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Viewing Single Post From: The giant space ship example
Chris Ho-Stuart
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Dec 4 2011, 07:40 PM
"You were correct to suppose a weaker lapse rate on the starship than on Earth or Mars; but it's weaker even than you had guessed."

So lapse rate for 1/10th gravity is 1 C per 1000 meters?
And so follows gravity exactly.
What factors would make it not, precisely follow gravity?

Differences in Cp. The DALR is equal to g/Cp. An atmosphere of mainly N2 and O2 has Cp very close to 1, and so DALR = g.

But on Mars, the atmosphere is mostly CO2, with Cp of 0.83. On Mars, therefore, g = 3.7 and DALR = 4.5

You can see this in the table of various properties I gave. (Oops. I goofed again. I actually had the right number in my spread sheet, but transcribed incorrectly. I have gone back to fix up the table in my above comment. Edit post, how I love you!)

Dec 4 2011, 07:40 PM

It seems if it rains on this planet, it will require more generated heat- raining is disruptive: dumps heat when vapor liquifies into droplets, causing upper air to warm. But having humidity in the air should cause inversions layers, allowing cooler air above it.

Any condensible component of the atmosphere adds a whole new dimension to the problem. I'm going to stick with dry atmospheres, so that we can use the DALR as a guide to the environmental lapse rate. It's going to be quite hard enough to solve without adding latent heat effects.

Dec 4 2011, 08:22 PM
"Combining, the total thermal energy being emitted out to space is 364 * 1.8e13 = 6.58e15 Watts, or 658,000 GigaWatts!"

Hmm my guess was 100,000 1 GW nuclear reactors. ...

Hmm... you estimated 20 W/m2; I gave 364 Wm/2, so there should be a factor of almost 20 difference....

Aha! I goofed! I said "6.58e15 Watts, or 658,000 GigaWatts!" That should be 6,580,000 GigaWatts. In other words, my post converted to GigaWatts incorrectly.

I'll update my post accordingly. With this correction, our guesses are indeed substantially different. But note that I omitted any impact from the atmosphere at all. With a greenhouse effect, my estimates are going to come back down again -- though not by a factor of 20, I think.

Dec 4 2011, 08:22 PM
Before humans are living on this planet, one could have very cold atmosphere and still have gaseous atmosphere.
Suppose we start with atmosphere which was 150 K [and surface 150 k]
And there was these nuclear reactors putting out 658,000 GigaWatts of heat.
How much power is needed to increase the atmosphere by 1 K if using these reactors
making 658,000 GigaWatts of heat?

That's a different question to the spaceship; it relates to the magnitude of Earth's effective heat sink. This is dominated by the ocean. More seriously, the question must consider that as temperatures increase on a planet, it radiates more energy. If you have a very simple planet, like the starship, we can ignore "climate sensitivity" worries and just use the "Planck response".

This is how it works.

For a surface at 150K, the thermal radiation is only 28.7 W/m^2. An additional 658,000 GW, spread out over Earth's surface area of 5.1e14 m2, means an extra 1.3 W/m2, so it enable the surface to radiate 30 W/m^2. That corresponds to a temperature of 152 K.

So you get an extra 2K of temperature. How long it takes depends on the heat capacity, which on Earth will be dominated by the ocean. On the starship, the heat capacity is dominated by the atmosphere. But once you have raised that additional 2K, you have to keep those reactors going full bore just to maintain the new equilibrium. Switch them off, and the surface will cool back down to where it started.

But an additional 6.58e15 W (which I should have used!) spread over the starship surface area of 1.8e13 m2 boosts the temperature to 288 K, an additional 138 degrees. That's 15C.

In other words, the same power output gives you 10C, or boosts from -123C to 15C.

Dec 4 2011, 08:22 PM
Btw: love the ability to edit. Too bad Judith doesn't have this function.
I am always finding errors, after clicking the post button.

Yes indeed... and the preview feature is a great help as well. We can do quite a bit more with a bulletin board structure. I've set the edit timeout to 24 hours. If you need an edit after that, just ask. You can ask using the "report post" feature, if you like. Similarly you can report any posts that you think ought to have some kind of moderator intervention of any kind. So far there are no rules. That will change only if problems start to arise!
Edited by Chris Ho-Stuart, Dec 4 2011, 10:09 PM.
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The giant space ship example · Physical theory for climate