Answer to Question #219593 in Mechanical Engineering for Molahlegi

Question

If the distance between the sun and the earth was the half of what it is L = 0.5 × 1.496 ×1011 m, what would the solar constant be? The sun is a nearly spherical body that has a diameter of D = 1.393 ×109 m and the effective surface temperature of the sun is Tsun = 5778 K. 𝜎 = 5.67 x10-8 W/m2K 4 .

Answer 1

Energy Emitted from sun $E=\sigma T^4$

$E=5.67 \times 10^{-8}\times 5778^{4} =63.1965 \times 10^6 W$

E = total energy intercepted (technically, energy flux = energy per unit time, in watts)

K_S = solar insolation ("solar constant")

R_E = Radius of Sun $= \frac{D}{2} =75.91 m$

$E = K_S\times \pi{ R_E}^{2}$

$K_s = \frac{63.1965\times10^6}{\pi\times 75.91^2} =3524.1 \frac {watt}{m^2}$