Solar radiation incident on the earth's surface may be divided into the direct and diffuse components described in Problem 12.6. Consider conditions for a day in which the intensity of the direct solar radiation is I dir = 2.10 x 107 W/m2 ∙ sr in the solid angle subtended by the sun with respect to the earth, ∆w1 = 6.74 x 10–5 sr. The intensity of the diffuse radiation is I dif = 70 W/m2 ∙ sr.

(a) What is the total solar irradiation at the earth's surface when the direct radiation is incident at θ = 30°?

(b) Verify the prescribed value for ∆ws, recognizing that the diameter of the sun is 1.39 X 109 m and the distance between the sun and the earth is 1.496 x 1011 m (1 astronomical unit).