## 6 Conclusions  
LEO satellite population is expected to grow dramatically in the coming years. To avoid a corresponding unacceptable increase in the rate of collision with debris or collision avoidance operations it is necessary to keep the LEO region clean. The current 25 year-limit, which corresponds to a natural decay from around 600 km, will become probably insufficient in the future and faster ways to deorbit are to be sought. This paper focused the attention on the means for effectively deorbiting a spacecraft. Four technologies for deorbiting have been investigated: drag sail, chemical propulsion, electric propulsion, electrodynamic tether. Both simplified numerical models and full integration of the dynamic equations with a 4 th order Runge-Kutta scheme have been used in order to compare the deorbit behavior of the different technologies and highlight their impact at system level. Solar sails have been excluded from deep analysis as they have been shown to be inefficient for deorbiting, as the force they produce from about 4.5 \(\upmu\)N/m\({}^{2}\) solar pressure is by far inferior to competing technologies, except maybe for drag sails at higher altitudes. In addition, they need to be controlled on each orbit for a very long time. Drag sails are very effective at low altitude and long decay times, and they can be passive after deployment. Sail mass is almost inversely linear with decay time. However, they become inefficient and too slow at higher altitudes. With a relative mass between 1 and 4% of the satellite, they can deorbit a satellite in less than 5 years up to 700-800 km, and less than 25 years up to 800-1000 km. Chemical propulsion allows for fast and controlled deorbit from any altitude but tends to be the heavier option if the time constraint is relaxed as this technology has limited sensitivity to deorbit time. Re-entry times of less than an hour can be achieved with a system mass fraction up to 20% at 1200 km. Chemical propulsion can deorbit the satellite with a Hohmann transfer to a lower altitude or can lower its perigee with a half Hohmann maneuver. The second option allows for nearly 40% propellant savings but keeps the satellite orbiting in a wide range of altitudes unless the perigee is already sufficient for direct re-entry. Electric propulsion can provide important mass savings compared with the chemical option, particularly for high delta-\(\
u\) (i.e., higher altitudes), thanks to its superior specific impulse. Delta-\(\
u\) losses for continuous firing have been shown to be negligible in LEO. However, the power (thrust) constraint forces a slower process, in the order of months. With mass fractions comparable to a drag sail, an electric propulsion system can provide much shorter deorbit times at higher altitudes, approximately starting from above 500 km altitude. For a fixed specific impulse, the electric propulsion system mass decreases asymptotically with the deorbit time down to the bare propellant tank wet mass. The electric thruster can be fired continuously in order to provide a spiral decay of the orbit or operated only near the apogee to lower the perigee. The second option provides significant propellant mass savings at the expense of longer operating times or higher thruster size (i.e., mass and cost). Near-continuous firing guarantees the minimum total mass for short deorbit times (few months) at high specific impulses while lower duty cycles have a potential for up to 40% mass savings for long decay times (several months) at lower specific impulses. Duty cycles below 20% provide no benefits. Electrodynamic tethers have the potential to be the most lightweight solution, especially for long decay time as their mass is inversely linear to decay time, with the exception of high orbital inclinations where they suffer from poor performance due to the alignment with the magnetic field. In fact, for the same mass budget, induced drag forces can be up to 2-3 times the one from a corresponding electric thruster for inclination up to 45\({}^{\circ}\).