## 2 Deorbiting Technologies
The delta-v for this option is slightly above one half of the complete Hohmann for the same decay time. This option is possible only for a high-thrust system that can perform an impulsive maneuver. Low-thrust systems are generally of electric type, require power and are consequently limited in thrust by it. The maneuver time is generally non-negligible or even comparable with the decay time, and in fact the two are superposed. The advantage of the electric system is a much higher specific impulse that can provide an attractive mass saving for high delta-v. Finally, the last option is the electrodynamic tether [17; 39; 40; 41]. In this case a tether is deployed for re-entry. Electrodynamic tethers collect ionospheric electrons from the plasma environment and re-emit them through a cathode or a \"Low-Work-Function\" segment of the same tether by using thermionic and photoelectric effects. In both configurations, the resulting electric current flowing through the conductive tether generates a drag Lorentz force thanks to interaction with the Earth's magnetic field. The drag force is rather small, and the deorbiting behavior is very similar to that of an electric thruster, but without propellant consumption. The technology is still not as mature as the classical propulsion; concerns arise regarding the oscillation stability of the tether-satellite system, the probability/consequences of debris impact on the tether and other engineering issues. The Lorentz drag force \(F_{\mathit{el}}\) is described by the following equation:  
\[F_{\mathit{el}}=m\frac{\sigma}{\rho}\frac{E_{m}^{2}i_{av}}{v}=m\frac{\sigma}{ \rho}vB_{m}^{2}cos^{2}(i)i_{av} \tag{9}\]  
\[E_{m}=vB_{m}cos(i) \tag{10}\]  
where \(B_{m}\) is the geomagnetic field, \(E_{m}\) the motional electric field, \(i_{av}\) the dimensionless averaged current along the tether, \(m\) the tether mass, \(\rho\) its density, \(\sigma\) is the tether conductivity. Typical values are \(\rho=2700\) kg/m\({}^{3}\), I = 3.54 \(\times\) 10\({}^{7}\)\(\Omega^{-1}\)m\({}^{-1}\), \(B_{m}\) = 0.3 Gauss, \(i_{av}\) = 0.25. For a fixed technology, the main parameters affecting the Lorentz drag force are the area and thickness of the tether and the orbital inclination \(i\). The tether becomes less effective approaching polar orbits due to the \(cos^{2}\) dependency. The average TRL of the tether systems is the lowest between all the possible options, anyway some devices are already sold as COTS on the market [42; 43; 44]. However, performance from datasheet seems to indicate a much higher relative auxiliary mass compared with literature projections. This is probably due to the small size of the devices and or to some compromises necessary to field such a new technology nowadays. The tether can be used also in reverse mode as a propulsion system for orbit raising (requiring power from the spacecraft), however the TRL of the technology is even lower in this case. The chemical thruster is an active system that requires the satellite to be effective only for a limited time after the start of the disposal maneuver, generally no more than several hours in case the apogee burn is split in several smaller impulses. On the contrary, both the electric thrusters and the tethers need to work reliably for a long time, meanwhile requiring the satellite to control its attitude and basic functions, increasing the probability of failure. Comparing the forces produced by the various technologies for 10 kg of device mass we obtain the results presented in the following \[p_{rad}=I/c \tag{2}\]0 The thrust of a chemical propulsion system is not represented as it is out of scale and not a particular limiting factor. For the electric propulsion only the fixed mass of the thruster is considered, i.e., the propellant mass is excluded as it depends on the specific altitude change. For the electric thruster the mass is computed as a linear function of the required power (\(m_{t}=\alpha P\), \(P=0.5T\)_Isp_\(g_{0}/\eta\)), considering \(\alpha=20\) kg/kW and a thruster efficiency \(\eta\) of 0.65.