- #1
Silviu
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Homework Statement
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
Homework Equations
##\frac{E}{St} = \sigma T^4## - Stefan-Boltzman law
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.
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