# Homework Help: Earth Temperature

1. May 6, 2017

### Silviu

1. The problem statement, all variables and given/known data
Calculate the temperature of the Earth assuming that the Sun and the Earth are black bodies. Assume that Earth is in a steady state as far as energy balance is concerned

2. Relevant equations
$\frac{E}{St} = \sigma T^4$ - Stefan-Boltzman law

3. The attempt at a solution
The power radiated by sun is $P=\sigma T_{sun}^4 S_{sun} = \sigma T_{sun}^4 4\pi R_{sun}^2$. The amount of this received by earth is proportional to: $\frac{\pi R_{earth}^2}{4 \pi R_{sun-earth}^2}$, with $R_{sun-earth}$ being the distance from sun to earth. The power radiated by Earth is $\sigma T_{earth}^4 4\pi R_{earth}$. As the earth is in a steady state we have in the end: $\sigma T_{sun}^4 4\pi R_{sun}^2 \frac{\pi R_{earth}^2}{4 \pi R_{sun-earth}^2} = \sigma T_{earht}^4 4\pi R_{earth}^2$ and from here we can get the temperature of the earth, as all the other constants are considered to be known. Is this correct? I obtained a numerical value of about 900K. I am aware that here we ignore the shielding of the atmosphere, the albedo and other effects that would influence the temperature, but it still seems to be pretty high.

Last edited: May 6, 2017
2. May 6, 2017