We’ve been told that the earth's surface is quite a bit warmer than calculations predict. Theory has it that heat-trapping “greenhouse gases” account for a 33° Celsius disparity. But it turns out that our airless moon is also quite a bit warmer than predicted. Might something be wrong with the prediction method itself, then? It's a natural question to ask, so let's look into it.
Climate science's method of deriving a surface temperature from incoming radiant energy (whose intensity is measured in watts per square meter) is based on the Stefan-Boltzmann formula , which in turn refers to a theoretical surface known as a blackbody – something that absorbs and emits all of the radiance it's exposed to. Since by definition a blackbody cannot emit less than 100% of what it absorbs, this fictional entity has no option of drawing heat into itself, for that would compromise its temperature response and thus its thermal emission. Its 100% thermal emission effectively means that a blackbody is a twodimensional surface with no depth.
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The pictures above illustrate how strange an actual blackbody would be. The purple balloon has been converted to a blackbody, which is just as smooth as the real balloon yet reflects no light from its surroundings — which is impossible because it's nearly as smooth as glass. Logically, then, this absolutely non-reflective balloon must be infinitely rough — but once again it can't be, because it is so smooth! In point of fact, a real-life blackbody can only be approximated by a hole, a dark cavity  that you can't see into, which is not something we normally regard as a “surface” to begin with.
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