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I read this book here: http://tiny.cc/Gravity-Atom-Myth

It claims that while gravity does affect individual atoms, it's not quantified like molecular mass due to lack of binding proteins which render air-oxygen trajectories improbable.

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Be careful to distinguish between 'does not influence' and 'any influence is too small to accurately measure'. –  David H Oct 18 '13 at 21:28

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Gravity affects everything including atoms and molecules. The problem is that the gravitational force between objects that have a small mass (like between the electrons and protons in an atom) is so small, that it is being ignored in some cases, i.e, the force of gravity is not considered or taken in account in those situations.

Just look at the gravitational force between a proton and an electron, where they are $10^{-11}\rm m$ distant, according to Newtonian theory: $$\begin{aligned} \mathbf F &= \text G \frac{m_e \cdot m_p}{d^2} \\ &= 6.67 \cdot 10^{-11} \frac{9.11 \cdot 10^{-31} \cdot 1.673 \cdot 10^{-27}}{(10^{-11})^2}\\ &= 1.016576701 \cdot 10^{-47} \text{N} \approx 0 \end{aligned}$$

The force $\bf F$ we calculated is too small that we can literally ignore it, that is, not taking it in account.

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