Why doesn't the sky fall?

[randy10926 at comcast.net]

      At the top of a planet's atmosphere, particles are running around in all directions, at all of the various speeds corresponding to the kinetic temperature, and to the predictions of the Maxwell-Boltzmann distribution. Some of the particles will be headed upwards, some downwards, and some sideways. Some of them will be moving slowly, some at an average speed, and some very quickly. Whether a planet will hold onto an atmosphere will depend upon the motions of those particles which happen to be moving upwards at a much higher than average speed. If those particles are moving upwards at less than the planet's escape velocity (the speed which an object must be traveling at in order to escape the planet's gravity, and go off into space), then the particles will follow curved paths which are ellipses with a focus at the center of the planet, and will go up for a while, and then fall back into the atmosphere. (This discussion assumes that we are in the very outermost reaches of the atmosphere, where there is so little gas that the particles don't collide with other particles very often. If we were talking about a lower region, the particles would be deflected from their paths, and change their energies, so frequently that any discussion of motions which resemble orbital motions would be pointless.)
      However, if the particles were moving upwards faster than the planet's escape velocity, they would follow hyperbolic paths which would take them out into space, never to return. Of course, only those particles which happened to be heading upwards at very high speeds would follow such paths, but as already discussed, there is a continual shuffling of particle motions and speeds, and as a result, in a short while, particles which did not originally have such motions would end up with motions identical to those particles which had been lost, and then those particles would also be lost.


Simple ain't it.

Randy

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I thought it was time to stir the pot while we wait for the results from the Worlds.
Can anyone explain why gravity doesn't pull all the air molecules down to earth?  Are they lighter than space?  What is their mean speed?
I don't think this will help answer the weathervaning question and won't help us fly any better but I thought it might be fun.
Jim O
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