Abstract
The exploitation of Dynamical Systems Theory to the study of the motion of objects in space has led to innovative mission designs and substantial propellant savings. Recent advancements in numerical continuation techniques have enabled a new class of dynamical structures known as quasi-periodic invariant tori (QPT) to emerge as an alternative option to periodic orbits for designing and operating spacecraft missions in chaotic dynamical environments such as the Circular Restricted Three-Body Problem. QPT have the potential to significantly increase the design domain of spacecraft missions as well as unlock new, fuel-efficient transfer opportunities in the vicinity of the secondary mass, e.g., the Moon. To demonstrate these advantages, we will showcase how heteroclinic connections between quasiperiodic invariant tori in the Earth-Moon system can be charted systematically by means of knot theory and the linking number, a topological property of curves in three-dimensional spaces. Heteroclinic connections are then continued throughout different members of is-energetic quasi-periodic families by means of two-parameter continuation tools.