Orbital and relative motion of a tethered satellite system

A simplified model for the orbital and relative motion of a tethered satellite system is presented. The tether acts as a light elastic string with small structural damping but without bending stiffness. Its mass is taken into account in the calculation of the total kinetic and potential energies of the tethered system. This formulation allows the inclusion of the complete gravity gradient influence on the dynamics of the system. The resulting three-dimensional motion is separated in the centre of mass orbital motion on the one hand and the relative motion of the end-bodies on the other. No restrictions on length of the tether or on mass ratio of the end-masses are imposed. It is found that the frequencies and amplitudes of the longitudinal tether oscillations are realistic as long as the tether mass is less than that of the subsatellite.