Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies the planar motion of a spacecraft among these periodic orbits in the Earth-Moon system modeled as a planar circular restricted 3-body problem. A new cylindrical representation of the coordinates, recently introduced by the authors, is used with two purposes: (ⅰ) determine periodic orbits around the Earth and the Moon and (ⅱ) investigate the relations between their manifolds and those of the Lyapunov orbits at the libration points. This research proves how heteroclinic connections between manifolds of distinct periodic orbits can be detected in a straightforward fashion through this original cylindrical representation. Moreover, optimal constant- energy maneuvers are determined through the use of an alternative three-dimensional mapping.
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