The motion of the spacecraft in the vicinity of the libration point is considered. As a result of the work have been obtained approximations for periodic and conditionally periodic orbits in the vicinity of the point L2. The resulting trajectories can be used to let the spacecraft to search and study asteroids, black holes, exoplanets and other astronomical objects in the Universe when it moves in the vicinity of the collinear libration point. On the example of Lyapunov’s flat orbits an analysis of the trajectories is presented demonstrating their behavior depending on the magnitude of the amplitude in the obtained approximations to determine the initial data.