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Viewing Single Post From: The giant space ship example
Chris Ho-Stuart
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Dec 9 2011, 10:24 PM
I think our assumption refutes "greenhouse effect" as described in Wiki.
In that greenhouse gases increase earth temperature by 33 C.
This because roughly our dwarf planet receives about same warming that earth receives per sq meter, it doesn't have greenhouse gases and it's 10 C.
Except that our dwarf planet does not receive the same warming as earth per square meter; not even close!

We've been using 364 W/m2 on the dwarf planet (calculated in post #6 of this thread). At least, that is what I have been using, and I think it is straightforward. There have been no objections to it so far.

If we boosted the Dwarf planet to 15C (which we have been taking as Earth's representative temperature), then the energy requirement for Dwarf would be 391 W/m^2

The Earth is heated by 240 W/m2. It needs so much less because of the greenhouse effect, and the whole point of this exercise, as I see it, is to apply physics to calculate power requirements for Dwarf, given greenhouse gases in its atmosphere. I'm getting ready to get to the next step, of using a hypothetical grey gas for the atmosphere. This will be a stepping stone to a realistic calculation with a mix of CO2, O2 and N2.

The basis of the 33K calculation is simply the difference between surface temperature, and the effective temperature; where the effective temperature is the temperature equivalent of the supplied power. 240 W/m2 corresponds to effective temperature of 255K, which is indeed 33K less than the real surface temperature.

To calculate the 33K effect using Dwarf would require giving Dwarf the same atmosphere and gravity as Earth. We'd have to consider the full complexity of moist lapse rates near the surface, and dry lapse rates higher in the troposphere, and non-adiabatic lapse rates even higher in the stratosphere. We'd have to consider variations of conditions over the whole surface. This can be done, and it IS done; but it is way too much to explain here.

What we CAN do here is explain the underlying physics of the atmospheric greenhouse effect in a very elegant situation, in which atmospheric composition is very simple, surface conditions are homogenous, lapse rates are simple, and there's no need to worry about albedo or solar absorption. As such, this problem you have proposed is excellent for the purpose of calculating the greenhouse effect with real physics in a context where the details are laid bare and visible.

We won't get the 33K, because Dwarf is not the same as Earth, and the magnitude of its greenhouse effect will be different. But the magnitude of its greenhouse effect will be calculated by the same methods in that simpler case.

Dwarf is thus an ideal example for teaching, or for testing out alternative ideas on the thermodynamics of an atmosphere with greenhouse gases.

Cheers -- Chris
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