## 4 Mission Description and Simulation Results  
The performance of the BIT-3-propelled CubeSat is studied in an interplanetary mission scenario that includes reaching a near-Earth asteroid. In this context, the heliocentric orbit of object 2000 SG344 was considered, which corresponds to an Aten-class asteroid with a size of just under forty meters. This asteroid has been considered several times in the literature as a possible target for exploration by robotic probes [58, 59]. The orbital elements which define the shape and the orientation of the target heliocentric orbit, as obtained by the JPL Horizons On-Line Ephemeris System, are summarized in Table 6.  
The solution to the optimization problem gives a minimum flight time of about 136 days and a propellant mass expenditure of 0.61 kg (roughly 41% of \(m_{p}\)) when the CubeSat hosts a single engine unit, and a transfer time of 105.5 days and a required propellant mass of 0.95 kg (roughly 31% of \(m_{p}\)) with two installed engine units. The optimal transfer trajectory of the CubeSat is reported in Figure 9, while Figure 10 shows the temporal variation of the optimal control laws in terms of thrust vector components \(\{T_{R},T_{T},T_{N}\}\) and operating level \(\mathrm{Id}\) as a function of \(t\). In particular, Figure 10 indicates that the propulsion system uses a single operating level during all the transfer, that is, \(\mathrm{Id}=5\) when the CubeSat has a single engine unit, and \(\mathrm{Id}=20\) when there are two units. In fact, these two operating levels correspond to the maximum magnitude of the thrust vector, as confirmed by Tables 3 and 5. This is a rather common result when the performance index to be optimized is the flight time and the thrust vector direction is not constrained. Furthermore, the power subsystem is sized to allow the delivery of the required electric power from the maximum thrust level up to a distance from the Sun of 1.1 AU, and the optimal transfer trajectory clearly indicates that the spacecraft is at a distance of about 1 AU during the entire heliocentric transfer; see the ecliptic projection of the optimal transfer trajectory shown on the left side of Figure 9. The situation is different when the electric power provided by the solar panels is not sufficient to allow the use of maximum thrust. For this reason, the last part of this section will analyze the transfer to the asteroid 2000 SG344 considering a value of \(P_{\oplus}\) smaller than the one that allows obtaining the results summarized in Figures 9 and 10. \begin{table}
\begin{tabular}{l c} \hline \hline
**Orbital Element** & **Value** \\ \hline semi-major axis & 0.97738 AU \\ eccentricity & 0.06688 \\ inclination & 0.11308 deg \\ long. of asc. node & 191.7688 deg \\ arg. of perihelion & 275.5316 deg \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Orbital elements of the target orbit, that is, the heliocentric orbit of asteroid 2000 SG344. In particular, by solving the optimal control problem several times, a parametric study of the mission performance as a function of the nominal electric power \(P_{\oplus}\) was carried out. The results of this specific study, in terms of the minimum flight time and the corresponding propellant mass consumption, are summarized in Figure 11. The figure shows that the transfer performance degrades as the value of \(P_{\oplus}\) decreases. For example, in the case of a single engine unit, the transition from \(P_{\oplus}=121\,\mathrm{W}\) to \(P_{\oplus}=90\,\mathrm{W}\) results in an increase in flight time of about \(60\,\mathrm{days}\), while the required propellant mass reaches almost \(1\,\mathrm{kg}\). This behavior is linked to the fact that the residual electric power (once the remaining on-board subsystems have been powered) is no longer sufficient to allow the activation of the maximum thrust level permitted by the propulsion system. Therefore, other operating levels are used that require a value of electric power compatible with the availability at that given distance from the Sun.