## 2 E-Sail Experiment Design for Solar Wind in Lunar Orbit
### ESTCube-Luna E-sail Experiment Requirements  
As discussed in Section 3.1 below, we consider a 2 km tether charged at 20 kV as an optimal solution between the nanospacecraft size of eight cubesat units and the E-sail experiment performance at a 1 au distance. With a Coulomb drag force of 500 nN m\({}^{-1}\) and a charge of 20 kV [44], a 2 km tether would yield a **propulsive E-sail force** of 1 mN. For a 15 kg cubesat, this force provides an estimated acceleration of 0.06 mm s\({}^{-2}\). The given thrust and acceleration estimates assume an idealistic case of the E-sail spin plane perpendicularly facing the solar wind stream (spin axis towards the Sun as in Figure 1). As discussed above, we have designed the ESTCube-LuNa concept assuming an inertially fixed spin plane; the setup is not optimal for trajectory control but can be conveniently used for demonstrating the E-sail fundamentals.  
We propose three **E-sail characterisation experiments** in two different scenarios: solar wind flowing perpendicular or parallel to the spin plane. Because the spin plane will remain stable with respect to the background stars, these two situations will each happen twice per year. ESTCube-LuNa is designed to determine the attitude in three axes, as described in Section 5.5, including the solar direction measured with Sun sensors. For our experiments, we assume the solar _wind_ direction to be anti-sunward and therefore provided by attitude sensors (i.e., ignoring local variations in the solar wind velocity vector).  
In the perpendicular case, represented in Section 1, the charging of the tether during the full spin cycle would result in small changes in the orbital period, which over time,  
Figure 1: Electric Sail Test Cube–Lunar Nanospacecraft (ESTCube-LuNa) experiment design in the Moon’s orbit (adapted from [42]). The solar wind, arriving from the right, is a space plasma flow of protons and electrons. The solar wind protons are deflected by the positively charged electrostatic sheath around the E-sail, creating thrust (spacecraft propulsion) as a result. The electron emitter compensates for the electron current gathered by the tethers by continuously pumping out negative charge from the spacecraft. Artwork credit: [PERSON], [PERSON] and [PERSON].  
would turn into a significant drift in the true anomaly, as well as in the orbital position (as compared with the original orbit without the E-sail thrust). In this scenario, the E-sail thrust would induce a coning angle on the tether, and the coning angle versus the centrifugal force could be tested.  
In the parallel case, represented in Figure 2, charging the tether while it is travelling downstream would result in a spin rate increase, as the force direction contributes to the angular momentum of the E-sail. The opposite effect happens if the E-sail is charged upstream, where the resulting force would go against the movement of the sail. The graphic depicts the spin plane parallel to the article's page as well as parallel to the solar wind. Details of each E-sail characterisation method for the ESTCube-LuNa mission are given in the following subsections.