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

Highlight
• Conductive bare-tape tethers are optimally sized for end-of mission satellite de-orbiting.
• Performance criteria are (1) very light tether, (2) high probability of survival to small debris, and low probability of big debris impact on (3) the satellite or (4) its tape.

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 mt/MS and probability Nf of tether cut by small debris, while keeping de-orbit time tf short and product tf ×× 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 MS 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 Nf is a small fraction of 1%, with tape dimensions ranging from 1 to 6 cm, 10 to 54 μμm, and 2.8 to 8.6 km. Performance drop from middle to high inclination proved moderate: if allowing for twice as large mt/MS, increases are reduced to a factor of 4 in tf and a slight one in Nf, 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.