We also use satellites for long-distance radio - they function as absurdly tall towers. But it’s far cheaper and easier, for many applications, to bounce signals off the atmosphere.
Examples for ya… over-the-horizon radar and also AM radio, as well 
Not directly related to OP, but worthy nontheles, imho.
Yeah, play with an AM radio at night and you can pick up stations from half a continent away - they fade in and out as the reflectivity of the ionized layer varies, IIRC. Whereas FM drops off at about 60 to 90 miles, depending on the height of the broadcast tower.
I assume as the atmosphere freezes, the ionized layer would thin out as the pressure drops; plus solar “wind” is what’s ionizing it…
I read that story many many years ago. It’s the first thing I thought of when I read the title here. Of course, I don’t think you can get airtight with layers of blankets…
Or, you might even say, satellites function as absurdly high atmospheric layers.
Especially since, without an athmosphere outside, you have a huge pressure difference. All the air inside would be aspired out in a fraction of a second. It would work exactly as well as a spaceship made out of blankets.
I started a thread on this story a couple weeks ago in rec.arts.sf.science. In it, I discussed three problems with the story. There are others that I didn’t discuss.
The first problem was the Big Jerk. It should not have happened that way. If another star steals the Earth, it should transition to its new orbit relatively seamlessly. And even if it does have a Jerk, the atmosphere will be jerked along with it, so there would be no possibility of the Earth being jerked out of its air.
The idea was not to make it air tight, but to reduce the amount of air escaping to a manageable level. With enough layers, that should be doable. Note that the innermost layer is aluminum foil, which should do the most to keep the air in.
But that brings up the second problem I discussed: the chimney. They may have the air loss slowed enough in the general room, but all the air is going to go right up chimney with the smoke. In the thread, someone said that if they made the chimney small enough, it should also make the air loss manageable. He then calculated the size of the chimney for that and came up with 1.5 mm in diameter. Yeah, right.
I suggested that they could fix this by routing the smoke to another room fixed up similarly (but with a bit more air loss) to the Nest, so the smoke can gradually escape just like the room air. He pointed out that there’s a risk of backflow in that scheme and suggested plugging the chimney with some noncombustible, porous material that’ll let the smoke out at just the right rate. It would have to be cleaned regularly, of course.
The third problem I pointed out was that they have a flame in a pure oxygen atmosphere. It’s going to burn up its fuel in no time. This could be fixed by having one or two pails of nitrogen evaporating with the oxygen. But then you have to burn a lot more fuel to do this.
There’s other problems with the story, but that’s enough for now.
Can anybody please answer this question? I’m especially curious about this, but nobody has given an approximation… or can we simply not know? Just a very rough approximation, would it take minutes, days, weeks, months or years?
“1) In what kind of timeframe does the Earth’s atmosphere freeze into a thick layer around the Earth with no external sources of heat? Not necessarily asking for an exact answer, but would it happen in minutes or months?”
Certainly not minutes or hours. The atmosphere survives just fine overnight. Given the amount of overnight cooling we see on Earth, my hunch would be on the order of a week or three.
I don’t think this is correct. If you only evaporate the Oxygen, you’d only evaporate enough to get to the Earth’s partial pressure of Oxygen. So you’d want no more than 1/5 of the sea level pressure. Since people can live just fine above 10,000 feet, even less, maybe 1/8 to 1/10.
The problem with air pressure always bothered me, although I never considered what the air pressure would be if it was pure Oxygen. It still seems like it would be a problem. I hadn’t thought past that to get to the chimney problem.
I’ve never been able to find a verifiable or agreed upon value for the total thermal load of the Earth’s atmosphere, but based purely on radiative loss on the dark side versus incident solar radiation on the Sun side, we would be looking at a period of several days–perhaps as much as a couple of weeks–before the temperature dropped to the point where oxygen and nitrogen start to condense (90 K and 77 K respectively). This is complicated by the fact that as the atmosphere becomes colder and thinner, water will condense out making it more conductive to radiation, accelerating the process. The thermal mass of terrestrial ground doesn’t offer much in the way of a thermal reservoir as dirt and rock are good insulators, but the heat stored in the upper layers of the ocean will delay freezing for a little while while the water loses its thermal energy, but once it gets down to 273.15 K it will only slowly release the specific heat as it transitions from a liquid to ice. This will create some churn in littoral areas, bringing warmer water to the surface, but eventually the layer of ice will cover the ocean’s surface, locking in the remaining heat (and incidentially allowing the oceans to remain liquid indefinitely, as natural water ice is also a good insulator).
A global radiative-hydrological model would be necessary to obtain a precise answer, but it certainly wouldn’t be months, and it would definitely be longer that minutes.
Stranger
There are probably untold numbers of planets out there in interstellar space, if this article is anything to go by (not guaranteed- it is wikipedia after all)
Some of these planets will retain significant amounts of heat, beneath frozen layers or think hydrogen atmospheres. Even an Earth-like terrestrial would have hot spots, hot springs, volcanoes, black smokers, etcetera.
Given sufficiently advanced technology, I think a frozen Earth could sustain a small population using the geothermal sources alone, but there would be severe problems with obtaining and recycling material in such small habitats with such limited power sources.
Ok, I found some interesting relevant stuff, I’ll post it here so that maybe it is of some use to somebody if they find this thread.
The layer would be about 11.6 meters, if the atmosphere were frozen on the Earth’s surface.
Sounds like most houses would collapse under such a weight, making survival more difficult… but maybe it would help in providing great insulation of warmth.
You’re assuming that the atmosphere would simply snow out as it gets colder. That’s unlikely to happen.
OK, water and CO[sub]2[/sub] will snow out for sure, but those are a small part of the atmosphere. When the temp gets near the boiling point of oxygen (about 90 K), that gas will start to condense. I doubt it will rain out, since there’s unlikely to be much dust in the air, but I could be wrong on that. There’s lots of oxygen in the air, so there should be massive amounts of LOX that’ll condense on everything and then flow to the low areas. The atmospheric pressure should still be high enough that it probably won’t go directly to a solid phase. The heat of condensation will probably stabilize the temp at 90 K for a while until most of the O[sub]2[/sub] is liquified.
So there’ll be seas of liquid oxygen when the temp lowers to the boiling point of nitrogen (77 K), at which point that gas will condense out. At some point the atmospheric pressure will probably drop to the point that the nitrogen will go directly to solid form, i.e. it starts snowing nitrogen. The liquid nitrogen (mixed with the liquid oxy) will then start freezing. I don’t know the relative densities of nitrogen ice and liquid oxy, so my analysis breaks down here. Whichever one is denser will mostly end up undeneath the other. Oxygen freezes at a lower temperature than nitrogen, but the difference is only 9 degrees, so I expect there may be a certain amount of mixing of the two in the resulting ice.
At any rate, the oxygen should all end up in the low lying areas (on top of seas and lakes and in local depressions) while there will be nitrogen snow everywhere. And the liquid helium that was seen in “A Pail of Air” will not be found. The Earth should end up with a thin atmosphere of helium and neon, since it should not get cold enough to freeze those two out.
I may have missed some factor(s) in the above analysis, but at least it’s a start on figuring out what happens to the atmosphere.