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 `r_0` is the radius of the Earth and `sigma` is Stefan's constant.

Options

A. `(pi r_(0)^(2) R^(2) sigma T^(4))/(r^(2))`
B. `(r_(0)^(2) R^(2) sigma T^(4))/(4 pi r^(2))`
C. `(R^(2) sigma T^(4))/(r^(2))`
D. `(4 pi r_(0)^(2) R^(2) sigma T^(4))/(r^(2))`

Answer

A

Explanation

(1) `I = (sigma . 4 pi R^(2) T^(4))/(4 pi r^(2)) = (R^(2) sigma T^(4))/(r^(2))`
`E = I . pi r_(0)^(2) = (pi r_(0)^(2) R^(2) sigma T^(4))/(r^(2))`