Optimum sizing of bare-tape tethers for de-orbiting satellites at end of mission

Abstract

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.

Comparison of technologies for deorbiting spacecraft from low-earth-orbit at end of mission

“…Since BET-to-spacecraft mass ratio decays as the inverse of t D , BET becomes more competitive for longer missions. However, mission durations should be designed by taking into account possible tether cut by small debris 9 . The use of tape instead of round cross-sections is essential to achieve good BET performance with a very high survival probability 10 as specified later on.…”

“…A simple comparison between Lorentz drag and air-drag, at any LEO altitude, is given by their ratio 11 , √ √ ( ) , (9) where a representative, moderate ohmic-effects, current law, 2…”

“…Although with a high cost in term of mass (see Fig.1), active technologies satisfy this criterion. BETs also satisfy it; an adequate selection of tether length, width and thickness, allows designing efficient and safe missions for critical mass and orbit altitudes and inclinations 9 . It is remarkable that different tape tether geometries with length, width and thickness within the ranges L = 1-5 km, w = 0.5-2.5 cm, and h = 50-100 µm, respectively, would not affect significantly to other BET systems like HC, deployment mechanism or power control unit.…”

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

“…Conventional wisdom is that something unusual happened to the first one. Even if that is not true these two tethers have lasted an average of five years, which is about an order of magnitude more than the expected time of a typical de-orbiting tether mission (Sanmartín et al, 2015).…”

“…To reduce complexity in calculating probabilities, the actual de-orbit operation is skipped, assuming that the flux corresponds to the altitude of 800 km all the time. The duration about 3 months is taken from recent results in (Sanmartín et al, 2015), giving de-orbit time t f from the equation…”