Question

Assuming the sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant powered incident of Earth at a distance r from the sun – (Where r₀ is the radius of the earth and s is Stefan's constant)

• A. $4\pi r_{0}^{2}R^{2}\sigma\frac{T^{4}}{r^{2}}$
• B. $\pi r_{0}^{2}R^{2}\sigma\frac{T^{4}}{r^{2}}$
• C. $r_{0}^{2}R^{2}\sigma\frac{T^{4}}{4\pi r^{2}}$
• D. $R^{2}\sigma\frac{T^{4}}{r^{2}}$

Answer 1

Answer: (B)

$\pi r_{0}^{2}R^{2}\sigma\frac{T^{4}}{r^{2}}$

Answer 2

Power received by Earth = $\frac{\sigma T^{4}R^{2}}{r^{2}}(\pi r_{0}^{2})$