How Is the Surface Temperature of the Earth Calculated?

[Shackleford]

This looks to be a fairly straightforward problem. I'm not sure why I'm having trouble.

The radiant energy flux density is the energy emission per unit area. Why would I not simply multiply the solar constant of the Earth times the surface area of the Earth? Of course, it would be a plane area approximation. Then, whatever that energy emission value that is, set it equal to the Stefan-Boltzmann constant*(T_E)⁴*4pi*(R_E)²?

Is the radiant energy flux density multiplied by the area equal to the power?

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110318_204153.jpg?t=1300499036

 

[AlexChandler]

The cross section of the Earth you would use is not its surface area. It will be Pi*R^2. It is the area of the shadow that the Earth would cast on a plane perpendicular to the sun's intensity vectors.

 

[Shackleford]

The cross section of the Earth you would use is not its surface area. It will be Pi*R^2. It is the area of the shadow that the Earth would cast on a plane perpendicular to the sun's intensity vectors.

Sorry, I was ambiguous. I meant plane area approximation, not surface area.

How do you calculate the radiant energy flux density at the Earth in terms of the Sun's temperature?

 

[Shackleford]

The manual has

J_E = sigma_B*(T_S)⁴*[(R_S)/(D_E)]²

I'm not quite sure why they multiplied it by the tangent squared.

 

[Shackleford]

Why did they multiply it by [(R_S)/(D_E)]²?