## 3 Simulations
### Analysis of Results
As shown in Figure 3b,d,f, the behavior of \(\Delta\
u\) with respect to the latitude of the emitter \(\Lambda\) was always decreasing, so  
\[\dfrac{\partial(\Delta\
u)}{\partial\Lambda}<0 \tag{63}\]  
in every case. In Figure 3e, the behavior of \(\Delta\
u\) with respect to the combined variation of both the orbit radius \(r\) and the true anomaly of the first satellite scaled with the actual position of the emitter \(\
u_{1}^{\Lambda}\) resembles a similar amplification and a change of scale with respect to \(r\) of (62), but without anti-symmetry, as shown in (64), where \(k_{1}(r),k_{2}(r)\in\mathbb{R}\setminus\{0\}\). \[\Delta\
u\Big{(}\Omega_{1,*},\
u_{1}^{\Lambda},\Lambda_{*},r\Big{)}\approx k _{1}(r)\Delta\
u\Big{(}\Omega_{1,*},k_{2}(r)\
u_{1}^{\Lambda},\Lambda_{*} \Big{)} \tag{64}\]Figure 3f shows the decreasing behavior of \(\Delta v\) with respect to \(\Lambda\), as stated in (63), but also reveals a minimal (if not negligible) effect of the orbit radius \(r\) when \(\Omega_{1}\) and \(v_{1}^{\Lambda}\) were not varying, so \(\Delta v\Big{(}\Omega_{1,*},v_{1,*}^{\Lambda},\Lambda,r\Big{)}\approx\Delta v \Big{(}\Omega_{1,*},v_{1,*}^{\Lambda},\Lambda\Big{)}\). The third set of functions were the ones reported in (54). From Figure 4a-c, the dependence of \(\gamma_{1,2}\) with respect to \(\Omega_{1}\) reveals macroscopic symmetric behavior, but with nonlinear influences due to other variables. The completely symmetric model predicted in [26], i.e., \(\gamma_{1,2}(\Omega_{1})=\gamma_{1,2}(-\Omega_{1})\), obtained in simplified scenarios, needed to be corrected with nonlinear influences that depended on the actual values of \(v_{1}^{\Lambda}\), \(\Lambda\), and \(r\). Possible additive models could be the ones reported in (65)-(67). \[\gamma_{1,2}\Big{(}\Omega_{1},v_{1}^{\Lambda},\Lambda_{*},r_{*} \Big{)} =\gamma_{1,2}\Big{(}-\Omega_{1},v_{1}^{\Lambda},\Lambda_{*},r_{*} \Big{)}+f\Big{(}v_{1}^{\Lambda},\Lambda_{*},r_{*}\Big{)} \tag{65}\] \[\gamma_{1,2}\Big{(}\Omega_{1},v_{1,*}^{\Lambda},\Lambda_{*},r \Big{)} =\gamma_{1,2}\Big{(}-\Omega_{1},v_{1,*}^{\Lambda},\Lambda_{*},r \Big{)}+f\Big{(}v_{1,*}^{\Lambda},\Lambda_{*},r\Big{)}\] (66) \[\gamma_{1,2}\Big{(}\Omega_{1},v_{1,*}^{\Lambda},\Lambda_{*},r \Big{)} =\gamma_{1,2}\Big{(}-\Omega_{1},v_{1,*}^{\Lambda},\Lambda_{*},r \Big{)}+f\Big{(}v_{1,*}^{\Lambda},\Lambda_{*},r\Big{)} \tag{67}\]  
From Figure 4a,d, the behavior of \(\gamma_{1,2}\) with respect to the true anomaly of the first satellite \(v_{1}^{\Lambda}\) (translated considering the actual latitude of the emitter) revealed two distinct trends: \(\gamma_{1,2}\) was decreasing for negative values of \(v_{1}^{\Lambda}\) and \(\gamma_{1,2}\) was increasing for positive values of \(v_{1}^{\Lambda}\), so  
\[\left\{ \begin{aligned} \frac{\partial(\gamma_{1,2})}{ \partial v_{1}^{\Lambda}}>0& v_{1}^{\Lambda}>0\\ \frac{\partial(\gamma_{1,2})}{\partial v_{1}^{\Lambda}}<0& v _{1}^{\Lambda}<0\end{aligned} \right. \tag{68}\]  
is a possible interpretation of the data. However, the trends in Figure 4a,d are related to low altitudes (i.e., \(h=400\) km); when the value of the altitude became higher, the main trend was the increasing one, as shown in Figure 4e, revealing a possible multiplicative influence of the orbit radius \(r\). Given two orbit radii \(r_{\mathrm{S_{A}}}\) and \(r_{\mathrm{S_{B}}}\), a possible model is the one shown in (69), where \(\Delta r_{A,B}=r_{\mathrm{S_{B}}}-r_{\mathrm{S_{A}}}\) is the difference of the orbit's radii, \(f\) is multiplicative function of the orbit radii, and \(k\in\mathbb{R}\) is an eventual additive shift. In particular, \(f<0\) for \(v_{1}^{\Lambda}<0\) and \(f>0\) for \(v_{1}^{\Lambda}>0\).