Determine the power per unit area arriving at the Earth

[physicsss]

a) Find the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5690 K. The Sun's radius is 7.0 108 m.

(b) From this, determine the power per unit area arriving at the Earth, 1.5 X 10^11 m away.

the formula for radiation is Power = (emittance factor)*(Stefan-Boltzmann constant)*(Area)*T^4. So I can find a) easily.

however for b, do I set up a ratio of some sort with the radius of the Earth being (1.5 X 10 ^11 + radius of the earth) or just 1.5 X 10 ^11 ?

 

[Astronuc]

The radiant flux, $\Phi$, at some distance from the sun is just the total power P_S divided by the area at that distance, 4$\pi$d².

 

[HallsofIvy]

What you need is the area of the Earth (more correctly the disk facing the sun) as a ratio of the surface area of the entire sphere centered at the sun with radius 1.4x10¹¹. Your "1.5x10¹¹+ radius of the earth" is simply assuming that that 1.5x10¹¹ is measured to the point on the Earth nearest the sun which simply isn't true. Any way, if you are keeping track of "significant figures", the radius of the Earth would just disappear!

 

[physicsss]

Is the 1.5 X 10^11 measured from the surface of the sun to the center of the earth? I have included the figure here:

 

[Astronuc]

Assume that 1.5 E11 m is from the center of the sun. The radius of the sun, 7 E8 m is only 0.5% of 1.5 E11.