Consider the spherical satellite of Problem 12.127. By changing the chemistry of the diffuse material used for the coating, engineers can control the cutoff wavelength that marks the boundary between αλ = 0.6 and αλ = 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 is?

(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?