gw quiz #1 if the earth were an ideal black body with no atmosphere what would its surface temperature be? this is a pretty good first question to see if someone has a clue about the basic science involved in any climate change discussion. i wouldn't require a numerical answer. and if given one i'd want to see the work. regurgitating facts does not equal comprehension. anywho, the answer you want to hear goes something like this. the sun's spectrum is a nearly ideal black body. all that radiation propagates away from the sun in a spherical shell. some tiny fraction of that energy hits the earth. in equilibrium, the earth would have to radiate that energy away. and from that we can calculate the temperature of the earth. well, this hypothetical earth.

the details: the power radiated by the sun (and the earth) is proportional to its surface area and its temperature^4. ie E = &sigma 4 &pi R^2 T^4. simple geometry gives us the fraction of the sun's energy that hits the earth. ie the cross sectional area of the earth divided by the area of a sphere with radius equal to the sun-earth distance. Eearth / Esun = &pi Rearth^2 / ( 4 &pi D^2 ). doing a little algebra we get: Tearth = Tsun sqrt( Rsun / 2D ). plugging in the numbers you get: Tearth = 5C = 40F. which sound pretty close except...

extra credit. the earth isn't a perfect black body. some fraction of the sun's energy isn't absorbed. it's immediately reflected back out into space. kinda like a mirror. a bad mirror. this is called the earth's albedo. and it's value is about 0.39. redoing the above to account for albedo we find Tearth = Tsun sqrt( Rsun / 2D ) ( 1 - albedo )^0.25. plugging in the new numbers and earth's temperature plummets to a chilly -28C = -19 F. which can't possibly be correct, can it? google puts it around 14C = 57F  ¶ 8:00 AM