In summary: That's because the average temperature is the same no matter what the hitting energy is because we're averaging over the same surface area.However, if we operate the square root first and then do the area averaging we get the average temperature of -18 or 255 degrees Kelvin.In summary, the blackbody temperature of Earth is supposed to be -18C or 255K. This can be derived by reworking Stefan Boltzmann law to:TK = (S*(1-a)/4*rho) ^0,25
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ykkhor
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What is the reason we assume black body when solving radiation problem?
A black body is the ideal radiator. Of course, the Earth is not really a black body and a correction factor needs to be applied; it's called emissitivity.
BTW, this is a very old thread and I can not vouch that it's correct. I also don't see much of a discussion of emissitivity either.