A growing interest of the space scientific community for trajectories towards, around and from Lagrangian points has been registered in recent years. In particular, the three-body problem is one of the most studied models not only in celestial mechanics, but also in mathematics. For the early first solar system exploration missions (like Voyager), a patched conics model was satisfactory to compute the trajectory. As interplanetary missions became more demanding (as far as fuel consumption or accuracy are concerned), this strategy connecting several two body-problems was applied as a first design approximation. Thus, other strategies (like three body-problem and more) can be preferred. Moreover, some science space missions take advantage of particular properties of the Lagrangian points. In recent decades, many theoretical studies have demonstrated the benefits of highly non-linear dynamics to space exploration missions.
R. Farquhar published the first papers on the utilization of co-linear EMLs (Earth-Moon Lagrangian Point) in the late sixties and early seventies, including the application for communication relay satellites, inhabited space stations in a Halo orbit around EML2 and moreover, on the utility of Lagrangian Points (LPs) for human solar system exploration. Beyond the study of utilization of the Lagrangian Points location, the interest in these models focuses on the emergence of invariant structures, such as periodic or quasi-periodic orbits and their related stable and unstable manifolds. These invariant structures make it possible first to design staging orbits in the vicinity of the Lagrangian points, then to establish low-energy trajectories for transfer between the Earth, the Moon and the Lagrangian points. This paved the way for mission’s concepts taking benefit of these invariant structures so as to minimize fuel consumption through various strategies like Indirect transfer, Weak Stability Boundary or Lunar flyby, for Earth-to-EML2 or Earth-to-Moon transfers.
More recently, new orbits families are emerging, like QSO (Quasi-Satellite Orbits for MMX), NRHO (Near Rectilinear Halo Orbit for the Lunar Orbital Platform Gateway, LOP-G) or DRO (Direct Retrograde Orbit for ORION) and are considered with an operational interest.