In this paper we consider the special problem of stabilization of controllable orbital motion in a neighborhood of collinear libration point $L_2$ of Sun-Earth system. The modification of circular three-body problem -nonlinear Hill's equations, which describe orbital motion in a neighborhood of libration point is used as a mathematical model. Also, we used the linearized equations of motion. We investigate the problem of spacecraft arrival on the unstable invariant manifold. When a spacecraft reaches this manifold, it does not leave the neighborhood of $L_2$ by long time. The distance to the unstable invariant manifold is described by a special function of phase variables, so-called ''hazard function". The control action directed along Sun-Earth line.
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