## 5 Final Remarks  
This paper has analyzed the performance of a CubeSat equipped with a propulsion system based on the BIT-3 electric thruster in a typical heliocentric scenario involving the transfer between two Keplerian orbits of assigned characteristics. This scenario has been studied in an optimization framework where the flight time required to complete the orbital transfer is minimized. The study of the transfer performance takes into account the actual thrust levels of the engine and also considers the presence of two propulsion units on board, even if the procedure can be easily extended to the case of three units. This possibility of installing two engine units on the CubeSat allows for a large number of possible combinations of thrust and electric power required for the operation of the propulsion system. In particular, in the case in which the electric power is sufficient to activate the operating level corresponding to the maximum available thrust magnitude, and since the direction of the thrust vector is not constrained as often happens in the use of solar electric propulsion systems, the solution of the optimal control problem in which the flight time is minimized provides the classic result where the maximum available thrust value is locally employed. This result corresponds to selecting a single operating level during the entire heliocentric transfer, although the situation is significantly different when the electric power provided by the solar arrays is no longer sufficient to allow the use of any operating level summarized in the engine's thrust table. In this case, the optimal control law prescribes the use of different thrust levels during the interplanetary flight, depending on the local value of the available electric power. This aspect causes an increase in the flight time and a consequent increase in the propellant mass required for the transfer. One of the assumptions of the mathematical model is related to the fact that the direction of the thrust vector is not constrained during heliocentric flight and, therefore, the thrust can be directed in any direction of space. The presence of a possible constraint on the direction of the thrust vector would lead to a degradation in mission performance. Figure 12: Optimal control laws when \(P_{\oplus}=100\) W and the CubeSat has a single engine unit. Blue dot \(\rightarrow\) start; red square \(\rightarrow\) arrival. A lower value of this (required) propellant mass could be obtained by solving an optimization problem in which the final mass of the spacecraft is maximized. The solution to this specific problem, together with the one in which three engine units are considered in the CubeSat preliminary design, is a possible extension of the work illustrated in this paper. A second possible and interesting extension of this work concerns the introduction of a more refined model for the schematization of the electric power supplied by high-performance solar panels. Such a model, for example, could consider the effects related to variations in performances due to the degradation of the film covering the solar cells or to the equilibrium temperature whose value also depends on the distance of the spacecraft from the Sun. A third and last possible completion of the model could concern the analysis of the uncertainties related to the interplanetary trajectory of the spacecraft and therefore, in essence, the possible presence of trajectory correction maneuvers that allow the CubeSat to be brought back along its nominal optimal transfer orbit. However, although it is theoretically possible to use a continuous-thrust propulsion system, generic trajectory correction maneuvers are planned and implemented assuming a substantially impulsive velocity change, and therefore, a high-thrust propulsion system is used.