Mission Design for the CubeSat OUFTI-1

CHAPTER 99.1 Passive thermal-controlThe thermal control of OUFTI-1 is a critical problem. In fact, as the satellite isnot-stabilized, we need to place solar cells on each face and, if we want enoughpower, we need their surface to be as big as possible: the place available forthermal control surfaces is really small. Anyway with an accurate choice of thecoating material we still can guarantee the respect of temperature limits.We chose a passive control system based on painting: we need therefore tochoose a coating and to verify that the limits are respected.The thermal equilibrium depends on the incoming and outgoing heat flux. Makingit on a satellite means to consider the spacecraft, the sun, the earth and thecold space. Basing on the Wien’s law, each body radiates mainly at a wavelengthwhich depends on its temperature: looking the temperatures of all thisbodies, we notice that the radiative exchanges are mainly at visible and infraredwavelength. Furthermore the Kirchhoff theorem says that the spectral directionalemissivity and absorption have the same value. Extending this theoremto the integrated absorption and emissivity, ESA and NASA adopted thereforea special convention: they call ɛ the absorption and emissivity factor in infraredand α the absorption and emissivity factor in visible.α = α V IS = ɛ V ISɛ = α IR = ɛ IRWe will use this rule.As the incoming flux is mainly visible and the outgoing infrared, the equilibriumtemperature of a body in space depends from the ratio α : the higher this ratio,ɛthe warmer the body.Doing passive thermal control based on painting means to choose the appropriatecolor to keep the body temperature within its limits. If we have a body inspace without any kind of power production on board and we neglect the earth,the thermal balance says:C s Aα = AɛσT 4 (9.1)where C s is the solar constant and σ = 5.67 · 10 −8 WBoltzmann constant.Hence we can obtain the equilibrium temperature as:m 2 Kis the Stefan-√4T eq∼ Cs α = (9.2)σɛIn table 9.1 the value of α end ɛ and of the equilibrium temperature for threecolors are reported.We see that if we want to have a cold satellite we can paint it in white, otherwisewe can choose between black and golden, depending on the temperaturewe would like to reach.Galli Stefania 86 University of Liège