# ReDSHIFT: A Global Approach to Space Debris Mitigation
## 2 Dynamical Mapping
The color map shows the residual lifetime, as a function of the initial inclination and semi-major axis, computed in 120 years for an object with \(A/m=1\) m\({}^{2}\)/kg, starting from \(e=0.001\), \(\Omega=0^{\circ}\) and \(\omega=0^{\circ}\). The red and green dots show the location of the spacecraft and fragments, respectively, according to MASTER2009. maps were produced for the Medium Earth Orbits (MEO) and the main resonances in that region were highlighted [4]. Figure 4 shows that there exists indeed the possibility to deorbit from the Global Navigation Satellite Systems (GNSS) altitude by exploiting the natural growth of eccentricity of the unstable orbits. Whereas the time required for this deorbiting exceeds the classical 25-year timespan, it is worth stressing that the actual time spent in the LEO protected region by a spacecraft re-entering from MEO in an elliptical trajectory is just a small fraction of its residual lifetime. For the GEO region, both the geosynchronous equatorial orbits and the highly inclined geosynchronous orbits (e.g., used recently by the Chinese Compass system) were explored. In the former case, whereas natural re-entry solutions cannot be found, stable graveyard orbits were identified. The map in Figure 5 (left panel) shows the maximum variation in semimajor axis of the graveyard orbits around the geostationary altitude. The right panel of Figure 5 alternatively shows the maximum eccentricity variations reached by a spacecraft starting from an inclined GEO, mainly due to lunar perturbations [3]. A significant increase in the orbital eccentricity can be noticed for these cases, paving the way to possible disposal manoeuvres, even from these high Earth orbits. Figure 4: Maximum eccentricity map for circular medium Earth orbits with inclination \(i=56^{\circ}\), in the GNSS region. The white regions indicate that the eccentricity needed to re-enter into the atmosphere is reached within 120 years. An \(A/m=1\) m\({}^{2}\)/kg is assumed. Figure 5: **Left panel**: Variation of \(\Delta a\) over 30 years. Initial orbit with \(a_{GEO}+[-50;+50]\) km, \(e_{0}=0.01\), \(i_{0}=0^{\circ}\) and \(\lambda_{0}=[0,360]\) deg. **Right panel**: Effect of the luni-solar perturbations for highly inclined initial GEO orbits (initial inclination equal to 55\({}^{\circ}\)). As the next step in the project, the end-of-life disposal manoeuvres needed to exploit the natural dynamics, revealed through the long-term orbit evolution maps, the analytical resonance study and the frequency analysis briefly described above, were computed (e.g., [9] for the LEO part). The main novelty of ReDBHIFT is that the natural dynamics are enhanced via impulsive manoeuvres, solar and drag sailing and a combination of manoeuvre and solar and drag sailing. The end-of-life manoeuvre requirements need to be designed based on mission characteristics such as the available on-board propellant and the area-to-mass ratio of the satellite. Exploiting the developed methods, it is possible to determine the optimal re-entry or graveyard orbit, given an available \(\Delta V\) on board the satellite. Slightly different design strategies are followed for the LEO, MEO and GEO environment. The strategy followed for disposal in LEO consists in computing the possible displacements in (_a,e,i_) for a given \(\Delta V\) provided in input, in order to identify the most suitable final orbit that can be achieved with that \(\Delta V\). The maximum \(\Delta V\) considered for the simulation is the one corresponding to a direct re-entry manoeuvre down to 80 km of altitude. The maximum value of \(\Delta V\) considered for the simulation is the one corresponding to a direct re-entry manoeuvre down to 80 km altitude. In this way, all the possible target orbits are selected and, among them, the one that will naturally evolve toward re-entry in a time less than 50 years is chosen. For all these cases, the required \(\Delta V\) is computed as a single burn manoeuvre in case the two orbits are intersecting.