Consider the total radiation power emitted by Sun as stated

Consider the total radiation power emitted by Sun as stated in the previous problem. How much of this power is received by Earth? r_Sun - Earth = 1.50 Times 10^11 m R_Earth = 6.37 Times 10^6 m

Solution

Radiation power emitted by Sun is refrred in a prvious problembut not given here.

Let is be P_s - substitute the real value in the answer

R_SE   = 1.5 e+11 m disatcne form Sun to earth.

The total power of sun is over a sphere of radius R_SE around it.

area of the sphere = 4piR_SE²

area of the earth exposed to the sun power:

earth is exposed to sun like a circular disc of radius R_e = 6.37e+6 m

area of earth exposed = pi R_e²

Power recieved by earth = P_s *(area of earth exposed)/(area of suns radiation sphere)

                                         = P_s *pi R_e² /4piR_SE²
                                          = P_s *(6.37e+6)²/4(1.5 e+11)²

                                          =P_s *4.51 e-10 W