Controllability of Keplerian Motion with Low-Thrust Control Systems

International audienceIn this paper, we present the controllability properties of Keplerian motion controlled by low-thrust control systems. A low-thrust control system, compared with a high or an even impulsive control system, provides a fuel-efficient means to control the Keplerian motion of a satellite in the restricted two-body problem. We obtain that, for any positive value of maximum thrust, the motion is controllable for orbital transfer problems. For two other typical problems—de-orbit problem and orbital insertion problem, which have state constraints – the motion is controllable if and only if the maximum thrust is bigger than a limiting value. Finally, two numerical examples are given to show the numerical method to compute the limiting value