De-orbiting satellites at end of mission would prevent generation of new space debris. A proposed de-orbit technology involves a bare conductive tape-tether, which uses neither propellant nor power supply while generating power for on-board use during de-orbiting. The present work shows how to select tape dimensions for a generic mission so as to satisfy requirements of very small tether-to-satellite mass ratio m/MS and probability N f of tether cut by small debris, while keeping de-orbit time t f short and product t f x tether length low to reduce maneuvers in avoiding collisions with large debris. Design is here discussed for particular missions (initial orbit of 720 km altitude and 63° and 92° inclinations, and 3 disparate M S values, 37.5, 375, and 3750 kg), proving it scalable. At mid-inclination and a mass-ratio of a few percent, de-orbit time takes about 2 weeks and N f is a small fraction of 1%, with tape dimensions ranging from 1 to 6 cm, 10 to 54 pm, and 2.8 to 8.6 km. Performance drop from middle to high inclination proved moderate: if allowing for twice as large m/MS, increases are reduced to a factor of 4 in t f and a slight one in N f , except for multi-ton satellites, somewhat more requiring because efficient orbital-motion-limited electron collection restricts tape-width values, resulting in tape length (slightly) increasing too.
The low earth orbit (LEO) environment contains a large number of artificial debris, of which a significant portion is due to dead satellites and fragments of satellites resulted from explosions and in-orbit collisions. Deorbiting defunct satellites at the end of their life can be achieved by a successful operation of an Electrodynamic Tether (EDT) system. The effectiveness of an EDT greatly depends on the survivability of the tether, which can become debris itself if cut by debris particles; a tether can be completely cut by debris having some minimal diameter. The objective of this paper is to develop an accurate model using power laws for debris-size ranges, in both ORDEM2000 and MASTER2009 debris flux models, to calculate tape tether survivability. The analytical model, which depends on tape dimensions (width, thickness) and orbital parameters (inclinations, altitudes) is then verified with fully numerical results to compare for different orbit inclinations, altitudes and tape width for both ORDEM2000 and MASTER2009 flux data.
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 3,000 kg spacecraft from 800 km altitude at 90 o 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.
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