Dynamic propagation of space tether system motion

Abstract

This paper aims at solving motion equations for a Spatial Tether System, composed by a principal satellite and a sub-satellite, through an initial know condition. The translational motion of the sub-satellite around the principal satellite is described in spherical coordinates, described by distance and the angles that position the vector between both satellites. The rotational motion of a sub-satellite S2 is described by Euler’equations and the cinematic equations for 3-2-3 Euler angles. The results of dynamic propagation show that the sub-satellite moves around the principal satellite in a precession anticlockwise motion, and that also vertically oscillates throughout this motion, with an amplitude of approximately 10°, for the adopted conditions. The numeric propagator of sub-satellite trajectory throughout the principal satellite and rotational motion of sub-satellite can be adapted for other types of Space Tether Systems.