4.31 If the Earth radiates as a blackbody at an equivalent blackbody temperature TE = 255 K, calculate the radiative equilibrium temperature of the satellite when it is in the Earth's shadow. [Hint: Let dE be the amount of radiation flux imparted to the satellite by the flux density dE received within the infinitesimal element of solid angle dw.] Then, dE = mr-Ido where r is the radius of the satellite and I is the intensity of the radiation emitted by the Earth, i.e., the flux density of blackbody radiation, as given by (4.12), divided by 7. Integrate the above expression over the arc of solid angle subtended by the Earth, as computed in the previous exercise, noting that the radiation is isotropic, to obtain the total energy absorbed by the satellite per unit time Q = 2.21r?oT£ Finally, show that the temperature of the satellite is given by Earth satellite 2,21\1/4 T, = TE

4.31 If the Earth radiates as a blackbody at an equivalent blackbody temperature TE = 255 K, calculate the radiative equilibrium temperature of the satellite when it is in the Earth's shadow. [Hint: Let dE be the amount of radiation flux imparted to the satellite by the flux density dE received within the infinitesimal element of solid angle dw.] Then, dE = mr-Ido where r is the radius of the satellite and I is the intensity of the radiation emitted by the Earth, i.e., the flux density of blackbody radiation, as given by (4.12), divided by 7. Integrate the above expression over the arc of solid angle subtended by the Earth, as computed in the previous exercise, noting that the radiation is isotropic, to obtain the total energy absorbed by the satellite per unit time Q = 2.21r?oT£ Finally, show that the temperature of the satellite is given by Earth satellite 2,21\1/4 T, = TE