Post by: sloanjh on March 15, 2010, 09:31:46 PM
The problem is that I remember calculating (back in college thermodynamics class) the expected temperature of a black-body, perfectly thermally conductive sphere that's sitting at the radius of the Earth's orbit away from the Sun. The really cool part is that this calculation gives you roughly 300 degrees K (i.e. room temperature) without tweaking anything - it's just based on the Earth sucking up all the solar energy hitting the disk it occludes, and radiating it back out over its entire surface at a rate proportional to the fourth power of the temperature.
The part that's been bugging me is that the same calculation should hold true for the Moon as holds true for the Earth - they're both roughly the same distance from the Sun, and they're both spheres. The big difference is that the Moon doesn't have any big heat sinks (read oceans) on its surface, and so will undergo bigger temperature fluctuations. Still, the "average" temperature of the moon should be roughly 25C (the same as the Earth), not -100C. This says to me that there's something seriously broken with the temperature model in Aurora.
I did some googling around for "average lunar temperature" and found the following link: http://www.lunarpedia.org/index.php?tit ... emperature (http://www.lunarpedia.org/index.php?title=Lunar_Temperature) which gives a pretty good analysis of all this. I also found a link to a paper claiming to measure the average Lunar temperature at the equator and getting 220C (but this is probably the surface temperature which undergoes wild fluctuations).
Oh, yeah, and Luna also claims to have a "10% Ice Sheet" Hydrosphere, the same as for Mars. I think this might be a bit over-optimistic
BTW, this also seems to indicate (to me at least) that maybe greenhouse are of more use in giving thermal "inertia" to a planet - preventing wild day/night temperature swings due to the night side radiating away all its heat overnight.
John
PS - If anyone other than Steve wants to respond to this, you should probably take it to another thread and reference the post (you can get the reference by searching for something like Lunar_Temperature in posts from me) so as not to clutter up the Bugs thread with a long discussion. I almost put this in a thread in mechanics, but at the end of the day I think that it's a bug that worlds at the same distance from the Sun don't have the same base temperature.
Post by: Father Tim on March 16, 2010, 07:13:04 AM
Post by: sloanjh on March 16, 2010, 09:05:00 AM
Quote from: "Father Tim"
Neither the Earth nor the Moon is a black body, which is why the temperature equations include albedo.
Excellent point, which I hadn't thought of.
Unfortunately, that doesn't explain the discrepancy, since:
1) There's a field called "albedo" which Steve has set to 1.0 for both Earth and Moon.
2) From a quick google around for albedos, it looks like the Moon is darker (i.e. absorbs more energy, and so will need to go to a higher temperature to dump it) than the Earth.
3) IIRC, the albedo at a particular temperature affects both absorbtion and emmission linearly. In other words at 50% albedo, the body only absorbs 50% of the solar energy (so it wants to be cooler), but it only radiates energy 50% as well too (so it wants to be warmer). My recollection is that this does affect the temperature, but when I tried to do the math, the two factors cancel out. I found this wiki article http://en.wikipedia.org/wiki/Standard_a ... cteristics (http://en.wikipedia.org/wiki/Standard_asteroid_physical_characteristics) which gets the same answer (no albedo dependence for grey bodies). As the article points out, what's actually important is the absorbtion in the visible spectrum compared to the emmision in the IR (which is how the greenhouse effect works), but I'm assuming here that there's spectrum dependent variation....
John
Post by: MoonDragon on March 16, 2010, 10:21:27 AM
Quote from: "sloanjh"
Oh, yeah, and Luna also claims to have a "10% Ice Sheet" Hydrosphere, the same as for Mars. I think this might be a bit over-optimistic
Didn't some recent news reports of impact experiments establish that there may be even more ice than that? I thought they established that even ordinary soil away from the poles has significant amount of water in it.
Post by: Randy on March 16, 2010, 12:27:03 PM
http://www.universetoday.com/guide-to-s ... -the-moon/ (http://www.universetoday.com/guide-to-space/the-moon/temperature-of-the-moon/)
Post by: sloanjh on March 16, 2010, 10:49:17 PM
Quote from: "Randy"
how about atmosphere effects? The moon doesn't have one, but earth does...
http://www.universetoday.com/guide-to-s ... -the-moon/ (http://www.universetoday.com/guide-to-space/the-moon/temperature-of-the-moon/)
That was what I meant at the end of the original post about greenhouse gasses preventing wild temperature swings - basically (I think) the atmosphere lowers the IR emissivity by trapping the IR radiation from the warm surface in the (cooler I suspect due to adiabatic cooling upper layers of the) atmosphere. I think most of this is due to water vapor, btw, which is why you get bigger temperature swings in the desert.
The other thing that I suspect water does is act as a heat sink - since it's got a large heat capacity and conducts heat fairly well it keeps the temperature more uniform between day and night (the high heat capacity means a smaller temperature change per unit of energy radiated, while the good conductivity increases the effect by increasing the depth of material subject to the fluctuations).
John