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In my world I would like to create a pit on the Moon filled with air.

  • How deep would the pit need to be to get 1 ATM of pressure
  • Could the pit maintain the air or would it be lost to space?
  • If it would be lost, how long would it take?
  • could a cap be enough to prevent any loss?
  • Is the needed depth feasible on the moon?
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  • $\begingroup$ Igor, welcome to the site, I edited your question for clarity, if I messed up the intent feel free to roll the change back. $\endgroup$
    – James
    Jan 2, 2019 at 17:12
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    $\begingroup$ Dan Bron If we count the solar winds, yes they will blow away the air in no time, but if we take off that from the equation by logic there is no reason for the air to climb up the pit and fly away $\endgroup$
    – Igor Novelli
    Jan 2, 2019 at 17:17
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    $\begingroup$ I would turn this question around – how deep pit can be without collapsing, and how fast or slow would it lose atmosphere if we would start with 1 atm at the bottom. $\endgroup$
    – Mołot
    Jan 2, 2019 at 17:28
  • $\begingroup$ Edit ad the "cap" question, please don't be too focused on the air loss thing $\endgroup$
    – Igor Novelli
    Jan 2, 2019 at 17:36
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    $\begingroup$ @IgorNovelli No, there is a logical reason: the pressure above the hole is lower than the pressure inside it. The air would diffuse out. A cap and strong, non-porous walls would prevent that, of course, but then all you're asking is "is it possible to build a pressure chamber on the Moon"? There would be easier, cheaper, and much more practical ways to do that than to dig a hole hundreds of km deep and fill it with air. No one would opt to do that, if all they wanted was 1atm of pressure for living purposes, or whatever. $\endgroup$
    – Dan Bron
    Jan 2, 2019 at 18:43

5 Answers 5

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How deep would the pit need to be to get 1 ATM of pressure

That's pretty simple - about 300 km deep. More or less. Depends on how long you expect to keep it. Atmospheric pressure is simply the weight of gas above the observer. On earth, 99% of the atmosphere is found below 32 km, and 99.9% below 50 km. On the moon, with a surface gravity of 1/6 that of earth, a similar column of gas would be 6 times longer or about 300 km. Since the radius of the moon is about 1700 km, the gravitational gradient down the pit would be about 1/3 - that is, the gravity at the bottom of the pit would be about 67% of the surface gravity. So the surface gas density would be something like that on earth at 33 km.

Could the pit maintain the air or would it be lost to space?

Gone, gone, gone. The pressure of the earth's atmosphere at 33 km is about .017 psi. Unfortunately, it's surrounded by a much better vacuum, and will dissipate at some speed, causing more air to rise and disappear.

If it would be lost, how long would it take?

Sorry, but that's beyond me. Weeks to years, I'd guess.

could a cap be enough to prevent any loss?

Sure. The total pressure difference is pretty small, so for a small-diameter pit a cap seems perfectly reasonable. If you're talking miles wide to support a colony - not so much.

Is the needed depth feasible on the moon?

Nope. With about 1/6 the gravity, this more or less equivalent to a hole 50 km deep on earth. At these depths rock will deform like toothpaste under the weight of the overlying burden. Well, slow toothpaste. Pressure is about 17,000 atmospheres or 260,000 psi. That's pressure in the rock, not the atmosphere.

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    $\begingroup$ The 300km would need to be adjusted for the fact that not all of it is experiencing 1/6 Earth gravity, right? $\endgroup$
    – Ben Millwood
    Jan 3, 2019 at 14:55
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    $\begingroup$ @BenMillwood is correct. But it doesn't matter, since the air will rather rapidly escape the hole into the surrounding vacuum. $\endgroup$
    – Carl Witthoft
    Jan 3, 2019 at 16:48
  • $\begingroup$ @BenMillwood - Yes. There are all sorts of adjustments to be made. This was just what you call a "back of the envelope" calculation. Very brief, not at all sophisticated, and only intended to get a ballpark number. $\endgroup$
    – WhatRoughBeast
    Jan 3, 2019 at 16:54
  • $\begingroup$ Does the depth change if it's pure O2 at a much lower pressure? 3-5 psi is a viable alternative to air at 1 atm. $\endgroup$
    – Robert Getter
    Jan 3, 2019 at 17:55
  • $\begingroup$ @RobertGetter - Since air is essentially oxygen and nitrogen, and nitrogen is only about 12% denser than oxygen, the answer is essentially no. Plus, operating in a pure oxygen environment has horrible fire issues. $\endgroup$
    – WhatRoughBeast
    Jan 3, 2019 at 18:01
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The other answers are wrong due to some oversight.

This is a graph of temperature vs. escape velocity for various gases in various places:

Numbers and s...

Source: https://en.wikipedia.org/wiki/Atmospheric_escape

Oxygen will stay on the Moon as a gas, as long as it doesn't get neither too hot or too cold. Close to 50K it will liquify; close to 60K it will escape the hole and the Moon.

And this is what the wiki article for the Moon says about her temperatures:

there are places that remain in permanent shadow at the bottoms of many polar craters, and these "craters of eternal darkness" are extremely cold: Lunar Reconnaissance Orbiter measured the lowest summer temperatures in craters at the southern pole at 35 K (−238 °C; −397 °F) and just 26 K (−247 °C; −413 °F) close to the winter solstice in north polar Hermite Crater.

So you dont need to dig a hole, some already exist. Just flush the gas in and keep an ideal temperature.

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    $\begingroup$ The oxygen may or may not stay "on the moon", but that doesn't help the people in the hole if the air keeps escaping out to the surface, because there's a pressure differential because the Moon has no atmosphere. And you can't keep an atmosphere on it even if you flooded the surface with billions of tons of gas; it would boil off in the 380*+K temps of the surface in daytime. You could cap the hole, of course, but then you're just making a ridiculously impractical and expensive pressure chamber. No one would choose to do that, given the more practical options. $\endgroup$
    – Dan Bron
    Jan 2, 2019 at 18:48
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    $\begingroup$ @DanBron if you got an actual 1 ATM atmosphere on the Moon, it would take millenia to escape and would keep a nicer temperature on it. As for my solution, the gas molecules would not have the kinectic energy to leave the hole; At 50K, even at 1 atm, the gas would stay in the hole, for much the same reason that dry ice sublimating tends to stay on the floor. $\endgroup$
    – The Square-Cube Law
    Jan 2, 2019 at 18:57
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    $\begingroup$ I'm inclined to agree with your proposition, but this " the gas would stay in the hole, for much the same reason that dry ice sublimating tends to stay on the floor" is a very bad analogy. Dry ice stays on the floor because it can only, the bulk gas being more buyant than air, diffuse upwards. $\endgroup$
    – Karl
    Jan 2, 2019 at 19:34
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    $\begingroup$ You proposal says "yes we can keep solid air in Moon's crater", but does not elaborate how 1 ATM gas mixture can be kept at those conditions. $\endgroup$
    – Alexander
    Jan 2, 2019 at 22:23
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    $\begingroup$ Oxygen will stay on the Moon as a gas, as long as it doesn't get neither too hot or too cold...... I dunno about you, but I would find 50K downright inhospitable: -223.15C or -369.67F. Presumably if the OP wants an atmosphere there he wants to put something that breathes the atmosphere there. $\endgroup$
    – Clockwork-Muse
    Jan 3, 2019 at 0:20
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Some time ago, answering to this question, I posted this answer (which I reused also here)

Yes, it is possible. Consider that at the bottom of a valley one is closer to the center of mass of the planet, thus gravity can be relatively stronger, and this could reflect on the local atmospheric pressure.

gravity vs distance from center

On Earth we don't have valleys deep enough to experience dramatic difference, but we have such feature on Mars: Valles Marineris.

Up to 7 km deep, the pressure at its bottom is about 0.168 psi, while the average atmospheric pressure on Mars is 0.087 psi. About double, as you see.

Still not high enough to take a walk in T-shirt, but if the atmosphere on Mars would be more dense, it would be first spot to achieve habitable conditions.

The main difference with the present question is that the Moon gravity is way lower than the one on Mars, and even at "ground" level there is no appreciable atmosphere, while there is on Mars. So, while on Mars the surface pressure is about 600 Pa, on the Moon it is 0.3 nPa.

Therefore, even digging a very deep hole or trench, and assuming a similar behavior of the gravity vs depth on Moon, there would be nothing to fill in that hole at an appreciable level.

Even assuming you could "flush" the hole with transported air, it would quickly escape just because the average velocity of the molecules would exceed the escape velocity for the Moon.

Unless you don't want to have a pool of liquid (better frozen) gases, which being protected from the exposure to direct solar radiation will sublimate very slowly.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. Topics include CO2 accumulation, gravity, the shell theorem, and the methods used in this answer. Please continue the discussion there. $\endgroup$
    – Monica Cellio
    Jan 4, 2019 at 2:13
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The total mass of the moon's "atmosphere" is something like 10t, that just isn't enough mass of atmosphere to fill a hole.

Instead you would need to use a cap to hold down the air. To hold down 1atm of pressure requires the equivalent of a 10m column of water on Earth. If we assume luna regolith is 3x denser than water then in the gravity of the moon, which is 1/6th that of Earth, the cap would need to be 20m thick.

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    $\begingroup$ The interesting variation I've seen on this is to use water as the cap. You need two solid layers, one to keep the water from falling down and one to keep it from escaping to space. Make the bottom flat and there's no appreciable force on the bottom layer (the water pressing down from above matches the air pressing up), the layer above only needs withstand the vapor pressure of the water and must be able to stand up to the vacuum and hard UV. There are transparent materials that are suitable--you get a clear cap that provides pressure, radiation shielding and micrometeorite protection. $\endgroup$
    – Loren Pechtel
    Jan 3, 2019 at 5:30
  • $\begingroup$ The nice thing about such a cap is, that it would provide the same protection against cosmic radiation as our atmosphere does. $\endgroup$
    – cmaster - reinstate monica
    Jan 3, 2019 at 11:07
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    $\begingroup$ A water cap would freeze at the top and give you a solid layer naturally. $\endgroup$
    – Tim B
    Jan 3, 2019 at 13:11
  • $\begingroup$ You probably don't need a massive cap, just put an efficient cooler on the lid. $\endgroup$
    – Karl
    Jan 3, 2019 at 17:52
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I just don't think you do it, although I don't have the exact math handy to prove it.

On earth, if you dig a 1km deep pit and stand at the bottom of it you get 1.12 atmospheres of pressure, or a 12% increase.

There is an Interplanetary Air Pressure Calculator that holds information for several planets (although not the moon - which is understandable considering the moon has virtually no atmosphere).

That says that even 5km deep into the martian crust you only increase the pressure from 0.01 atmospheres to 0.02 atmospheres.

The deeper you go the weaker gravity becomes as well which will start working against you.

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    $\begingroup$ 5 km was way less than a scratch, for experience aa change in gravity you must go a LOT more down $\endgroup$
    – Igor Novelli
    Jan 2, 2019 at 17:52
  • $\begingroup$ @IgorNovelli The moon has a radius of 1,737km. 5km is indeed only about 0.2% but the problem is that as you go deeper than that gravity starts dropping. $\endgroup$
    – Tim B
    Jan 2, 2019 at 18:07
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    $\begingroup$ @IgorNovelli Jup, at 50km, gravity has dropped by just 8%, 150km 24%. Still not too bad. $\endgroup$
    – Karl
    Jan 2, 2019 at 19:46
  • $\begingroup$ Tim, I hate to point it out to you, but your last line is just completely wrong. ref. Assuming an uniform density, the gravity inside a stellar body will remain constant. On Earth, since the core has higher density, it actually goes up. On the moon you can assume gravity remains constant inside the craters, ravines and trenches. $\endgroup$
    – Mindwin Remember Monica
    Jan 3, 2019 at 13:04
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    $\begingroup$ @Mindwin For short distances yes, due to increasing density and other factors gravity doesn't drop or even slightly increases as you start to dig. As your own reference shows though once you are past that the gravitational force starts dropping and eventually reaches zero at the core. $\endgroup$
    – Tim B
    Jan 3, 2019 at 13:09

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