Plasma Brake Approximate Trajectory. Part II: Relative Motion

Space debris mitigation is a challenge for the immediate future. Its solution represents a necessary step to guarantee a safe operation of satellites in low Earth orbits. Many strategies have been proposed to address this crucial issue, and meet the requirements of the Inter-Agency Space Debris Coordination Committee, according to which an out-of-order satellite should de-orbit within 25 years from its end-of life. Among all the proposed methods, the plasma brake represents an interesting and innovative option, as it is propellantless and requires a small amount of electric power to work properly. In this paper, the performance of a plasma brake system is analyzed to de-orbit a CubeSat from an initial altitude of 1000 kilometers above the Earth’s surface. The total decay time is evaluated using an iterative process, in which the altitude loss is computed starting from the linearized equations of the relative motion with respect to the position that the satellite would occupy on the osculating (nearly circular) orbit. The effectiveness of this procedure is investigated by comparing the results with those obtained through numerical integration of the equations of motion. In particular, the computational time is reduced by four orders of magnitude with an error of 0.1% only. In terms of the decay time, it is shown that the satellite reaches a final altitude of 300 kilometers within a few years when the plasma brake-induced acceleration is about 10^-3 mm/s2.