The problem of deorbiting large space debris (SLD) by means of a tethered space tug is considered. A mathematical model that describes the plane motion of the system is developed. The model takes into account the effects of the atmosphere and the rotary motion of the SLD around the SLD center of mass. The effects of the moment of tension force, gravitational moment, and pitch moment on the SLD behavior are studied. The evolution of the phase space of an angle of attack during the SLD descent is considered. Singular points are found for special cases of motion. It is shown that the effect of the atmosphere on the SLD dynamics can be neglected above an altitude of 300 km. The situation that a tether becomes slack is observed. In this case, the SLD can oscillate with increasing amplitude and even pass into rotation. This is a dangerous situation that can lead to tether rupture. A method of thrust control that provides tension in the tether during the SLD deorbiting is presented. A slack tether is also observed at atmospheric entry. This phenomenon is caused by the difference in drag forces that act on the SLD and on the space tug. The obtained results can be used in the preparation of missions of space debris deorbiting.
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