Evolution of space tethered system’s orbit during space debris towing taking into account the atmosphere influence

Abstract

Space debris removal by a low thrust tethered spacecraft is considered in this paper. The objective of the work is the development of a simplified mathematical model describing the perturbed motion of the space tethered system under the influence of the aerodynamic drag forces and low thrust of the spacecraft’s engines and study the evolution of the space tethered system’s center of mass orbital parameters on large time intervals. The mathematical model describing the plane motion of a space tethered system with inextensible massless tether is constructed. Linearization and averaging of the mathematical model over the angle of the tether deflection are carried out. Separation of fast and slow variables is performed using Van der Pol approach. The obtained system is averaged over a fast variable. It is used to study the evolution of the center of mass orbit during space debris removal. The effect of the space tethered system attitude motion on the center of mass motion is analyzed. It is concluded that the greatest influence of the relative motion is observed in the case when the tether oscillates near the local vertical so that the space tug is located above the space debris.