The stability of the relative equilibrium in an Earth–Moon orbital station system with a small reactive acceleration

The problem of stabilizing the relative equilibrium of an orbital station in an Earth–Moon system by imparting a small constant-modulus acceleration with constant orientation of its vector with respect to the body of the station, which is assumed to be a rigid body of variable mass, is considered. It is shown that, in the case of a small displacement of the centre of mass of the station (by means of a small reactive acceleration) with respect to the collinear libration point beyond the Moon, its relative equilibrium position can become stable by virtue of the equations of the first approximation.