Ballistic capture is a transfer method which was first applied in 1990. It allows a spacecraft to approach a target celestial body and enter a (temporary) orbit around it without requiring manoeuvres in between. Ballistic capture is a promising concept, as it is expected to be safer, cheaper, and more flexible in terms of launch windows than a traditional Hohmann transfer. Currently, a computationally efficient method which simulateneously allows for an inisghtful description of the dynamics of the ballistic capture problem remains to be found. A potential solution lies within the field of Lagrangian Coherent Structures (LCS). LCS is defined as a separatrix of regions in a flow with distinct dynamics. It may be possible that LCS around a planet have some correspondence to results found using stable set manipulation, a classic technique for obtaining capture trajectories. In this research three new areas within the field relating LCS to ballistic capture are explored. Firstly, it has not yet been shown what LCS can be found in an area around a planet, without making use of a priori stable set information. Furthermore, it is unclear what the effect is of changing the integration time in the procedure of extracting LCS. Finally, there has not yet been an analysis to show how the LCS relate to stable sets with different number of revolutions n. In this work two algorithms for extracting LCS have been developed. One is based on the simple but efficient computation of the Finite Time Lyapunov Exponent (FTLE). Another is based on the more involved Variational Theory. Both algorithms are validated on a toy problem used frequently in LCS extraction studies, and are then applied to the Elliptic Restricted Three Body Problem (ERTBP). It is shown that LCS around a planet yield resemblance with stable set results. The FTLE-based algorithm is able to quickly and efficiently identify the shape of the stable set. The Weak Stability Boundary, however, can not be extracted distinctly. The Variational Theory-based algorithm yields more distinguishable results for the Weak Stability Boundary. It is shown that large and constant integration times are beneficial. It is shown that extracted LCS form an approximation of the average resulting WSB for all stable sets.

This report presents the Final design of the Design Synthesis Exercise (DSE) to 'Capture a Small Asteroid and Change its Orbit' at the Faculty of Aerospace Engineering at Delft University of Technology. The bachelor programme 'Aerospace Engineering' comprises several projects enabling students to explore aeronautics and space from different kinds of perspectives. The Design Synthesis Exercise serves as the conclusion to this programme. During this final project students integrate their previously obtained knowledge and skill to examine a specific design problem in groups of ten students for the duration of eleven weeks. This final report is the last in a series of four and documents the detailed design of the concept that was chosen in the mid-term report.