Mathematical modeling of a tethered satellite system (TSS) with the focus on the effect of fuel sloshing

The removal of space debris from Earth orbits is one of the main tasks of space agencies around the world. The presence of ineffective bodies in the way of other spacecraft rises the probability of accidents. Pulling a satellite with the help of a cable and removing it from orbit can be a proper solution for removing space debris. However, most malfunctioning satellites usually still have some fuel in their tanks and this liquid slosh directly affects the satellite's movement. Studying this problem while considering the unburned propellant improves mathematical modeling. The main focus of the present paper is to derive of the mathematical governing equation of a tethered satellite considering the effects of sloshing for the debris. In this context, both the classical and modified forms of the Lagrangian method are used to derive the governing equation, which needs to calculate the total kinetic and potential energy of the system. The above system is simulated using MATLAB software.

Keywords:

Tethered Satellite systems , Mathematical Dynamic Modelling , Fuel Slosh