An analysis of studies in space lunar trajectories – from the pioneer studies in 1950th years (Egorov V.A., Okhotsimsky D.E., Lidov M.L., et al.) to modern investigations of new low-energy trajectories - is given in the presentation. An optimal method for space flight to the geostationary orbit from a cosmodrom with high enough latitude using gravity of the Moon was discovered, it was realized then. For flights from the geostationary orbit GSO to the Earth, there are constructed the trajectories with “tangential” and “normal” entrance to the atmosphere (the last ones are more stable to variations in initial data), with fly-by of Moon near both its ascending and descending orbit nodes, with the re-entry of the spacecraft from a point on the GSO having a fixed geographical longitude. For flights between Earth and Moon, there is performed an analysis of the “detour” trajectories in frame of the four-body problem (Earth, Moon, Sun and a particle) with the capture by the Moon for the Earth-Moon flight or with the escape from lunar gravity for the Moon-Earth flight near the after-luna libration point L2 or near the before-luna libration point L1. The capture orbits are also used for constructing low-energy Earth-Moon trajectories with a low thrust. Examples of these trajectories and their characteristics are given. These new trajectories result in decreasing the fuel consumption for lunar missions.

Theoretical and applied problems of mechanics