Gravity on air molecule vs. diffusion into vacuum

[houlahound]

OK the atmosphere by definition envelopes the earth.The force keeping it here is solely gravity.

The "force" opposing this is diffusion across a pressure gradient into the vacuum of space.

Assuming that is correct how could I prove this other than looking out the window.

Newton's law of gravity will give the force Earth exerts on a single molecule, the force of the vacuum??

 

[BvU]

The force keeping it here is solely gravity. yes

The "force" opposing this is diffusion across a pressure gradient into the vacuum of space.

Diffusion isn't really a force; it's more the consequence of a force. But I understand what you mean.

What kind of proof did you have in mind ? A derivation of the http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap2.html probably isn't what you mean, or is it ?

[edit] made a quote of the quote

 

[houlahound]

A proof that is self evident and not too hard-core in the math.

 

[BvU]

But what is it you want to prove ?

 

[houlahound]

That the Earth's atmosphere sticks to the earth.

Other than just breathing the proof.

The question is motivated by many, many...many years ago as an undergrad I used to hang out in the postgrad e2e collision lab and saw the engineering involved to keep in gassing of the atmosphere screwing up the low vacuum chambers enclosing the experiments.

I figure if air can leak into those elaborate chambers to be such a measurable problem then what's the physics stopping same air leaking out of the wall-less chamber of the earth.

I get we exist therefore we have an atmosphere, I just want to get the physics of the opposing "forces".