Multi-fidelity modelling of low-energy trajectories for space mission design. - Neves, Rita (Cranfield University, 2019)
The proposal of increasingly complex and innovative space endeavours poses growing demands for mission designers. In order to meet the established requirements and constraints while maintaining a low fuel cost, the use of low-energy trajectories is particularly interesting. These paths in space allow spacecraft to change orbits and move with little to no fuel, but they are computed using motion models of a higher fidelity than the commonly used two-body problem. For this purpose, perturbation methods that explore the third-body effect are especially attractive, since they can accurately convey the system dynamics of a three-body configuration with a lower computational cost, by employing mapping techniques or exploring analytical approximations. The focus of this work is to broaden the knowledge of low-energy trajectories by developing new mathematical tools to assist in mission design applications. In particular, novel models of motion based on the third-body effect are conceived and classified by the forces they account for (conservative or non-conservative). The necessary numerical tools to complement the trajectory design are developed: this includes differential correction methods and targeting schemes, which take advantage of the Jacobian matrices derived from the presented models to generate full low-thrust control laws. One application of this analysis focuses on the trajectory design for missions to near- Earth asteroids. Two different projects are explored: one is based on the preliminary design of separate rendezvous and capture missions to the invariant manifolds of libration point L₂. This is achieved by studying two specific, recently discovered bodies and determining dates, fuel cost and final control history for each trajectory. The other covers a larger study on asteroid capture missions, where several asteroids are regarded as potential targets. The candidates are considered using a multi-fidelity design framework. Its purpose is to filter through the trajectory options using models of motion of increasing accuracy, so that a final refined, low-thrust solution is obtained. The trajectory design hinges on harnessing Earth’s gravity by exploiting encounters outside its sphere of influence, the named Earth-resonant encounters. An additional application explored in this investigation is the search and computation of periodic orbits for different planetary systems, following the current interest for missions involving distant retrograde and prograde orbits. In summary, this thesis presents four novel methods to model the third-body perturbation, distinct in their suitability for applications from real-time computations to long-term orbital predictions. These, together with the additionally developed tools for trajectory design, are applied in two asteroid mission cases. The developed Earth-resonant encounters allow for a very large increase in retrievable mass with respect to the state-of-the-art, namely for the cases of six near-Earth asteroids presented.
Keywords: Low fuel cost; low-energy trajectories; mission design applications; third-body effect; motion; novel models