This paper explores the rich dynamics of quasi-satellite orbits (QSOs) with out-of-plane motions in the Earth–Moon and Mars–Phobos systems. The first part of the paper computes families of spatial periodic QSOs in the circular restricted three-body problem via bifurcation analyses and presents their orbital characteristics. We pay special attention to unstable families of spatial periodic QSOs of weak instabilities. The second part of the paper presents three applications of the obtained spatial unstable periodic QSOs to space mission trajectories. The first application is concerned with a ballistic landing concept on the surface of Phobos via unstable manifolds emanating from spatial weakly unstable periodic QSOs. The second application identifies stability regions of spatial, long-term stable, quasi-periodic QSOs based on phase-space structures of invariant manifolds emanating from spatial unstable periodic QSOs. The third application proposes a method of designing nearly ballistic, two-impulse transfers from a low Earth orbit to a spatial, long-term stable, quasi-periodic QSO around the Moon in the bicircular restricted four-body problem including solar perturbation.
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