A spherical satellite of diameter D is in orbit about the earth and is coated with a diffuse material for which the spectral absorptivity is aA = 0.6 for A 3 µ,m and aA = 0.3 for A > 3 µ,m. When it is on the "dark" side of the earth, the satellite sees irradiation from the earth's surface only. The irradiation may be assumed to be incident as parallel rays, and its magnitude is GE = 340 W/m2.
On the "bright" side of the earth the satellite sees the earth irradiation GE plus the solar irradiation GS = 1368 W/m2. The spectral distribution of radiation from the earth may be approximated as that of a blackbody at 280 K, and the temperature of the satellite may be assumed to remain below 500 K. intends to use a checker pattern for which a fraction F of the satellite surface is coated with an evaporated aluminum film (s = 0.03, aS = 0.09), and the fraction (1-F) is coated with a white, zinc-oxide paint (s = 0.85, aS = 0.22).
Assume the satellite is isothermal and has no internal power dissipation. Determine the fraction F of the checker pattern required to maintain the satellite at 300 K.