Without ever really being exposed to how to do this, I have an idea of how you might at least hack it.
At a given temperature Kelvin, the molecules in a gas will have an average speed which you could easily calculate, although I don't want to dig out any books right now. You could probably look up the average kinetic energy of a molecule in a gas from a table. Set that to (1/2)(m)(v^2), and solve for v. If there's not an easier way.
Then, figure the escape velocity for a planet of a given mass. An integral figuring out how much work has to be done to lift an object to a distance of infinity is how you do that. Set that amount also equal to (1/2)(m)(v^2) and solve for v. Just do an object with mass m, and it will cancel out of the equation.
Voila. If the average speed of the gas molecules at your atmosphere's temperature is greater than the escape velocity, the atmosphere dissipates. If it is lesser, the atmosphere is trapped. (Although remember that the speeds are an average, and there will always be some molecules with a speed higher than the average. You could have some fudge factor, too...)
Hope that helps! You'll probably want to make a table or something that your spreadsheet can use, rather than have it do integrations. You would approximate, but still... With any luck you could find both figures in tables. Good luck! Sounds fun! |
