Debris mitigation guidelines recommend all artificial satellites to be removed from orbit upon completing a mission. The generally accepted 25-year lifetime requirement is often a challenge for small satellites with a simplified attitude and orbit control system unless the aerodynamic drag mechanism is sufficient enough for quick spacecraft disposal. Of specific interest is the deorbiting problem for the densely populated low Earth orbit altitudes of 800-1200 km. In this case, a thruster or some drag enhancing actuator is needed. The purpose of the present paper is to investigate the feasibility of designing a low-thrust deorbit control for passively stabilized satellites. Most passive stabilization techniques allow only one spacecraft axis to be stabilized. Therefore, one can install at most two opposite directed thrusters aligned with the stabilized axis: the orientation of any other spacecraft axis is likely to be poorly identifiable, which is unacceptable for a continuous low-thrust orbit control. As a result, the optimal control problem can be formulated in the following way: to design the minimum fuel thrust magnitude control ensuring the desirable change of the satellite mean orbital radius. What concerns the thrust direction, it is exogenously determined at any instant of time by the orientation of the stabilized axis. For spin-stabilized spacecraft, the stabilized axis is almost fixed in absolute space (to be exact, a slow precession occurs), while in the case of passive magnetic stabilization, the thrust vector is aligned (within 10-15 degrees of pointing accuracy) with the direction of the local geomagnetic field. Both these passive stabilization methods are considered. The optimal control problem is shown to be reduced to the nonlinear programming problem by simply averaging the Gaussian equations of orbital motion and applying the two-time-scale optimization approach. The numerical results obtained indicate the possibility of deorbiting passively stabilized LEO satellites in a timely and efficient manner.
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