# Keeping air in a well

Let's say I've got an Earth-like planet with no atmosphere: it's just a barren ball of rock. I want to live there, but I don't like domes, so instead I'm just going to dig a big hole and let gravity keep the air in.

How deep a hole do I need?

According to a chart I found, the density of the atmosphere drops to pretty much zero by about 50km, at the top of the stratosphere. But 'pretty much zero' is not zero; the mesosphere beyond that extends up to about 80km and while vanishingly thin is responsible for dealing with most meteors.

If my hole is a mere 50km deep, then, some of my air is going to diffuse out of the hole and onto the planet's surface. But the surface of my planet is largely flat; there's nowhere for the air to go, so it's just going to hang around and form a dynamic equilibrium. (Unlike, say, if I built a 50km wall and tried to keep the air inside. Air would leak over the top of the wall, fall down into the vacuum on the other side, and be lost forever. Which is why the Ringworld had walls 1000km high.)

So I don't really know how shallow a hole I can get away with. I can replace the air, but I would like it to go without maintenance for at least small geological timescales. Any advice before I start up the earth-moving equipment?

(Yes, it's SF worldbuilding.)

• For what it's worth: Mars's Hellas Planitia is 23km below datum and has 30km-high walls, and the atmospheric pressure at the surface at the bottom is 1155 Pa; normal atmospheric pressure is only 610 Pa. Not good enough for humans either way. :( Feb 21, 2012 at 0:53
• Can we assume that the planet has enough gravity to keep an atmosphere of the composition you're aiming for? (I guess that would be part of the definition of "Earth-like"...) Feb 21, 2012 at 1:16
• If the planet is Earth-like in its geology, digging a hole deeper than 50km is going to be problematic since you'd be up against the mantle. Feb 21, 2012 at 1:25
• This is equivalent to constructing a shell around a planet at some arbitrary altitude. The pressure at the bottom of your hole will remain steady as long as the air pressure at the top is the same as the 'natural' pressure for that altitude.By which I mean if you start with some global specific (low) pressure at the top before you start digging, the pressure at the bottom of the hole will simply be the pressure you would get if the atmosphere was as much thicker as your hole is deep. Feb 25, 2012 at 20:51