## 4 Results
### Drag Compensation  
A completely different approach to the deorbiting issue is to reverse the paradigm. Instead of taking care of deorbiting the spacecraft at the end of life, the satellite is placed directly at an altitude where the deorbiting is quick and assured by the natural aerodynamic decay. In this case, the propulsion system is not used to deorbit but to keep the satellite at the required altitude for its entire lifespan. This approach has important advantages. The first is the complete reliability of the deorbit process. While all the system previously discussed can fail preventing the proper deorbit of the spacecraft, in this case the deorbit is guaranteed. A failure of the propulsion system will lead to a failure of the mission and a premature re-entry of the spacecraft. From the standpoint of the space debris concern, this option is much more attractive. It is interesting to compare the propellant mass required to keep a satellite at a certain altitude vs. the propellant mass required to deorbit the satellite. This is presented in the following Figures 44-50. Figure 43: Deorbiting with the serial combination of a chemical propulsion system and a drag sail, altitude with time, 1-year total duration: (a) full Hohmann; (b) half Hohmann. Figure 46: Propellant mass fraction vs. lifetime for station keeping and deorbiting (from flight altitude) with a chemical thruster (\(Isp=300\) s, satellite mass 50 kg, density 400 kg/m\({}^{3}\)), parametric with flight altitude (km): (**a**) natural re-entry time of 1 month; (**b**) natural re-entry time of 1 year. Figure 44: Natural decay time for a 50 kg spacecraft, parametric with satellite density. Figure 45: Propellant mass fraction vs. lifetime for station keeping and deorbiting (from flight altitude) with a chemical thruster (\(Isp=300\) s, satellite mass 50 kg, density 200 kg/m\({}^{3}\)), parametric with flight altitude (km): (**a**) natural re-entry time of 1 month; (**b**) natural re-entry time of 1 year. Figure 47: Propellant mass fraction vs. lifetime for station keeping and deorbiting (from flight altitude) with a chemical thruster (_Isp_ = 300 s, satellite mass 50 kg, density 800 kg/m\({}^{3}\)), parametric with flight altitude (km): (**a**) natural re-entry time of 1 month; (**b**) natural re-entry time of 1 year. Figure 48: Propellant mass fraction for station keeping and deorbiting (from flight altitude) with a chemical thruster (_Isp_ = 300 s, satellite mass 50 kg, density 200 kg/m\({}^{3}\)), parametric with satellite lifetime (years): (**a**) natural re-entry time of 1 month; (**b**) natural re-entry time of 1 year. Figure 44 shows the natural decay time of a spacecraft as a function of its initial altitude, parametric with the satellite density. The black lines correspond to the 1-month and 1-year limits. A higher ballistic coefficient allows a satellite to fly lower for the same decay time. From Figure 44, it is possible to infer the altitude required to naturally deorbit in 1 month (between 250 and 300 km) or 1 year (between 350 and 450 km). The total propellant mass for the entire mission is the sum of the propellant mass for station keeping (i.e., drag compensation) at a certain altitude, plus the propellant mass required for repositioning at the altitude of the 1-month or 1-year limit. The propellant mass for drag compensation is linear with the satellite lifetime and (inversely) exponential with the flying altitude. Conversely, the propellant mass for deorbiting is independent from the satellite lifetime and almost linearly increases with the flying altitude. The resulting total propellant mass is a straight line that starts at a certain level (deorbiting needs) that is higher as the flying altitude increases. The slope of the straight line is related to the propellant mass consumed for station keeping. The lower the altitude, the higher the slope of the straight line because of the increased drag. The final pattern is visible in Figures 45-47.