In the framework of JAXA's MMX mission to explore the Martian moon of Phobos, an analysis of the stability of three-dimensional quasi-satellite orbits in the Mars-Phobos circular restricted three-body problem was conducted. For this analysis, notions of co-orbital motion, interpreted as the slow motion of the guiding center of the trajectory along the disturbing potential of Phobos, were used. After identifying and analyzing different regions of stability for three quasi-satellite orbits at 100, 50 and 30 km from the center of Phobos, several conclusions were drawn regarding the dynamics of the ballistic escape of the spacecraft, interpreted in terms of co-orbital motion. By making use of these insights, a novel methodology to find periodic quasi-satellite orbits able to reach high latitudes over the surface of Phobos was derived. This methodology consists of two steps: a multi-objective minimization using co-orbital parameters as target functions, to isolate regions with potential periodic orbits; followed by a shooting algorithm to arrive at the final periodic orbit. As a result of this new methodology, two periodic orbits were found at 50 and 30 km from the center of Phobos, able to reach latitudes as high as 54 deg and 32 deg respectively. This result represents an important contribution to both the operations and the scientific return of the Phobos proximity phase within MMX.

Many interplanetary missions massively leverage the lunar gravitational pull in the so-called low-energy regime to converge to their aim, saving consistent amount of fuel. Among these, two future Japanese spacecraft are expected to repeatedly encounter the Moon along their trajectories to either facilitate the escape from the Earth–Moon system or opportunely target a specific region in its neighbourhood. Although never actively employed for preliminary trajectory design, lunar collision orbits have shown a rich dynamical structure and an applicability for both medium- and low-energy regimes. These characteristics, together with their intrinsic nature of being close to trajectories experiencing lunar fly-by, have encouraged this research. In this work, lunar collision orbits are employed to delineate a method for obtaining ballistic transfers between two successive lunar encounters, briefly addressed as Moon-to-Moon. This study is first carried out with the assumptions of the autonomous Circular Restricted Three-Body Problem, subsequently extended to the nonautonomous Bi-circular Restricted Four-Body Problem, including the solar gravitational influence.
Poincaré cuts are extensively used as a dimensionality reductant for lunar collision orbits: this allows to ascertain their similar behaviour with trajectories flybying the Moon, whose characteristics are partly foreseen by determining the associated intersection with the same cut. A patching is performed at the cut to obtain both single and multiple ballistic Moon-to-Moon transfers. The strict bond of lunar collision orbits with the invariant manifolds of simple periodic orbits about Lagrangian points is confirmed and exploited to design ballistic itineraries connecting highly elliptic orbits about the Earth to horizontal Lyapunov orbits of the Earth–Moon system, via a single Moon-to-Moon transfer. With the usage of the lunar collision orbits and the Poincaré cut, a simple optimization technique is implemented to retrieve a properly defined Moon-to-Moon transfer from a trajectory missing a second fly-by with the Moon. Including the presence of the Sun, a similar method for obtaining single and multiple Moon-to-Moon transfers is developed. A classification of lunar double-collision transfers is then performed within the same framework, highlighting their similarity with other studies in past literature, eventually leading to the construction of a database of Moon-to-Moon transfers. The latter, conceived as an improvement with respect to the former version by adding the lunar gravitational influence, shows its applicability in real preliminary trajectory design.