## 7 Numerical Results
### Results
It is important to underline that the maximum energy consumption achieved by a single satellite is limited by the amount of energy available on board, as can be seen in Figure 9. Instead, the total energy consumption on both satellite 13 and the space segment is intermediate for \(\alpha=12\). Finally, we separately report the space segment energy consumption due to processing and transmission, again for \(\alpha=\{5,12,20\}\), in Figures 11 and 12, respectively. From these figures, we can observe that the energy consumption due to on-board processing is predominant with respect to the energy amount used for data transmission in the considered realistic scenario. Figure 5: Ground station energy saving obtained by solving the optimization problem and by applying the proposed GSESH algorithm, varying the number \(\alpha\) of services processable on a satellite in a time cycle and fixing \(\
abla=0.1\%\) to limit the available energy for OEC operations to the 0.1% of the energy available on Sentinel-2 (1020 J). Figure 6: Ground station energy saving obtained by solving the optimization problem and by applying the proposed GSESH algorithm, varying the number \(\alpha\) of services processable on a satellite in a time cycle and fixing \(\
abla=0.2\%\) to limit the available energy for OEC operations to the 0.2% of the energy available on Sentinel-2 (2040 J). Figure 7: Ground station energy saving obtained by applying the proposed GSESH algorithm and two benchmarks (FoG and AG), varying the number \(\alpha\) of services processable on a satellite in a time cycle and fixing \(\
abla=1\%\) to limit the available energy for OEC operations to the 1% of the energy available on Sentinel-2 (10,200 J). We also propose an analysis aiming at studying the impact on the percentage of ground station energy saving of the amount of energy available on board satellites. In Figure 13, we show the energy consumed on GSs by varying \(\alpha\in[0,\ldots,50]\) and \(\
abla\in\{1\%,5\%,10\%,15\%\}\), by applying the GSESH algorithm. It can be noticed that, by increasing the energy available on board, there is an extension of the region of \(\alpha\) values where the ground station energy saving increases, and the peak ground station energy-saving percentage also increases with \(\
abla\). In particular, it can be noticed that with only the 10% of energy available on Sentinel-2 to be dedicated to OEC operations, it is possible to obtain 99.95% of ground station energy saving when \(\alpha=27\), while with the 15% of energy available on Sentinel-2 we reach 100% ground station energy saving when \(\alpha=28\). Please notice that drops in energy saving, which can be seen in the cases \(\
abla=10\%\) and \(\
abla=15\%\), are due to a particular interaction between the set of services and the empirically determined energy margin calculation, leading to a drop in services that can be managed by the satellites when \(\alpha=23\) and \(\alpha=29\), respectively. Figure 8: Ground station energy consumption as a function of the time cycle for the GSESH heuristic; the values \(\alpha\) equal to 5 (**a**), 12 (**b**), and 20 (**c**) are considered; the value \(\
abla=1\%\) is fixed to limit the available energy for OEC operations to the 1% of the energy available on Sentinel-2 (10,200 J). Finally, we have evaluated how the ground station energy saving is influenced by the number of cores available on board of satellites. In particular, by increasing the number of cores but leaving \(\alpha\) fixed, we linearly increase the number of services which can be processed in a time cycle, and in this case the energy consumption increases linearly, too, since the CPU clock frequency of each single core remains the same, and consequently the energy demand of each core does not change.