## 4 Results
### Comparison  
It is now interesting to compare the different behavior and performance of the various deorbiting technologies. Figure 31 shows the time profile of the altitude for the different technologies sized in order to have the same decay time. The initial orbit is circular, the initial altitude is 680 km and the decay time is one year for all cases. The behavior of the electric thruster and the tether are the same if the thruster is fired continuously. Both systems induce a linear decrease in the orbital altitude until the drag prevails. The drag sail spends the majority of time near the initial altitude, and fall steeply near the end due to the atmospheric density profile with altitude. The chemical thruster immediately (compared with the total time) displaces the spacecraft to a new orbit at an altitude around 400 km to then fall slowly with the atmospheric drag in the same way the drag sail does at the higher altitude. This aspect is interesting to consider, as the decay altitude profile influences with time the way the system interacts with the other spacecrafts or debris. Even if the comparison is done for the same total decay time, there is a dramatic difference between spending almost one year in a crowded orbit or few hundred km below, for example. A similar comparison can be also performed for an initial elliptical orbit. Again, comparing the deorbiting with a drag sail vs. a tether (or a continuously firing electric thruster), it is possible to recognize the different behavior. As the drag sail force is almost an exponential function of altitude, the decay is slower at the beginning and faster near the end. Moreover, the first phase is characterized by an orbit circularization, as the perigee (where the maximum force is applied) remains nearly constant while the apogee altitude decreases significantly. Near the end, the spacecraft spirals down. An increase of the drag sail area by a factor of ten causes a reduction of the deorbit time by the same amount (34 vs. 344 days in Figure 32a). Figure 31: Comparison of different deorbit technologies’ behavior, 680 km initial altitude. Orbital altitude with time. For the tether, the force is almost the same for the entire orbit and during the whole decay. The resulting effect is an almost parallel linear decrease in both the perigee and apogee altitudes. When the perigee starts to be low, the satellite drag adds to the tether force and the circularization process begin. In this phase the perigee fall is still linear while the apogee one is more exponential. Finally, the spiraling down occurs. The nonlinear sum of the satellite drag with the tether force is more relevant when the two forces are comparable, i.e., at low altitudes and low tether forces. For this reason, a tenfold decrease in the tether thrust from 2 mN to 0.2 mN induces a sublinear increase of the decay time from 42 to 301 days (Figure 32b). Regarding the performance aspect, it is interesting to compare the deorbiting time at different altitudes for a similar mass budget. In the following Figures 33-35, a fixed mass budget of 4% has been imposed to the propellant-less systems, i.e., the sail and the tether, leaving the decay time to adjust consequently to the initial altitude. In the case of the electric thruster, the mass budget has been fixed equal to 4% mass for an initial altitude of 400 km (Figure 33). For higher altitudes the constant thruster mass has been kept the same and the propellant mass has been adapted to the higher delta-v, producing a slow variation (increase) of the total mass. The parameters for the electric propulsion are \(\eta=0.65\), \(k=0.12\) and \(Isp=3000\) s. For higher values of \(k\) and lower \(Isp\) the sensitivity of the total mass with the initial altitude increases. For the chemical propulsion system, the mass budget is mainly dependent on the propellant mass and thus the delta-v (\(k=0.12\), \(Isp=300\) s). As shown before, there is little room for the chemical system to trade mass for time.