Chapter 12, Problem 12.10P

Solar radiation incident on the earth’s surface may be divided into the direct and diffuse components described in Problem 12.9. Consider conditions for a day in which the intensity of the direct solar radiation is $I_{dir}=201{\text{x10}}^{7}W/m^2·$ in the solid angle subtended by the sun with respect to the earth, $\Delta {\omega }_s=6.74{\text{x10}}^{-5}sr$ . The intensity of the diffuse radiation is $I_{dif}=70W/m^2·sr$ .
(a) What is the total solar irradiation at the earth’s surface when the direct radiation is incident at $0={30}^{\circ }$ ?
(b) Verify the prescribed value for $\Delta {\omega }_s$ , recognizing that the diameter of the sun is $1.39{\text{x10}}^{5}m$ and the distance between the sun and the earth is $1.496{\text{x10}}^{11}m$ (1 astronomical unit).