# ReDSHIFT: A Global Approach to Space Debris Mitigation
## 2 Dynamical Mapping  
As also shown by the long term simulation of the environment performed within the project [1], the disposal of objects after the end-of-life is one of the most important mitigation measures needed to reduce the growth of space debris in the forthcoming years. In order to facilitate this action it is important to identify stable and unstable regions in the phase space where the objects could be moved to exploit either long term \"graveyards\" or, possibly and preferentially, faster escape routes. To this purpose, a dynamical mapping of the circumterrestrial space was performed within ReDSHIFT. The whole space, from LEO up to the geostationary orbit, was divided in a fine grid in the orbital elements space. Figure 1 shows a sample of the LEO grid. It highlights the fact that the grids are not uniform and are made denser were the population of objects is more abundant. About 20 million of the initial conditions were propagated, using three different orbital propagators, having similar dynamical models expressly tailored to the explored orbital regime, but different underlying computational engines. All the orbital propagations were repeated twice: once assuming for the test object an area-to mass ratio, \(A/m\) equal to the standard satellites (0.012 m\({}^{2}\)/kg) and then assuming an augmented \(A/m\) (1 m\({}^{2}\)/kg, thus simulating the presence of some sail). In both cases the reflectivity coefficient \(c_{R}\) was considered equal to 1 and the drag coefficient \(c_{D}\) equal to 2.1. The output of these massive orbital propagations was stored in terms of maps displaying, e.g., the lifetime or the maximum eccentricity growth for all the orbits during the 120 year time span of the propagation (the so-called Maximum Eccentricity Maps). Examples of the maps obtained, for the different orbital regimes are shown in Figures 2-5. All the maps produced can be found in the website of the project (http:  
Figure 1: Example of the grid adopted in semimajor axis and eccentricity for the LEO region. The black dots represent the location of the satellites currently in space according to MASTER 2009.  
and the theoretical analysis of the results obtained in the mapping can be found in [2; 3; 4; 5; 6] and cannot be repeated here for lack of space. Figure 2 shows the location of the resonances determining the long-term behavior in LEO [7], superimposed on a residual lifetime map. The objects considered start from initially circular orbits and have an area over mass ratio \(A/m=1\) m\({}^{2}\)/kg. The dark blue regions at the bottom of Figure 2 correspond to residual lifetimes compliant with the 25-year rule [8]. The small green and red dots show the location of all the objects present in the MASTER 2009 population. Similarly, Figure 3 shows the same map but with only the satellites now highlighted with red circles. It can be noticed how many of the satellites now in space lie in orbits quite close (in terms of orbital elements) to some of the resonances. It could be argued that some specific missions, populating the long lifetime yellowish regions, might be preferentially steered, already in the design phase, towards the resonance spots, in order to benefit from the augmented disposal speed granted by the unstable resonant orbits, saving the propellant needed to move the satellite toward the entry into the resonance, at the end-of-life. Of course such steering should be leveraged with the mission purposes and might sometime be unfeasible. Nonetheless, this issue will be further explored also in the framework of the legal aspects of the project (see Section 5). On the same line, maximum eccentricity  
Figure 3: The same as Figure 2, but showing, with small red circles, only the location of the satellites (active and non active), according to MASTER2009. Figure 2: Location of the dominant resonances determining the long-term behavior in LEO (green lines).