Low-thrust trajectory design in low-energy regimes using variational equations

This paper proposes a novel description of the equations of motion for low-thrust trajectory design in the presence of a third-body perturbation. The framework is formulated using Gauss’ Variational Equations (GVE) with two distinct accelerations: the one produced by the electric engine and the disturbing term of the third-body effect, which is computed using the disturbing potential of the previously studied Keplerian Map. The presented GVE third-body (GVE-3B) framework allows for a simple and intuitive description of the low-thrust optimisation problem. It is accurate until very close to the sphere of influence of the perturbing body, and thus can be used to target trajectories in low-energy regimes. Together with the framework, this paper develops a methodology to generate low-energy first-guess solutions for low-thrust trajectories. Both the methodology and the framework are showcased in the design of two distinct missions: a rendezvous with asteroid 2017 SV19 during its next Earth encounter, after departing from the unstable invariant manifold of the L2" role="presentation" style="display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">L2 point in the Sun-Earth system, and the capture of asteroid 2018 AV2 to a stable invariant manifold of the same point