## 3 Numerical Experiments with Real Debris Orbital Data
The redder colors show the peak amplitude of the eccentricity of the debris. Thus, besides choosing \(A/m\), the pair \((g,h)\) also contributes to direct the debris to a previously established graveyard orbit. Figure 2a was generated considering \(A/m=1\) m\({}^{2}\)/kg, that initially the debris is not disturbed enough to reach the graveyard orbit, as shown in Figure 1c. However, according to Figure 2a, some values of \((g,h)\) help to amplify the eccentricity of the debris. That is, taking \(A/m=1\) the perturbation was not enough to increase the initial value of the eccentricity for the values of \((g,h)\) considered initially (see Figure 1c), but Figure 2a shows that there are some values of \((g,h)\) that can amplify the eccentricity and so the debris can enter the bounded region for the graveyard orbit. Note that Figure 2b shows the regions where the values of \((g,h)\) contribute to amplifying the eccentricity, and the color scale shows the time for this eccentricity growth to occur. Thus, we can observe that, even with a solar sail with \(A/m=1\) m\({}^{2}/\)kg, the debris had its eccentricity increased, allowing the object to be directed to the graveyard orbit. Then, it is possible to say that, using a solar sail with a lower area-to-mass ratio, which contributes in technical terms to reduce costs, it is possible to perform the desired maneuver by directing the debris to a certain value of \((g,h)\). Note that we used \(g=0\) and \(h=0\) as initial conditions in the simulations that generated Figure 1c but, as we can see in Figure 2a, this value contributes little to the growth of the eccentricity, highlighted in the blue color scale. However, for other initial values of these angles, a region with accentuated values of eccentricity is obtained, which contributes to the purpose of this work. Case 2 takes into account the TITAN 3C TRANSTAGE DEB-1968-081H debris. The initial conditions can be seen by looking at the legend of Figure 3a. Comparing Figure 3a with Figure 1a, we can see that the eccentricity growth shown in Figure 3a is more pronounced than in the case of Figure 1a. We also see that the pattern remains the same, that is, increasing \(A/m\) the eccentricity variations are larger. However, we can see that, in this case, the eccentricity is more affected by the SRP. Figure 3c shows that, with the ratio \(A/m=1\) m\({}^{2}/\)kg, the debris enters the chosen graveyard orbit, except for Case 1 (see Figure 1c), when \(g=0\) and \(h=0\) were considered. However, for a range of values of \((g,h)\) that includes Case 1, it was possible to see that the debris reached the graveyard orbit. Figure 3b shows the variation in the inclination for six values of \(A/m\). As in Case 1, there are large variations in this orbital element. Figure 3c shows that the debris takes a certain amount of time (around half the year) to reach a height largerenough to enter the defined region of the graveyard orbit, here defined as 1000 km above the GEO region. This time can be smaller for other values of \((g,h)\), as shown in Figure 4b. The map in Figure 4a shows the amplitude of the eccentricity when varying the angles \(g\) and \(h\). The reddest region is the one with the largest variation in eccentricity, but the debris already enters the graveyard orbit for smaller eccentricity values, as we can see in Figure 4a,b. Finally, analyzing the two cases, we can verify the possibility of removing space debris from the GEO region to a graveyard orbit using a small solar sail, unlike the case analyzed in [27], in  
which the authors conducted a study to remove debris from the GEO region by pushing the object towards Earth to be incinerated in the Earth's atmosphere. Since a large solar sail is needed to carry out the removal, then it is more complicated, in terms of technical feasibility, to use the solar sail to clean the space environment.