Originally posted by JohnMartin
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Technically, yes, the gravitational equation would suggest an infinite gravitational attraction between two objects with a coincident gentre of gravity. However, the equation assumes that the two bodies are sufficiently small and far apart that they can be considered to be points, i.e. the distance between any two parts of either object is negligible in comparison to the distance between the two objects. This is obviously not the case for the Earth and the Earth's atmosphere.
IIRC, by summing the gravitational attraction of the component parts of a hollow spherical shell w.r.t. an object within it you can show that the gravitational effect within a hollow shell is zero, i.e. at any point the gravitational forces from the mass of the shell balance out exactly. Even if the object inside the shell is very off-centre, the attraction of the nearby shell due to proximity is offset by the greater mass of the shell beyond the object. Thus even if you could consider the atmosphere as a whole, which you can't because it's neither solid nor stationary, its gravitational effect on the Earth would not only not be infinite, it would be relatively small.
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