Station-keeping of small amplitude motions around the collinear libration point in the real Earth-Moon system

Compared with the circular restricted three-body problem, various perturbations exist in the real Earth-Moon system. Out of them, the ones from the Moon's orbit eccentricity and the Sun are the most prominent. For mission design around the collinear libration points in this system, these two perturbations should be taken into consideration. In fact, the collinear libration points are not equilibrium points anymore due to these perturbations. Instead, special quasi-periodic orbits called dynamical substitutes around them exist, playing the role of time-varying equilibrium points. Generally, these dynamical substitutes are unstable, thus station-keeping is necessary for probes around them. In the paper, a short description of the dynamical properties of these dynamical substitutes was made. Then two station-keeping strategies were proposed for small amplitude motions around them. The first strategy has no requirements on the motion amplitude in the x-y plane while the second one has. Taking the point L2 as an example, some numerical simulations were made. Motions with amplitude of 380 km and 3800 km were studied. It turns out that the cost of the two station-keeping strategies increases with increasing amplitude. Besides, the second strategy generally costs more than the first one.