## 4 Results
### Comparison
For this reason, the chemical propulsion mass is a strong function of the initial altitude. All the technologies consider a full deorbit down to 150 km. In case of the chemical propulsion system, both \(n\) Hohmann transfer to 150 km and a half Hohmann transfer to 150 km are considered for simplicity. The two are not exactly equivalent as shown before, as the first will provide immediate deorbit while the second should require a slightly lower perigee to be exact, otherwise the deorbit time is a bit longer but still negligible compared with the other technologies (Figure 34b). The delta-v of the Hohmann and half Hohmann are plotted in Figure 34a as a function of the altitude together with the delta-v required by the electric propulsion system. The electric propulsion system is considered spiraling down through a continuous firing. For the reasons just explained, the delta-v of the half Hohmann is around 50% the full Hohmann (while it will be more correct to stay on a 60% value for the same decay). Figure 32: Deorbiting behavior with different technologies and a tenfold increase in the drag force (**a**) drag sail; (**b**) tether. The delta-v of the electric thruster is theoretically higher than the one of an impulsive full Hohmann transfer but, as stated earlier, at LEO altitudes the difference is negligible. However, as the descent with the electric thruster is slower, part of the delta-v is provided  
Figure 34: Deorbiting with different technologies from LEO up to 150 km altitude: (**a**) delta-v; (**b**) decay time. Tether data calculated for 45\({}^{\circ}\) orbital inclination. Figure 35: Decay time vs. altitude for different technologies: (**a**) full picture; (**b**) zoom-in. Tether data are parametric with orbital inclination. Figure 33: Deorbiting with different technologies from LEO up to 150 km altitude, mass budget: (**a**) full picture; (**b**) zoom-in. by the drag at the lowest altitudes (roughly the last 100 km, i.e., around 50 m/s), so the final result is the one plotted in Figure 34a and provides some propellant mass saving. The decay times for the different technologies are shown in Figures 34b and 35. It is possible to see that the chemical propulsion system is always the fastest but also generally the heaviest, except for small displacements, particularly with the half Hohmann strategy. The drag sail is very efficient at low altitudes but becomes dramatically inefficient at higher altitudes due to the exponential behavior of atmospheric density. As already pointed out earlier, the electric propulsion system and the tether have a similar behavior, with a slow, almost linear variation of decay time with initial altitude for the same mass budget. The tether is theoretically the best system in the majority of cases, except for high orbital inclinations where it becomes much less efficient than the electric thruster. A similar analysis has also been performed at higher altitudes. In this case, instead of a full deorbit, it has been considered to reposition the spacecraft to a final circular orbit with a 5-year natural decay time (slightly below 500 km). The drag sail has been excluded from the analysis because at this altitude the repositioning time becomes unsustainable. The results (Figures 36 and 37) are analogous to the previous analysis. This time the delta-v of the full Hohmann transfer and the electric spiraling down are coincident, as the drag does not come into play at these altitudes (Figure 36a). For large displacements, the propellant mass budget of the chemical system grows to very high levels, and even the electric propulsion system is significantly affected. The analysis has been repeated for a final natural decay time of 25 years. A 5-fold increase in the decay time provides only a few dozen km of higher final parking orbit altitude. For this reason, the results are almost equal to the previous ones (Figures 38 and 39). Figure 36: Deorbiting with different technologies from high altitudes in LEO up to the altitude of a 5-year natural re-entry: (**a**) delta-v; (**b**) active descent time.