This paper is devoted to the problem of a small payload delivery from an orbit to the Earth by a reusable space tether system consisting of a satellite in circular orbit, a tether, and a bottom module. The payload is placed in a dynamically symmetrical bead capsule, which can slide along the tether. Three scenarios for the payload delivery are proposed: an uncontrolled sliding of the capsule, a soft docking with the bottom module following separation, and a soft docking and the tether spin-up. The objectives of the paper are developing a mathematical model of the system, conducting a numerical analysis of its behavior, and comparison of the descent scenarios. The mathematical model that takes into account the friction between the bead capsule and the inextensible three-segment tether is developed using the Lagrange formalism. The results show that high-frequency oscillations of the bead capsule, its sharp stop, and the tether tangling can be observed. The scenario comparison allows concluding that the third scenario is more effective in terms of the capsule’s orbit perigee radius minimizing, butitrequires considerable time. The first scenario, compared with the second one, yields a significant decrease in perigee altitude, but it is more dangerous.
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