Consider a spherical satellite with a 0.5 m radius, a uniform temperature, and a surface that acts (for now) as a black body. The satellite is near Earth but not in its shadow, so the satellite is exposed to the sun. Let the temperature of the sun, radius of the sun, and sun-to-satellite distance be, respectively, T = 5800 K R = 7 108 m D = 1.5 1011 m . These values imply an equilibrium temperature for the satellite of 280 K. It is often necessary to cool a satellite as much as possible, for instance to limit elec- tronics noise. Assume our satellite is given a reflective coating that reflects 99.9% of incoming sun light. Also assume this coating reflects light only above a suitable cut-off frequency so as not to significantly alter the radiative behavior of the (cool and thus emitting at lower frequencies) satellite. You may or may not need the numerical value of the Stefan-Boltzmann constant: = 5.67108 W/m2/K4.

(a) What is the equilibrium temperature of the coated satellite? (b) Assume the coated satellite has an internal power source (say, a radioiso- tope thermoelectric generator) that continuously dumps 300 W into the satellite. What is the equilibrium temperature? (c) If you were to include the effect of the coating on the outgoing radiation, which answer - (a) or (b) - would change more, and why?