## 3 ESTCube-Luna E-Sail Payload and Experiment Operations
### E-Sail Deployment  
A 2 km tether is selected as the baseline for the E-sail thrust experiment analysis. The tether length is based on an estimated total unreeling time, which should not exceed one year (design decision). The angular momentum required to extend the tether is provided by highly miniaturised and fuel-efficient field emission electric propulsion (NanoFEEP) thrusters developed at TUD (also responsible for high-voltage source and electron emitters). These have already been demonstrated in orbit and provide 8 uN of thrust each. The preliminary deployment system analysis uses two NanoFEEP thrusters for nanospacecraft spin-up. A longer tether could be deployed by providing more thrust to produce the required angular momentum (more and/or upgraded thrusters) or by extending the allowable deployment time beyond one year. Numerical simulations were used to estimate the spacecraft and tether behaviour during deployment. The simulation considers the spacecraft-tether system in an ideal case without external disturbances. The tether was simulated as a chain of high-stiffness springs with a changing length and the changes in mass distribution due to the tether reel-out were considered. The following is a list of assumptions used in the analysis. The nanospacecraft has a uniformly distributed mass of 15 kg and a moment of inertia of 0.25 kg m\({}^{2}\). The tether has a mass per unit length of 2.27 \(\times\) 10\({}^{-5}\) kg m\({}^{-1}\), which results in a total mass of 45.4 g for the whole tether. An endmass of 2.5 g is attached to the end of the tether. The expected E-sail force per unit length of tether is 500 nN m\({}^{-1}\), which gives 1 mN for a 2 km tether. The centrifugal force (\(F_{cf}\)) expected to keep the tether stable should be at least five times the E-sail force, based on the previous simulation experience. Therefore, the tension along the deployed tether should be at least 5 mN. The centrifugal force of a point mass is given by \(F_{cf}=mR\omega^{2}\). Considering the 3.35 m centre-of-mass shift due to tether extension, the required rotation period to achieve the given tension is 629 s. The moment of inertia of a thin rigid rod rotating around one of its ends is given by \(M_{I}=\frac{1}{3}mr^{2}\). Accounting for the centre of mass shift, the inertia of the longer part of the tether is 60,230 kg m\({}^{2}\). Adding the effects of the endmass, the satellite and the remaining tether, the total moment of inertia comes out as 70,380 kg m\({}^{2}\). Combining this with the required angular velocity produces an angular momentum of 703 N m s. Table 1 lists the estimated deployment parameters for various tether lengths at 5 mN tension. For ESTCube-LuNa's planned tether length of 2 km, the final angular momentum is 702 N m s. With an undeployed tether, this requires an extremely high spin rate, which the communication and electrical power systems cannot handle. Therefore, the deployment must be executed in steps, as shown in the following figures. Figure 6 depicts the deployment of the first 60 m of tether and shows a potential safety issue; during the initial deployment, up to approximately 6 m, the tether tension increases from 5 mN to 85 mN instead of decreasing. This is because the relative increase in the endmass distance is very high, while the relative increase in the system inertia--and hence the reduction in angular velocity--is low. For an actual mission, the initial spin-up and deployment strategy must be analysed in more detail to avoid over-stressing the tether. Figure 7 shows the deployment of the full 2 km. The exact sizes of the steps depend on the minimum and maximum tether tensions allowed during deployment. The maximum is limited by tether strength, and the minimum by the tether deflection angle from the side normal. The most critical parameters to control during the deployment to avoid damaging or tangling the tether are spin and torque axis alignment accuracy and tether deflection angle from the side normal.