The analysis of payload exchange failures between staged space tethers

The focus of this paper is the analysis of the asymmetry that arises due to the failed handover of payload between staged space tethers. The potential for such failures has been identified in previous research but not yet considered in any detail. The paper builds on previous research on staged tethers and uses many of the same data in the simulations, to provide a degree of continuity. The mathematical model and equations of motion for the planar tethers are presented, and the important discrepancy between centre of mass and centre of orbit are shown. This is highlighted with an example on a symmetrically laden tether on a circular orbit, before proceeding to analyse the more complex asymmetric cases. It was found that the tether system begins to displace either away from or towards the Earth, depending on whether it is the upper or lower payload that has failed to release, respectively. A key result was the discovery that even with an ideal, successful release the tether still undergoes some displacement due to changes in its centre of orbit after release. This is then further investigated in elliptical orbits which show how the behaviour of an initially fully laden tether, failing to release the lower payload but successfully releasing the upper payload, is very similar to the behaviour of an initially empty tether, failing to acquire the upper payload but successfully acquiring the lower payload. The results also show that a loss of payload effectively results in either an increase or decrease in orbital eccentricity, depending again on which payload is lost. Finally, a general data study is presented to provide insights into the influence of eccentricity of orbit, initial orbital radius, tether length, and angular velocity on the difference in apogees of asymmetric tethers.