Thanks Dan. The thing keeping the atmosphere from flying out of the hole under its own pressure is gravity. Imagine releasing 1m³ of air-at-sea-level in the base of the vacuum-filled pit; does all that air climb the 1,737km against gravity to escape at the top? How far does it get? I've selected "unobtanium" for the walls of the pit because the absolute depth of the pit is a distraction; I'm more interested in knowing whether humans could survive there without relying on a mechanical airlock for their survival.

@RobertK.Bell Yes, the air would still escape. The moon's gravity will never be strong enough to hold in the gasses, no matter how deep you go. This is because, generally speaking, gravity will decrease the deeper you go, eventually reaching zero at the center (it might increase a bit at first depending on whatever the exact composition of the moon turns out looking like, but at no point will it ever be nearly enough to hold the atmosphere). The weight of the atmosphere is simply not enough to keep it from escaping, so to speak.

so even the last atom of gas would necessarily travel up the hole and escape? I understand gravity is strongest at the surface and only decreases on the way inward, but where does the energy come from for that last particle to jump ~1700km upwards? Solar wind would be a hindrance if anything, as it would have to come down the hole to reach it.

@RobertK.Bell The energy comes from heat. Areas of the moon's surface in direct sunlight reach temperatures of over 200 C (~400 F). Since the kinetic energy of the gas is directly related to it's temperature, the molecules will have a high kinetic energy. Even if you could stick an atmosphere the size of Earth's atmosphere on the moon, and somehow the daytime temps were a few hundred degrees cooler, then at best you might get a couple of centuries before it all bleeds off, but it will happen. (As I indicated earlier, there might be some random stray atoms hanging around, but that's it.)

Thanks Dan, but the gas in the pit isn't on the surface, and not subject to the same temperatures.

@RobertK.Bell Even if you cover the hole with shade, the point is that those gases at any temperature will eventually escape. I was merely trying to illustrate a point that if the entire surface was covered with a huge atmosphere it would still escape. Sorry I worded that poorly.

You asked where the energy came from. The answer is heat. Even a frozen fluid will slowly evaporate. 20 C might as well be 200 C. It's simply an inherent property of gas. Those gases are just too light.

Also, to your solar wind concern, that wouldn't even be the main factor. Unfortunately, even without any solar wind, those particular gases will never permanently stabilize in that way. I wish I had better news, but unless you want to maintain an atmosphere of heavier elements, it just won't work.

@RobertK.Bell Let me word it this way. When you say, "The thing keeping the atmosphere from flying out of the hole under its own pressure is gravity," that's not correct, because gravity cannot keep the atmosphere from escaping the hole in the first place. You might end up with some trace molecules for a bit, but essentially all of it will escape because the Moon's gravity is simply insufficient.

@RobertK.Bell I've amended my answer with a more clear conclusion based on our discussion. If that and the above few comments don't help, please let me know where my explanation is falling short, and I'll try to rephrase or elaborate.

The trouble I'm having is that, comparing the Earth and the Moon, by dividing the surface gravity by ~6 means you go from "some atmosphere" to "absolutely no atmosphere of any kind". Is it a sudden cutoff? What fraction of Earth gravity means zero atmosphere? Is there no temperature/pressure below which individual atoms cannot exceed escape velocity?

Having a look at other similar(?) moons such as Triton, Europa, Io and Callisto; they each still have atmospheres, even without "pits" to preserve them from solar heating.

I'll give you some additional details on some of the moons you mentioned:

Triton's atmosphere is primarily nitrogen, just like Earth (Triton's nitrogen comes directly from evaporating nitrogen ice on the surface, as well as ice that erupts from beneath the surface). The upper layers of the atmosphere are still escaping into space, however the rate this happens at is much slower than the rate it would happen on our moon.

One reason is because it's so dang cold there; another is that Triton is much further away from the sun. But there might not be any atmosphere left today if the geological activity wasn't always replenishing it by bringing more ice to the surface.

Europa is a different situation. It does have a very, very thin atmosphere of oxygen, and an extremely weak ionosphere. The main reason why the oxygen gas is there is because the surface ice (and probably subsurface water) are constantly being smacked by radiation from Jupiter and the Sun, breaking down the H20.

The hydrogen released from the H20 escapes into space; it's simply too light. But some of the oxygen, being a little heavier, will fall back down for a while. Yet eventually, that, too, escapes. There would be no atmosphere there if the process wasn't continuously producing more.

Io has an atmopshere that's mainly sulfur dioxide, plus a few other things like oxygen and sodium chloride that probably all make it smell wonderful. Jupiter is constantly stripping Io's atmopshere away, but the volcanic activity is replenishing it.