented and their relations with ballistic capture are discussed: following, a new heuristic, the Stroboscopic Strainline, is introduced. This new tool is therefore applied to different case studies at Mars, in order to approximate the capture sets associated to different numbers of revolutions and geometries. While a real-ephemerides model has been used to model the dynamical environments, different levels of fidelity have been investigated: perturbing forces have been introduced not only to obtain more accurate results, but also to test the robustness of the proposed technique with respect to different features of the underlying dynamical model. Finally, it is shown how Stroboscopic Strainlines are a good candidate for characterizing the qualitative behaviour of ballistic trajectories, both forward and backward in time.