UnSpace

One of the common arguments about global warming is that the other planets and satellites are undergoing global warming, too, so this means global warming must be caused entirely by the Sun. A good example of this line of argument can be found on SEO Black Hat. The author links to articles that discuss warming on Mars, Jupiter, Triton, and Pluto, as well as claiming that nothing can be learned about the greenhouse effect from Venus. I left a comment, based on an off-hand comment an astronomer friend had made on the subject, pointing out the absurdity based on the inverse square law. But for some reason, the whole thing bugged me. My training in heat transfer was nagging at the back of my mind. See, you can calculate the expected temperature of a planetary body based on some simple calculus. I looked up how to do that calculation and realized my post had been wrong.

I hate being wrong. This series of post is an attempt to set the record straight.

If you want to see where I went wrong, go visit the Wikipedia entry on black body radiation. I'd done a quick dimensional analysis of the problem, and in doing so neglected to include the part about black body radiation relating to temperature by a 4th power law. I made a stupid mistake. Dimensional analysis is a quick engineering trick to look at any problem, but if you don't understand all the relationships between the various factors, can lead you far astray. I'll say it again. I was wrong.

The actual equation is:

The above equation is from Wikipedia and used under fair use. It is consistent with the results from Bird, Stewart and Lightfoot's Transport Phenomena, 1960, pp. 443-444, and other sources. To deal with the question of albedo (none of the planets is a perfect black body radiator), I would need to modify the above equation based on a similar method to Taking Earth's Temperature. Note that they use a solar constant, which the above equation doesn't use. Now, in deriving the equation shown above, I'm assuming the Earth is in thermal equilibrium. The albedo affects this equilibrium, reducing the amount of solar energy seen by a factor of (1-A), where A is the albedo. To get the temperature, I take a 4th root, which means I'd take the fourth root of 1-A. On the side of the equation where we look at the energy radiated out into space, there would be another albedo, which would be the albedo for the Earth retaining thermal radiation. Now, it's obvious that albedo for radiation reflected from the sun is not the same as the albedo of the energy radiated thermally; that's called the greenhouse effect. But they're about the same size, they both get the fourth root taken (which makes 1-As that are greater than .5 closer to 1), and I'm only going to be looking at the change in temperature expected. So I'm going to assume that ((1-As)/(1-At))^.25 is pretty close to 1. For the purpose of these calculations, it's a good enough assumption, and besides, I don't know where to find the thermal albedo for Pluto and Triton.

If you don't like that assumption, you're free to work it out yourself, write up your own post, and laugh at me for being off by some small percentage. Before you do, throw in some reasonable numbers for the various albedos and figure out what the difference is when you change the temperature of the sun by some small bit. You still want to do the work, go ahead.

I'll evaluate the evidence for Pluto, Triton, Saturn, Jupiter, and Mars over the next couple days.

What's that? No one's claiming that Saturn's undergoing global warming? Right now, Cassini's orbiting Saturn all up close and personal, getting tons of cool pictures and data that would point out global warming at Saturn and on Titan. No, no one's claiming that Saturn and Titan are undergoing global warming, are they? But if the warming of the Earth, Mars, Jupiter, Triton, and Pluto are all caused by solar output, then wouldn't Saturn be experiencing global warming, too?

I'm having fun with this!