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Joe Smith asks on Gravity, Moon, Ocean Tides and Atmospheric tides

My primary question: If it’s true that oceanic tides can be caused when the moon’s gravity pulls the molecules of ocean water up and away from earth by a certain distance, and if it’s also true that earth’s atmospheric tides can, likewise, also be caused by the moon’s gravity pulling the molecules in the atmosphere up and away from earth by a certain distance, then what stops the atmospheric molecules, once they have accelerated even just a tiny distance in the direction away from earth and towards the moon, from continuing on their journey to the moon?  (Let’s, for example, say that the atmospheric molecules in question are—to simplify matters—the ones at the very top of earth’s atmosphere, so that no other atmospheric molecules are between these particular atmospheric molecules and the moon, as the moon pulls on them.)
The details: In other words, my question is, if the moon’s gravity is strong enough to cause a particular atmospheric molecule to start accelerating towards the moon, then, since this molecule, in the very beginning of this acceleration, will now be slightly further away from earth’s gravity and slightly closer to the moon’s gravity than it was when it was in its original position, what would cause this molecule’s acceleration towards the moon to stop?  As we know, the very instant the molecule’s distance from earth increases by even the tiniest amount, earth’s gravitational pull on it instantly begins to decrease exponentially, while at the same time, i.e., simultaneously, the now shorter distance between this molecule and the moon, would cause the moon’s gravitational pull on it to become even greater (exponentially greater) than it originally was when it first started to pull on the molecule, and these two facts (the now weaker and ever weakening earth gravity, combined with the now stronger and ever strengthening moon gravity) it would seem, would cause the molecule to keep heading in the direction of the moon.  And this “snowball effect” would be exponential, according to the inverse square law of gravity.  What device or mechanism, in the theory of gravity, would stop the moon from stealing this atmospheric molecule from earth?
(A side question I have here, which I hope doesn’t detract attention from my real question, is the following: if the atmospheric molecule accelerating towards the moon is affected by the moon’s gravity according to the inverse square of the distance, and this same molecule, which is also accelerating away from the earth, is affected by the earth’s gravity according to the inverse square of the distance, doesn’t this mean that the above mentioned “snowball effect” on the atmospheric molecule would actually occur not according to the inverse square of the distance, but rather, according to the sum of the inverse square of the molecule’s distance from the earth, and the inverse square of its distance from the moon?  It seems like “summing” is the correct operation to perform on the forces of both the earth’s and the moon’s gravity upon the atmospheric molecule here, rather than multiplying these two forces.  Is this correct?)1393043699
The above, is my primary question.  It is perplexing, because it seems to me that if the moon could cause a single atmospheric molecule to accelerate towards it for even the briefest instant, then the theory of gravity (as far as I am familiar with it) has no way of explaining why this single molecule wouldn’t be stolen by the moon.  (In other words, the “inverse square law” of gravity should lead to a runaway molecule, shouldn’t it?) And if the moon could steal one single atmospheric molecule, then I can see no reason why it wouldn’t eventually steal the whole of earth’s atmosphere.  I understand that the very general answer here is that, ultimately, earth’s gravity is stronger than the moon’s, so the moon can’t steal anything from earth; earth’s pull is stronger than the moon’s.  But, as I hope I’ve demonstrated above, when one doesn’t stop at the general picture of atmospheric tides, but instead delves into the details, problems seem to arise—at least from the perspective of my admittedly not all-encompassing knowledge of the theory of Newtonian gravity.
A secondary, related question is as follows: If, when the moon is overhead, the center of gravity of my body (and, presumably, every single atom in my body) is ever so slightly accelerated away from earth and towards the moon, what mechanism in the theory of gravity reverses this acceleration so that I don’t simply fly upwards to the moon?  After all, it seems to me that the same principle is at work here as in the atmospheric tides.
Another point: I realize that in my primary question, the single atmospheric molecule, and, in my secondary question, the center of gravity of my body (and all the atoms of my body), are not being spontaneously pulled perpendicularly away from the earth by the moon.  In order for this to occur, the moon would have to spontaneously just “materialize” directly overhead.  So, I realize, that instead what is happening in both my primary and secondary questions is that the atmospheric molecule (X) and the center of gravity of my body(Y) (and all the atoms of my body [Z]) are accelerating away from earth and closer to the moon, not perpendicularly to the earth (except when and if the moon is exactly overhead), but rather, X Y and Z are accelerating away from earth and towards the moon in a kind of arc over a period of time roughly equal to the time that the moon is “in the sky”.  Nevertheless, this “arc of acceleration”, rather than acceleration from a spontaneous perpendicular gravitational pull from the moon (as in the case where the moon were to suddenly and spontaneously appear directly overhead), doesn’t seem to me to change or negate the gist of my question.  Furthermore, regarding my entire question here about the workings of gravity with respect to atmospheric tides, even if one were to argue that my “arc of acceleration” scenario (scenario A) was significantly different than my “moon spontaneously appearing overhead” scenario (scenario B) so that scenario A were somehow easily explainable due to some factor I’ve failed to account for, then my response to such an explanation for scenario A would simply be: ok, then what about scenario B?  The reason this would be my response is because, in scenario B, where the moon suddenly materializes directly overhead, my current understanding of Newtonian gravity can offer no reason why, when the moon suddenly appears, that molecules at the top of earth’s atmosphere wouldn’t begin to accelerate towards it; and once this acceleration begins, it seems to me that the above mentioned “snowball effect” of gravity’s inverse square law should take over.
My appeal to those smarter than myself: If anyone sees some faulty assumptions I’ve made above, or some facts I’ve neglected to account for, which would explain not only how it’s possible that atmospheric tides due to the moon’s gravity do in fact exist, but also how the implied acceleration changes and distance changes (with respect to the earth and the moon) of the constituent molecules of these tides (scenario A) would not ultimately lead to the moon stealing the earth’s atmosphere, I would really appreciate it; likewise, even if my question about scenario A is easily explainable due to something I’ve missed, I’d equally appreciate an explanation for scenario B, if scenario A’s explanation doesn’t already cover it.  I’m literally losing sleep over this question, so thanks, in advance.

 

Joe Smith

Please refer to

https://en.wikipedia.org/wiki/Atmospheric_tide

http://www-eaps.mit.edu/faculty/lindzen/29_Atmos_Tides.pdf

http://www.scientificamerican.com/article/does-the-moon-have-a-tida/

http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-810-dynamics-of-the-atmosphere-spring-2008/lecture-notes/chapter_9.pdf

 

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