# Tutorial Review on Space Manipulators for Space Debris Mitigation
## 4 Space debris Mitigation
The probability of collision is given by [26]:  
\[P_{c}=1-exp(-\rho v_{rel}A\Delta t)\approx\rho v_{rel}A\Delta t \tag{1}\]  
where \(\rho\) = spatial density (n/km\({}^{3}\)), \(v_{rel}\) = relative collision velocity (km/s), \(A\) = collision cross-section of satellite (km\({}^{2}\)) and \(\Delta t\) = temporal duration of risk. Unlike at LEO, there is no natural cleansing mechanism at GEO. The UN General Assembly COPUOS (Committee on the Peaceful Uses of Outer Space) recommend guidelines to minimize further debris generation [27]. The primary means for debris mitigation must be the prevention of on-orbit breakup and de-orbit or re-orbit of dysfunctional satellites. There are three strategies for the mitigation of space debris [28]: (i) prevent on-orbit breakup; (ii) reduction of object creation during the mission; (iii) removal of objects after mission completion. It is the last option that concerns us here for which there are four further options [29]: (i) built-in self-disposal into graveyard orbits; (ii) robotic sweepers to remove small debris; (iii) retrieval of large objects such as spacecraft and spent stages; (iv) re-use of spent hardware (on-orbit servicing). To minimise debris in GEO, it is recommended by the International Telecommunications Union (ITU) that space assets are self-disposable and manoeuvred into a graveyard orbit at a minimum altitude h above GEO given by:  
\[h=235+1000\Big{(}\frac{C_{R}A}{m}\Big{)} \tag{2}\]  
where \(C_{R}\) = solar radiation pressure coefficient, \(A\) = spacecraft cross sectional area and \(m\) = spacecraft mass. This equates to an altitude range of 300-500 km higher than GEO, which equates to approximately 3 months of income-generating mission operations. With GEO satellites, there is a high compliance rate of 80% of 160 EOL satellites being boosted into disposal orbits close to 300 km above GEO despite there being no legislation [30]. However, early mortality can prevent such boosting, e.g., Skynet 4b was boosted into 150 km altitude above GEO. The GSV (geostationary servicing vehicle) was a proposed service concept for the disposal of spent satellites into graveyard orbits 245-435 km above GEO [31]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Orbital Region** & **Number of Trackable Objects** & **Debris Percentage** \\ \hline LEO & 12,376 & 77.9\% \\ HEO & 2087 & 13.1\% \\ GEO & 987 & 6.3\% \\ MEO & 223 & 1.4\% \\ Other & 215 & 1.3\% \\ Total & 15,888 & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Debris population in different utility orbits. However, the current GEO graveyard will not be sustainable as its population grows. It has been proposed the GEO satellites might be delivered to a \"Necropolis\" at 36,386 km altitude (600 km above GEO) where would reside an 8 tonne truss-based stack (terminus) with a 12 m tower to which dead comsats are transported and attached by a 2.4 tonne ion engine-propelled tug spacecraft (hunter) with 0.5 tonnes xenon propellant [32; 33]. End-of-life comsats would inject themselves into this new graveyard orbit, but failed comsats would be ferried. To prevent the explosions in upper stages that generate large numbers of fragments, a European code of conduct recommends that European launcher upper stage tanks be fully vented [34]. To minimise debris in LEO, it is recommended, but not mandatory, to ensure that space assets are removed within 25 years of EOL (only 14% and 8% of LEO spacecraft complied with this recommendation in 2010 and 2014 respectively). Perhaps even a 50-year removal timescale might suffice if it were observed [35], but this has never been realised. There have been recent proposals for large constellations of thousands of small satellites such as up to 12,000 for SpaceX. Existing de-orbiting strategies will require much more aggressive solutions than the current 25-year rule. DAMAGE (debris analysis and monitoring architecture to the geosynchronous environment) indicates that there is a nonlinear increase in the number of catastrophic collisions with constellation size [36].