Survivability analysis of tape-tether against two concurring impacts with debris

It has recently been shown that a thin-tape tether, as opposite to a round one, has a high probability of survival to single impacts by space debris, under a broad range of de-orbit operation conditions. The purpose of the present work is to extend that analysis to survival to multiple impacts by smaller, but more abundant, debris. The method used here consist, essentially, in separating the particles into “large” and “small” ones. The large ones are so rare that the probability of them concurring on the same spot can be neglected. The small ones are a sort of background, and it is shown that the probability of them impinging close enough to a large particle crater to cause malfunction of the tape is negligible. A particular mission is considered, de-orbiting a 3000 kg spacecraft from 800 km altitude at 90°90° inclination by means of an aluminium tape of dimensions 10,000 m × 0.06 m × (5 × 10−5) m. It is shown that the probability that this mission survives to multiple impacts is at least 0.978. The application of this method to missions of different parameters is also discussed.