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While watching experiments with vacuum chambers, I had a thought.

If you put a sealed box at normal atmospheric pressure inside a vacuum chamber, pumped out the air and pierced the pressurized box I'd feel confident predicting the pressurized air would push out into the vacuum chamber, seeking equalization.

I would further predict that the above would be true no matter where precisely the piercing was located on the box - bottom or top.

If the box was pierced on the top side, the air would push out against the force of gravity.

So, my question is: If gravity can't overcome the equalization pressure of a relatively weak vacuum at sea level gravity, how does gravity hold on to Earth's atmosphere up on the fringes of space where it is weaker and against a far more powerful vacuum?

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    $\begingroup$ Gravity at the fringes of space is still pretty strong. Eg, at 100 km the acceleration is ~96.9% of g at sea level. sagecell.sagemath.org/… $\endgroup$
    – PM 2Ring
    Commented Jun 14 at 4:59
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    $\begingroup$ Size matters. If your sealed box were several hundreds of kilometers tall, and standing on the surface of the Earth, then I think you would find that the gas pressure was not the same everywhere inside of it. $\endgroup$ Commented Jun 14 at 10:01
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    $\begingroup$ The atmosphere is not a pressurised container. It's a smooth gradient all the way out. $\endgroup$
    – OrangeDog
    Commented Jun 14 at 13:56
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    $\begingroup$ Vacuums don't have power so it's meaningless to talk about 'overpowering' a vacuum. $\endgroup$
    – JimmyJames
    Commented Jun 14 at 16:34
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    $\begingroup$ "A more powerful vacuum" is cute ;-). $\endgroup$ Commented Jun 14 at 16:47

3 Answers 3

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The escape velocity of the Earth is 11.2 km/s. In other words, you need to move faster than 11.2 km/s to leave the Earth permanently. The Earth's gravity is strong enough to attract everything moving slower back to Earth.

Meanwhile, the speed of an air molecule depends on 1) what type the molecule it is, heavier molecules move slower and 2) the temperature. If you work through that, then you find that an order of magnitude estimate for oxygen and nitrogen (which make up most of air) is about 300 to 400 m/s. This is obviously much slower than 11.2 km/s, and hence they do not escape to the fringes of space.

The experiment you describe is not relevant; in particular you seem to assume that the vacuum in your vacuum chamber is "relatively weak" while the vacuum in space is "far more powerful". That's not wrong, but it's not precise. What causes air to flow into your vacuum chamber is the pressure difference. If the vacuum in your vacuum chamber has pressure 3 kilopascals, while the vacuum in outer space has pressure 100 micropascals, then you can indeed say that outer space is a much-better vacuum, but that's not what is important, what matters is the pressure difference. The difference in pressure is $101 kPa - 3 kPa$ (where $101 kPa$ is the atmospheric pressure) in one case and $101 kPa - 100 \mu Pa$ in the other, and the difference between those two is not that big.

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    $\begingroup$ While what you say is true but you mix two ways of looking at things: The single-molecule way and the "gas is a continuum with pressure" way. "What causes air [molecules] to flow into your vacuum chamber" is that there are not enough molecules colliding with them on the way out, or even flying in the opposite direction. $\endgroup$ Commented Jun 14 at 16:51
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    $\begingroup$ You don't need to move 11.2km/s to escape Earth's gravity. You could escape if you moved at .001mph as long as your acceleration was constant. Escape velocity means "moving that fast to begin with" $\endgroup$
    – Richard
    Commented Jun 14 at 19:36
  • $\begingroup$ @Richard But once you are realistically past the top of the atmosphere there's nothing to push off of. Thus you need to be moving 11.2km/sec to escape. $\endgroup$ Commented Jun 15 at 22:23
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In addition, there is no point in the atmosphere where there is sudden "pressure to vacuum", like your question suggests. Pressure is the highest at sea level, and drops as we move higher, so that at the highest points the pressure is the same as it is in space.

how does gravity hold on to Earth's atmosphere up on the fringes of space where it is weaker and against a far more powerful vacuum

Note that at sea level, pressure is a lot higher than it is in the upper atmosphere/space. At sea level, if you put air in a small parcel and placed it in a partial vacuum, because of the large pressure difference, it will push on the insides of the parcel trying to escape into the vacuum. How hard it pushes depends on the difference in pressure. As we approach the highest points in the atmosphere, this pressure difference becomes zero.

There is no "far more powerful vacuum"; just no more pressure differential.

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    $\begingroup$ Slight correction, the pressure doesnt decrease because the decrease in gravity (it doesnt change a whole lot as you go higher in the atmosphere), but because there is less air above it pushing down, the same as how hydrostatic pressure works. $\endgroup$
    – JMac
    Commented Jun 14 at 11:39
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    $\begingroup$ What JMac said. The variation in g is pretty small. The variation in temperature is much more important. But the main factor is simply the weight of atmosphere at any given height. See en.wikipedia.org/wiki/Scale_height $\endgroup$
    – PM 2Ring
    Commented Jun 14 at 14:11
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    $\begingroup$ Indeed, you'd still have decreasing pressure with height even if the force of gravity increased as you went higher. Any type of gravity gradient will make the air want to move downward, and since there isn't an infinite amount of air, the atmosphere has to end somewhere in a vacuum with 0 pressure. $\endgroup$ Commented Jun 14 at 17:23
  • $\begingroup$ @JMac ...Noted. $\endgroup$
    – joseph h
    Commented Jun 14 at 21:27
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I think you are making a common error when thinking about vacuums. We tend to intuitively to think about vacuums as 'pulling' but that's not really the right way to think about it and while it seems like a workable model in certain circumstances, thinking about vacuums as generating a force will definitely lead you astray. Note that we are not talking about 'vacuum energy'. That isn't relevant to the question at hand.

I think one of the more relatable ways to think about this is drinking through a straw. The intuitive way I think most people think about this is that you 'suck' on the straw and that pulls the drink into your mouth. But that's not really how it works. What happens is that you are reducing the pressure in your mouth below that of the atmosphere. This creates a pressure differential and the atmosphere 'pushes' the drink up the straw.

Centuries ago, there was a great mystery around pumps. No matter how powerful a vacuum pump or suction pump was, no one could get them to pump water higher than a little over 10 meters. Even Galileo wasn't able to figure out. The answer requires understanding that the vacuum doesn't apply any force. It's the weight of the air that pushes the water up. There's only so much air above us and that's the reason for the limit. To pump water higher than that, you increase the pressure pushing the water upwards.

Going back to the straw example, imagine some sort of setup where there is a drink is inside a vacuum chamber with a tube that extends out of the drink. If you try to suck the drink up, it won't work. There's nothing pushing the drink up the tube.

The last thing to point out here is that, as mentioned above, it's the weight of the air in the atmosphere that creates the net force on a vacuum pump or drinking straw. Another way to say it is that the weight of the air that creates atmospheric pressure. That is to say, it is gravity that creates air pressure. Gravity is not in opposition to the earth's atmospheric pressure. It's what causes the earth's atmospheric pressure.

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