Fun With Lunar Temperatures

Guest Post by Willis Eschenbach

A while ago, I wrote a post called “The Moon Is A Cold Mistress”. In that post I discussed how the average temperature is not accurate when there are huge swings in temperature. Or to be clearer, I discussed why the average temperature of the moon is much lower than you’d expect given the distance from the sun. Read the post for the full discussion. Here’s the money graph from that post.

Unfortunately, the only data that I had for that post was the temperature from the Apollo mission. I still didn’t have a good measure of the temperature of the entire lunar surface.

Looking around, I found a study called “The global surface temperatures of the Moon as measured by the Diviner Lunar Radiometer Experiment“, which contained the following graphic of lunar surface temperature. This shows temperature around the moon at a single moment in time.

Original Caption: Global instantaneous temperatures of the Moon in (a) cylindrical equidistant projection (ϕ_ss = 180°) and (b) orthographic projection (ϕ_ss = 180°, 120°, and 0°).

Unfortunately, nowhere in the graphic or the article itself did it say what the average temperature of the moon is. So … I had to take a long way around.

The long way looks like this. I took the graphic of the moon temperatures and the graphic of the temperature scale. And after more experimentation than it should have taken, I was able to use the scale to assign a temperature to each pixel in the graphic. What I did was to compare the red, green, and blue values of the color of each pixel to the color scale, figure out which color in the scale it was nearest to, and convert it to the corresponding temperature. What we used to call a “SMOP”, a “small matter of programming”, which is always a bigger matter than you’d like.

At the end of all that fun, I checked my results by printing them up on my usual globe, the Mollweide projection.

Works for me …

Once I’d converted it to temperature, I then converted each gridcell to the equivalent Stefan-Boltzmann radiation and averaged those. This gave me an average outgoing radiation of some 303.5 W/m2.

And this let me check the accuracy of my figures. The lunar albedo is generally thought to be on the order of 11-12%. The results I have give an albedo of 10.7% … I’d call that confirmation.

Finally, to compare my results to those in my previous post, I have:

                                Previous Post     This Post
Temperature by Direct Average        -77°C         -75°C
Temperature by Radiation Average     -2.5C        -2.7°C

Conclusion? Well, at last, I have some real numbers for the lunar temperature. And they confirm that the Stefan-Boltzmann equation does a good job of estimating the lunar temperature, whether we do it by averaging radiation and converting to temperature, or whether we average the temperature directly.

And which of the two ways of averaging temperature is correct? Well, both, or neither. You can use either one, depending on your needs. The underlying problem is that you can’t average an “intensive” variable like temperature … but that’s a discussion for another day.

Here, because we’re just past the full moon the forest is alive at night, and our cat wants to go outside no matter the hour. However, there are coyotes, raccoons, badgers, foxes, and the occasional mountain lion out there, so he has to stay inside at night. Ah well, in the morning I’ll have to let him out. Can’t use a “doggie door”, the raccoons love those, so … they say dogs have owners, but cats have a staff, and I can only agree.

Best of the night to all,

w.

NOTE: As is my custom, I ask that to prevent misunderstandings, when you comment please quote the exact words that you are discussing.