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

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(t)/M-s 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 mu m, and 2.8 to 8.6 km. Performance drop from middle to high inclination proved moderate: if allowing for twice as large m(t)/M-s, increases are reduced to a factor of 4 in tf 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.This work was supported by the European Commission FP7/Space Project 262972 (BETs), the Ministry of Science and Innovation of Spain (BES-2009-013319 FPI Grant), and Universidad Politécnica de Madrid (Research Grant RR01 2009)