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Our atmosphere is only about 100km thick before the official start of space. That is a mere 1.57307% of the radius of Earth (6,357km). The difference between the gratitational force at sea level and 100km up would be minimal. If that is what regulates the size, there would be a fine line between having a thin atmosphere only a few times that of Mars, and a very thick one like Venus (about 90 times the pressure of Earth's).

Are we just lucky that the amount of gas left on top when Earth formed, plus what was outgassed, plus what was mopped up from around Earth's orbit later, was the right amount, or does something else determine the amount?

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    $\begingroup$ there is nothing exactly lucky about that. If we had double the amount of gas or half, it would just adjust itself. The gravity just keeps it in; just like the level of water in a fish tank is most strongly determined by how much water you poured in, the amount of atmosphere is most strongly determined by how much air there is. $\endgroup$
    – naturallyInconsistent
    Commented Apr 8 at 4:16
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    $\begingroup$ Related: en.wikipedia.org/wiki/Scale_height $\endgroup$
    – PM 2Ring
    Commented Apr 8 at 4:32
  • $\begingroup$ Are you asking why we have a certain number of oxygen and nitrogen molecules in the atmosphere or why they are distributed with height in a certain way? $\endgroup$
    – ProfRob
    Commented Apr 8 at 8:02
  • $\begingroup$ @ProfRob Just the amount we happen to have, especially since the original atmosphere was a totally different mix, especially before the water condensed. $\endgroup$
    – Peter R. McMahon
    Commented Apr 12 at 1:23
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    $\begingroup$ The relative abundances seem to be somewhat stable, but the exact composition is a list of random variables that depend upon the history of the types of earlier supernova-ed stars in the vicinity of the planet. Earth did not originate with an oxygen-rich atmosphere. Things can change quite a lot. Advanced life can live in under water. You need to have more clarity on what it is you are wanting an answer for. $\endgroup$
    – naturallyInconsistent
    Commented Apr 12 at 2:23

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Yes, we are just lucky! And not just about the amount of air, but about nearly everything that has made this little blue planet able to sustain life.

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  • $\begingroup$ Life would be just as happy with twice the atmosphere (and once probably was) or with half of it. Life would, of course, adapt to the conditions. We could probably get away with slightly smaller lungs or we might need slightly larger ones, but I suspect that lung size is not all that critical. There are plenty of people who have to live with one lung or even less for medical reasons. There are also plenty of lifeforms that can live without any oxygen at all, so the goldilocks arguments are not supported by actual biology. $\endgroup$
    – FlatterMann
    Commented Jul 22 at 2:30
  • $\begingroup$ Amazing isn't it? No matter how benign and noncontroversial the comment, there's always someone who want's to argue! $\endgroup$
    – BlastWave
    Commented Jul 22 at 3:15
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The Karman line of 100 km, as you might guess, is a fairly arbitrary legal definition rather than one based in physics or meteorology. But it is roughly the altitude where a plane would have to travel so fast to achieve lift with so little air density, that it would attain orbital velocity. It was most likely chosen as a dividing line between air and space based on what type of craft could operate there.

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