Our correspondent Peter Newnam points us to a new paper that's being talked about on the Internet, Greenhouse Effect on the Moon?, by Hertzberg et al. The gist of the paper is that no planet acts like an ideal black body, therefore any calculation that is based upon the assumption that a planet is a black body is unreliable.
We use ideal objects like black bodies, the frictionless planes, and thin lenses all the time in physics and engineering. We use these ideal objects to estimate the behavior of the real world, and as we do so, we try to keep track of the error we are likely to make as a result of our ideal assumptions. Our hope is that the error is small compared to the accuracy we require of our calculation.
When Hertzberg et al. say that planets are not ideal black bodies, they are of course correct. But in the case of the moon, we see that the black-body model they present is pretty good. The actual temperature change on the moon is 80 K to 370 K, while the black-body model they present predicts a change of 35 K to 385 K. But Hertzberg et al. point out that the average temperature of the moon is roughly 40 K higher than predicted by a black-body model, and they claim that this difference invalidates the black-body analysis of planetary temperatures.
If we want a better understanding of the moon's surface temperature, we must add the heat capacity and conductivity of the surface rocks, as well as the absorption spectrum of these rocks for short-wave and long-wave radiation. Hertzberg et al. present a graph of the moon's surface temperature versus time during the day-night cycle. We see that the surface reaches its hottest temperature after the sun has passed the zenith, which indicates that the surface rock is taking time to heat up, by virtue of its heat capacity. The surface does not have a chance to reach its equilibrium temperature in the presence of the strongest sunlight. So we are not surprised that the moon fails to reach its black-body equilibrium temperature during the day. During the night, we see the temperature is still dropping at night when the sun rises again.
The albedo of the moon for short-wave radiation is around 0.1. It absorbs 90% of incident short-wave radiation from the sun. The emissivity of the moon's surface for long-wave radiation appears to be around 0.9. It emits 90% of the radiation that a black body would radiate. If the incident radiation from the sun is a uniform 350 W/m2, we expect the moon's surface temperature to be around 280 K. But the incident heat is not uniform. The moon spends half its time very cold, at around 80 K, in which state it radiates only 0.6% of the heat it would radiate at 280 K. For less than a third of the time, the temperature is above 300 K, reaching a maximum of 370 K. At 370 K, it radiates only 300% of the heat it would radiate at 280 K. We see that the excess of heat radiated during the day cannot compensate for the deficiency of heat radiated in the cool of the night. The moon does not radiate its own heat as efficiently as it absorbs the sun's heat, and so it is warmer than a constant-temperature black-body calculation predicts.
Hertzberg et al. conclude, "The ability of common substances to store heat makes a mockery of blackbody estimates." Quite the opposite is the case. If the moon conducted and stored heat well, its surface temperature would vary less, and the black-body estimate would be more accurate.