## 4 Results
### Initial Validation  
An example was created with randomly generated task requirements for a constellation with two 3U nanosatellites, as presented in Table 4, and battery parameters as presented in Table 5.  
A total of 15 unique tasks are considered in this hypothetical constellation. Five of them are constellation tasks, meaning that they can run on either or both satellites, and five unique and individual tasks can be executed only by the owner satellite. The mission plan obtained for an orbit in this constellation is presented by Figure 3, in which Figure 3,b show the scheduling for each task in each satellite--satellite 1 and satellite 2, respectively. Notice that tasks are labeled from 1 to 10, the first five (1 to 5) being \begin{table}
\begin{tabular}{c c} \hline \hline Orbit inclination [\({}^{\circ}\)] & 97.95 \\ Angle of the ascending node [\({}^{\circ}\)] & 225.78 \\ Eccentricity [-] & 0.0016 \\ Argument of perigee [\({}^{\circ}\)] & 111.38 \\ Mean anomaly [\({}^{\circ}\)] & 248.91 \\ Mean motion [rev/day] & 14.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Orbital parameters. constellation tasks, and the remaining (6 to 10) individual. Furthermore, task 2 is required to be synchronous. From the results shown in Figure 3, we can observe that the task schedule is consistent with the requirements of each task. Task 2, for instance, has the highest priority among the constellation tasks, being accordingly invoked five times in each satellite which is the maximum number of activations allowed (\(y_{j}^{\max}\)). Moreover, we can verify that task 2 starts and finishes execution at exactly the same time in both satellites, as it must since this task is synchronous. In contrast, task 1 bears the lowest priority, being invoked the minimum number required, which in this case is not \(y_{j}^{\min}\) (0) but the global minimum, \(\delta_{j}^{\min}\) (2). Figure 3c,d show the power footprint for this mission plan. The solid blue line represents power coming directly from the solar harvesting system for each orbit instant, including the eclipse period when it drops to zero. Note that the eclipse time does not occur simultaneously in both satellites, since we consider each satellite to be equidistant from the others on the orbit plane; hence, when one is in eclipse, another is not--a property which is ensured by all problem instances considered in this paper. Conversely, the solid red line represents the total energy consumption by constellation tasks, whereas the dashed teal line tracks the full energy usage of the satellite's tasks. The dotted coral line shows the total power consumption at any given instant, along with the wheat-colored shade that indicates whether the power is being drawn from or stored in the battery, together with the consequent SoC impact represented by the solid green line. Compared with the schedule, we can verify that this power behavior is consistent with the schedule in each satellite, directly correlated with the on/off of each task. The battery power is most intensely used in eclipse time, as expected, whereby the state-of-charge drops accordingly in this period, while not violating any of the constraints (10). Now let us investigate how the objective functions A and B values and solve time varies when increasing the constellation size. For this, we maintained the task parameters constant presented in Table 4 for the constellation tasks and randomly created new task parameters for each of the satellites added.