# ReDSHIFT: A Global Approach to Space Debris Mitigation
## 2 Dynamical Mapping
As an example, Figure 6 shows the solutions for re-entry from low-Earth orbit, the colour bar represents the \(\Delta V\) requirements. Moreover, as mentioned above, a solar radiation pressure-augmented case, considering an \(A/m\) of 1 m\({}^{2}\)/kg, was studied. In this case the corresponding resonant inclination bands, presented in [2; 7], are targeted. This corresponds to a two-phase deorbiting strategy: a relatively small manoeuvre is performed to reach a resonance where the atmospheric drag or the solar radiation pressure can then be exploited to re-enter by means of a passive stabilised sail. For the MEO and GEO region, a similar design strategy was devised: given the initial post-mission orbit and the maximum available \(\Delta V\) on-board the satellite, the reachable orbital element domain is computed via a single manoeuvre. From all the reachable orbits, we exclude orbits in the GEO protected region and a MEO protected region, that was defined in ReDBHIFT around the GNSS satellite constellation. The required manoeuvre sequence to reach each one of this target orbit is computed. In the MEO case, a transfer with 1 and 2-burn manoeuvre given at the characteristic points of the orbit (i.e., apogee, perigee, nodes) is performed. In the GEO case, the optimal transfer between the last operational orbit and any of the possible target orbits is computed with a 2-burn manoeuvre, through the Lambert problem solved on a grid of initial and final transfer times. The best results are chosen by representing the Pareto front solutions in terms of the minimum \(\Delta V\) and re-entry time. Figure 7 shows an example of Pareto front solutions for re-entry orbit of graveyard orbit started from a GEO orbit [10]. Figure 6: Example of solutions for re-entry from low-Earth orbit, the colour bar represents the \(\Delta V\) requirements, in km/s. **Left panel**: results for the direct re-entry solutions. **Right panel**: minimum-cost re-entry solutions, \(a_{0}=R_{E}+1520\) km. For the conventional GEO ring, graveyard solution exists and their stability can be measured in terms of the maximum variation of eccentricity in 120 years (see Figure 7 left). For higher initial inclinations, instead, re-entry is possible in less than 120 years as it is shown in Pareto front in (see Figure 7 right). The quality of a re-entry solution can be represented in terms of \(\Delta V\) to reach the natural re-entry corridor and the re-entry time. An example of the Pareto front solutions for re-entry orbit from MEO is instead shown in Figure 8. For all 1-burn (dark triangles) and 2-burn Hohmann (light grey point) manoeuvres found. The blue/red curve is the Pareto front. A number of possible solutions with \(\Delta V\leq 200\) m/s and \(T_{r}\geq 60\) years can be seen. Within the ReDBHIFT project, the disposal via solar and drag was studied too, with particular emphasis on the use of solar sailing that allows deorbiting for orbits with perigee higher than  
Figure 8: Map of the \(\Delta V\) needed to deorbit a typical Galileo spacecraft versus the time \(T_{r}\) needed to reach the re-entry for all 1-burn (dark) and 2-burn Hohmann (light grey) maneuvers found. The blue/red curve is the pareto front. A number of possible solutions with \(\Delta V\leq 200\) m/s and \(T_{r}\geq 60\) years can be noticed. Figure 7: Example of solutions for re-entry and graveyard solution from GEO [10]. **Left panel**: Pareto front for graveyard solutions for equatorial GEO orbits. **Right panel**: Pareto front of re-entry solutions from inclined GEO orbit. 600 km. Conventional active solar sailing for deorbiting aims at maximising the cross area of the sail perpendicular to the spacecraft-Sun direction when the spacecraft is moving towards the Sun, while the sail area is minimised when the spacecraft is flying away from the Sun. A second strategy keeps the reflective surface always oriented towards the Sun and controls it through passive stabilisation.