What Is Earth's Equilibrium Temperature Assuming Blackbody Radiation?

[FreeAnnyong]

Homework Statement

The energy reaching Earth from the Sun at the top of the atmosphere is 1.36x10^3 W/m^2, called the solar constant. Assuming that Earth radiates like a blackbody at uniform temperature, what do you conclude is the equilibrium temperature of Earth?

Homework Equations

Stefan-Boltzmann law: R=$$\sigma$$T^4, Wein's displacement law: ($$\lambda$$max)T=2.898x10^-3 mK

The Attempt at a Solution

I know that the Earth radiates the same amount of energy it takes in if it is acting as a black body, but I am stuck at figuring out how much energy the Earth is actually absorbing from the sun. If I can figure that out I know what to do with the rest of the problem.

 

[Dick]

If you look up the radius of the Earth and assume it absorbs all of the energy that crosses the circular cross section it presents to the sun, wouldn't that do it?

 

[FreeAnnyong]

Ah, you're right, I was stupidly using the full surface area of the Earth instead of a cross section.