title: Low energy capture of near-Earth asteroids in the circular restricted three-body problem
Creators: name: Tan, Minghu
Publisher: name: University of Glasgow
Year: 2018

description: Near-Earth Asteroids (NEAs) can provide useful resources in terms of feedstock for spacecraft propellant, crew logistic support and a range of useful metals. The possibility of capturing small NEAs using low energy transfers would therefore be of significant scientific and commercial interest. Although NEAs may make close approaches to the Earth, and so represent a potential impact threat, the exploitation of their resources has long been proposed as a necessary element for future space exploration.
The objective of the research presented in this thesis is to develop methodologies for the trajectory design of capturing NEAs in the neighbourhood of the Earth. Firstly aimed at capturing NEAs around the Earth-Moon L2 point, a new type of lunar asteroid capture is defined, termed direct capture. In this capture strategy, the transfer trajectory for capturing an NEA into the Earth-Moon system is modelled in the Sun-Earth-Moon restricted four-body. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid’s initial obit to the stable manifold associated with Earth-Moon L2 point. The direct asteroid capture strategy requires a shorter flight time compared to an indirect asteroid capture strategy, which couples capture in the Sun-Earth circular restricted three-body problem and subsequent transfer to the Earth-Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth-Moon system.
As ideal locations for space science missions and candidate gateways for future crewed interplanetary missions, the Sun-Earth libration points L1 and L2 are also preferred locations for the captured asteroids. Therefore, the concept of coupling together a flyby of the Earth and then capturing small NEAs onto Sun–Earth L1 or L2 periodic orbits is proposed. A periapsis map is then employed to determine the required perigee of the Earth flyby. Moreover, depending on the perigee distance of the flyby, Earth flybys with and without aerobraking are investigated to design a transfer trajectory capturing a small NEA from its initial orbit to the stable manifolds associated with Sun-Earth L1 and L2 periodic orbits. NEA capture strategies using an Earth flyby with and without aerobraking both have the potential to be of lower cost in terms of energy requirements than a direct NEA capture strategy without the Earth flyby. Moreover, NEA capture with an Earth flyby also has the potential for a shorter flight time compared to the NEA capture strategy without the Earth flyby. Following by this work, a more general analysis of aerobraking is undertaken and the low energy capture of near-Earth asteroids into bound orbits around the Earth using aerobraking is then investigated. Two asteroid capture strategies utilizing aerobraking are defined, termed single-impulse capture and bi-impulse capture, corresponding to two approaches to raising the perigee height of the captured asteroid’s orbit after the aerobraking manoeuvre. A Lambert arc in the Sun-asteroid two-body problem is again used as an initial estimate for the transfer trajectory to the Earth and then a global optimization is undertaken, using the total transfer energy cost and the retrieved asteroid mass ratio (due to ablation) as objective functions. It is shown that aerobraking can in principle enable candidate asteroids to be captured around the Earth with, in some cases, extremely low energy requirements. 
The momentum exchange theory is also applied to the capture of small near-Earth asteroids into bound periodic orbits at the Sun-Earth L1 and L2 points. A small asteroid is first manoeuvred to engineer a flyby with a larger asteroid. Two strategies are then considered: when the small asteroid approaches the vicinity of the large asteroid, it will either impact the large asteroid or connect to it with a tether. In both strategies, momentum exchange can be used to effect the capture of one of the asteroids. Then, a two-impulse Lambert arc is utilized to design a post-encounter transfer trajectory to the stable manifolds of the Sun-Earth L1 or L2 points. By investigating the outcome of the impact on the small asteroid, or the tension of the tether, the maximum velocity increment available using these momentum exchange strategies is investigated. Again the capture strategies using momentum exchange in principle have the potential to deliver low-energy capture of asteroids.
The methods presented in this thesis are intended to be used as a preliminary analysis for these asteroid capture strategies. Although some significant practical challenges remain, the transfer in the CRTBP models can serve as a good approximation for the trajectory in a more accurate dynamical model.