## 4 Results
### Electric Propulsion  
Similarly to the chemical thruster, an electric thruster can also be used to lower the altitude up to a point where the aerodynamic drag will complete the deorbit. To do so for a fixed total time, it is necessary to increase the thrust of the electric propulsion system in order to speed up the active phase of the descent and let the natural decay do the rest of the deorbit in the remaining time. In this way, the delta-v is reduced and consequently some propellant is saved. However, this requires a larger thruster, and thus is heavier and more expensive. This situation is represented in Figures 19-22. Figure 19: Electric propulsion deorbiting with a combination of an active phase and a passive natural decay, parametric with thrust (0.5–1.5 mN): (**a**) active time vs. release altitude; (**b**) total time vs. release altitude. Black line is the one-year limit. Figure 20: Electric propulsion deorbiting with a combination of an active phase and a passive natural decay: (**a**) passive time vs. release altitude; (**b**) thruster mass vs. thrust. A satellite of 50 kg, with a density of 400 kg/m\({}^{3}\), has been considered. The electric propulsion system has an _Isp_ of 1000 s, \(\alpha\) = 20 kg/kW, \(\eta\) = 0.65 and \(k\) = 0.25. The initial altitude is 850 km. The spacecraft is deorbited with the propulsion system up to a release altitude where it is left decaying naturally. The total deorbit time has been fixed in one year. The total time is the sum of the active phase and the passive decay. The passive decay is an exponential function of altitude, see Figure 20a. The release altitude should be less than 400 km in order to be compliant with the one-year limit. The active time is almost linear with the release altitude (Figure 19a), except at low altitudes where the drag force is comparable with the propulsion system thrust. The active time is almost linear with the thrust. The total time increases exponentially with the release altitude but intercepts the same limit at lower altitudes for lower thrusts. The propellant mass follows the active time behavior with respect to the release altitude, and it is slightly dependent on thrust at low altitudes because of the increased aerodynamic drag savings at lower thrusts. The thruster mass is proportional to the thrust and consequently increases as the active decay time is reduced. The total mass of the propulsion system increases with the thrust and as the release altitude is decreased. Once a specific total decay time is fixed (in this case one year), it is possible to plot the total mass of the propulsion system as a function of a single parameter, for example the thrust of the electric thruster. Higher thrusts mean shorter active descent time and the  
Figure 21: Electric propulsion deorbiting with a combination of an active phase and a passive natural decay, with parametric thrust (0.5–1.5 mN): **(a)** propellant mass vs. release altitude; **(b)** total mass vs. release altitude. Figure 22: Electric propulsion deorbiting with a combination of an active phase and a passive natural decay, total mass vs. thrust: **(a)** lower thrusts; **(b)** higher thrusts. possibility to release the satellite at higher altitudes, saving propellant mass. However, as already seen with the chemical system, the exponential behavior of density and decay time with altitude gives a relatively low variation of the release altitude. Moreover, in this case, the total mass behavior seems dominated by the variation of the thruster mass with thrust (Figure 22b) even if a minimum of the curve is present (Figure 22a). The results are dependent on the choices of thruster efficiency and specific impulse. Higher _Isp_ and lower thruster efficiencies will exacerbate the optimization toward a minimum thrust solution. Higher initial altitudes will do the opposite. It is worth noting that larger thrusters, particularly at small scales, could provide much better performance in terms of _Isp_ and efficiency.