The growing space debris environment poses a significant threat to operational satellites and the future of spaceflight. To assess the collision risk between space objects, often probabilistic methods are used, which suffer from the fact that very uncertain states will lead to a low probability of collision, described as the dilution effect. Apart from this drawback, satellite operators are required to decide whether to mitigate a risk well before the time of closest approach. However, the time horizon available for this is often too short. This research aimed at studying whether novel risk assessment metrics could increase the reliability of risk quantification and extend the time horizon available for decision making. Outer probability measures have proven to be a reliable method for mitigating the dilution effect, whereas a geometry-based metric has proven more challenging to use. Together with the theoretical analysis of the metrics, their operational application has been studied.

For several decades, humanity has worked on cataloguing the population of near-Earth asteroids (NEA's). Knowledge of these small members of the Solar system not only helps in defending Earth from asteroid impacts; study of the population might also provide valuable scientific insights, and open economic possibilities through developments such as asteroid mining. Surveys from Earth currently face challenges in detecting the smallest NEA's: day- and night cycles, weather patterns, and atmospheric distortion have encouraged several recent studies into the possibility of NEA surveys from deep space.

In this thesis, an extension to these proposals is studied: using multiple spacecraft co-operating on the survey. Next to the immediate increase in the data gathering capabilities, such systems offer synergistic benefits: Firstly, spacecraft can be placed in such a way as to cover each others blind spots caused by e.g. Solar glare. Secondly, imaging from multiple directions allows for triangulation to more quickly determine the orbit. Lastly, such a system could feature implementation of advanced search strategies, for example utilizing a part of the system as follow-up telescopes.

As one of the first works on predicting and optimizing the performance of such a multi-spacecraft NEA survey system, the work aims to provide a foundation on how to compose such a system, and what orbital configurations to select for its operation. A simulation tool was developed which explicitly models a NEA survey, and this model was validated against other research works and surveys. Using this tool, the behavior of the system is studied under changing of various parameters such as the number of spacecraft, thermal infrared or visual light telescopes, and various orbital elements. Following this, numerical optimization was performed to obtain conclusions with regards to the optimal composition and position of the system. The findings are supported by an investigation into the underlying principles driving the performance of the survey. Ultimately, results are obtained which can be used for more detailed studies into design of future NEA survey missions, or trade-offs against other concepts.

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.