## 4 ESTCube-Luna Stretch Goal: Lunar Escape Manoeuvre  
This section discusses the possibility of expanding the scope of the ESTCube-LuNa mission by performing a lunar escape manoeuvre using the E-sail tether as the sole source of thrust. The successful completion of such a manoeuvre achieved by an ESTCube-LuNa-based architecture would confirm the potential of E-sail as source of thrust outside the Earth's magnetosphere, thus allowing other innovative mission scenarios to be planned. The analysis is based on the outcomes of the lunar escape scenario discussed in [PERSON] et al. [42], and assumes a representative tether length and voltage values of 2 km and 20 kV, respectively (with a characteristic acceleration of \(a_{c}=0.06\) mm s\({}^{-2}\)), in agreement with the rest of the experiment analysis described in this paper. To perform a lunar escape manoeuvre, the spacecraft must be able to effectively control the orientation of its spin plane. Accordingly, in the remainder of the analysis, it is assumed that the spacecraft is constantly capable of adjusting the E-sail spin plane during the escape trajectory, and the required attitude control effort is estimated. The ESTCube-LuNa design is not optimal for spin plane control because the attitude thrusters are placed on the main spacecraft and the tether endmass consists of a few grams of aluminium to provide the necessary cable tension due to centrifugal force. The positioning of the thrusters can be optimised for control purposes by introducing a remote unit, which would house the attitude thrusters for spin rate and spin plane control. A remote unit could also effectively exploit the maximum arm length for thruster-controlled rotation and centrifugal tether deployment. However, to keep the design of the ESTCube-LuNa (i.e., the endmass solution) simple and to facilitate the spin rate modification experiment, the variant with remote unit is not considered for the baseline design. Nevertheless, it is worth noting that a similar architecture has been proposed by [PERSON] et al. [43] and could be combined with the ESTCube-LuNa concept as a possible next step _after_ the demonstration of the E-sail concept. The same E-sail also provides spin plane control capabilities; however, this aspect has yet to be designed and demonstrated by the ESTCube-LuNa or a similar mission. Based on the previous discussion, the spin plane modification of the E-sail represents a significant technological challenge for the design of the E-sail control system and remote unit (if any). Accordingly, a preliminary estimate of the attitude control effort required by a lunar escape manoeuvre is performed to assess the feasibility of the objective. In particular, the average daily attitude changes required by the escape manoeuvre are obtained. The lunar escape manoeuvre is analysed by modelling the spacecraft as a point mass in a selenocentric orbit, subject to the gravitational force of the Moon, the E-sail thrust, the gravitational attraction of the Earth (third body) and the perturbative force due to the Moon's oblateness. The spacecraft is assumed to be governed by a locally optimal control law, discussed at length in the work of [PERSON] et al. [42], which can be summarised as follows. The time derivative of the pericentre radius and eccentricity can be maximised by appropriately orienting the propulsive acceleration vector along the two unit vectors \(\hat{\mathbf{k}}_{p}\) and \(\hat{\mathbf{k}}_{e}\), respectively. Consequently, if the pericentre radius \(r_{p}\) of the osculating orbit is less than a given threshold value \(r_{p}^{\min}\), the E-sail spin axis \(\hat{\mathbf{k}}_{B}\) is oriented so as to maximise the projection of acceleration along \(\hat{\mathbf{k}}_{p}\) to avoid impact with the lunar surface; otherwise, the unit vector \(\hat{\mathbf{k}}_{B}\) is oriented so as to maximise the projection of propulsive acceleration along \(\hat{\mathbf{k}}_{e}\) to reach the escape conditions as quickly as possible.