Chapter 12, Problem 12.140P

Consider the spherical satellite of Problem 12.130. By changing the thickness of the diffuse material used for the coating, engineers can control the cut- off wavelength that marks the boundary between ${\alpha }_{\lambda }=0.6\text{ and }{\alpha }_{\lambda }=0.3$ .

(a) What cutoff wavelength will minimize the steady-state temperature of the satellite when it is on the bright side of the earth? Using this coating, what will the steady-state temperature on the dark side of the earth be?

(b) What cutoff wavelength will maximize the steady- state temperature of the satellite when it is on the dark side of the earth? What will the corresponding steady-state temperature be on the bright side?