Missions such as Genesis and THEMIS-ARTEMIS demonstrated the usefulness of heteroclinic connec-

tions, transfer trajectories between regions of space with unparalleled fuel efficiency. These connections

are of greater importance than ever as efforts to establish space infrastructure in the lunar region have

progressed in the past few years; the return of a manned lunar program in Artemis, and the devel-

opment of the multinational Lunar Gateway, have been followed by calls for a better understanding

of cislunar space. Additionally, as active spacecraft reach the end of their planned mission duration,

engineers seek methods of extending their life by providing new objectives, often paired with a need

to enter a new orbit; such cases are ideal applications of heteroclinic connections. However, tools

for detecting and mapping these connections have remained reliant on non-robust methods. In this

thesis, a novel method of detecting heteroclinic connections is presented and ways it can be exploited

to extend the life of existing missions are demonstrated.

The detection method itself is firstly parsed. By exploiting invariant topological properties asso-

ciated with the hyperbolic manifolds of the departure and arrival orbits, intersections between these

manifolds can be found and ultimately better understood. As the method is topological in nature,

the chance of failing to detect all available heteroclinic connections is largely mitigated by this new

approach. The method is then employed to more robustly initialise a multi-parameter continuation

scheme, avoiding failure when bifurcations or extreme changes in the tangent of the solution family

occur. Finally, the detection method and multi-parameter continuation schemes are proven to be

a useful tool for mission extension; the hyperbolic manifolds of orbits in the Sun-Earth system are

evaluated by their potential for near-Earth asteroid interception, and connections between desirable

orbits are investigated, ultimately leading to a greatly improved mission design domain over similar

existing work.