Mission Design for the CubeSat OUFTI-1

CHAPTER 8order to prevent any failure due to the switching it on and off, but we need toguarantee enough power. Furthermore, turning on and off the payload impliesthat commands have to be generated by the on-board computer or sent fromthe ground station.All the following analysis is made for the elliptic orbit in the hypothesis of Ω = 0and ω = 0. However at the end of this chapter a parametric study for the powerproduced in orbit will be carry out making vary this two parameters: the resultsare basically the same but shifted in time and the most critical situation withthe minimum power always happen. Furthermore, the orbital parameters aresupposed to remains constant.8.1 Eclipse’s durationThe first step to have an idea of the available power is to know the time ofeclipse: to have it, we need to know the direction of the sun rays on the orbitplane.As shown in figure 8.1, three planes play a role in this calculation with theirreference system: the ecliptic plane, the equator plane and the orbit plane.Figure 8.1: Reference sistemsAs shown in figure 8.1, the sun rays arrive to earth on the ecliptic plane onthe direction:ˆN S = {cos (θ e ) sin {θ e } 0} (8.1)As above mentioned, the goal of this part is to express this direction intothe orbit reference. We can transform a vector from the ecliptic plane into theequatorial plane thanks to a rotation about the x ecl = x eq with the the rotationmatrix R 1Galli Stefania 74 University of Liège