Contains spoilers for the first couple of chapters of Seveneves

Highly speculative on my part, I know very little about most of these topics

In Seveneves Neal Stephenson does the classic sci-fi trick of assuming that exactly one thing in the universe is different, and seeing where that takes us. In his case that one thing is the moon has somehow exploded.

And where that takes us is the complete destruction of the earth. As the initially huge chunks of moon rock hit into each other they break into smaller and smaller pieces, and take up more and more space. Eventually this process increases exponentially, the loosely held collection of rocks that was the moon disperses into a planetary ring, and earth is bombarded by lunar leavings for 5000 years:

There will be so many [meteors] that they will merge into a dome of fire that will set aflame anything that can see it. The entire surface of the Earth is going to be sterilized. Glaciers will boil. The only way to survive is to get away from the atmosphere. Go underground, or go into space.

They have only two years to prepare. Which option should they take? The choice seems obvious!

But they respond with the absolutely batshit insane solution. They go into space. And not to mars, or some other friendly location. Low Earth Orbit..

This is a terrible choice for all sorts of reasons:

They are even more at risk of meteor collision there, since all meteors that hit earth pass through LEO, but at least the atmosphere protects earth from the small ones.
There's simply no way to get people up there at scale. No matter how you slice it, at most an insignificant fraction of people can get to LEO. We simply don't have the capacity to send rockets at scale, and two years is not enough time to develop and scale the technology enough to make a dent in the 7 billion people on earth.
To prepare as well as possible in two years, the earth economy will have to keep running and sending stuff up to space. But if people know they are going to die, and don't have any real chance of being one of the lucky survivors, why would they bother? I would expect the economy to collapse fairly rapidly, followed by looting, and the collapse of government structures.
There's a thousand things that can kill you in space, and just staying alive requires lots of advanced technology. If society isn't able to keep a highly technologically advanced society going in space, everyone will die.
Keeping a technologically advanced society going with a small number of people is essentially impossible.
Earth technology and processes often don't work in space since they rely on gravity. New technological processes will need to be developed just for space, but with only a tiny number of people able to work on them and extremely limited resources.
There are no new resources in LEO. There'll have to be 100% perfect recycling of the resources sent up from earth. But propellant has to be expelled every time they manoeuvre to avoid meteors, so this is impossible.

Stephenson works with these constraints, and comes up with what are IMO wildly optimistic assumptions about how society could function. Whatever. But the obvious solution, is to just go underground, which doesn't suffer from any of these problems:

The ground + atmosphere protects them from all but the largest of meteors.
Digging is well understood technology, and we can do it at scale. There's no reason why we wouldn't be able to create enough space underground for hundreds of millions, or even billions, of people in two years if everyone's lives depended on it.
Since people know they can survive, there are strong incentives to keep working, especially if money will be needed to buy one of the spaces in the underground shelters.
Living underground requires a power source (e.g. nuclear), lighting, ventilation, and AC. All are very well developed, widely understood and deployed technologies. Even if our technology reverts by a hundred years we could keep this stuff going.
Hundreds of millions of people is plenty enough to keep us going at our current technological level.
The vast majority of existing processes and technology should translate directly to usage underground.
It's easy to transfer huge quantities of resources underground, and if we need more we can always just dig it.

Going into LEO does provide 4 major benefits though:

The earth will heat up as a result of all the meteors striking it. Space won't.
It's easy to manoeuvre in space to avoid meteoroids. That's basically impossible for an underground habitat.
A near miss on earth can still send shock-waves and debris far from the impact sight. In space a near miss will have no impact at all.
There's solar energy in abundance, which can also be used to grow food.

So how do we deal with those problems?

Heat

How much will the earth heat up by?

Later in the book it's implied some of the earth's oceans evaporated in the first 3 years (enough to lower sea level by a few meters). After 5000 years, much (but not all) of the water on the planet is gone.^[1] Let's say that implies a steady state temperature about 100 degrees Celsius hotter than current.

In the short term this isn't a problem - it will take tens of years for rocks a hundred metres underground to heat up significantly. But over 5000 years everything will reach equilibrium.

The ideal solution is geoengineering. Sulphur Dioxide injection in the atmosphere is a very doable and effective method to cool the earth. Assuming the linear relationship holds, injecting about 100 million tonnes of SO2 a year should be sufficient to cause a 100 degree drop in temperatures. This is about equivalent to total global sulfur production, so doable. Even if the relationship isn't linear, it should be sufficient to cool temperatures significantly.

The poles are currently about 80 degrees colder than the equator. It's difficult to say how this will be impacted by the moonfall:

On the one hand most of the chunks of moon will hit near the equator because the moon orbits the earth in the same plane as the earth orbits the sun. This means

a) The poles represent a tiny surface area towards the moon, and the equator presents nearly all its surface area to the moon, so all else being equal a chunk of the moon is more likely to hit the equator.

b) I believe (but am not sure) that to hit the poles the rocks will need to be pushed into a new orbit that passes through the poles instead of the equator. This will require a significant amount of energy.

Since the poles will remain mostly safe from moon-debris, this will cause them to heat up significantly less.

Also the reduction in ocean currents caused by falling sea levels will reduce heat exchange between the poles and the equator.

On the other hand, increased water in the atmosphere acts as a greenhouse gas, which will increase heat exchange between the poles and the equator.

Either way, the closer towards the poles we build our underground shelter the better (for other reasons too, as we'll discuss next). The south pole would be ideal, but might be too difficult to prepare in two years (although significantly easier than space - we already have a station there with even a winter population of 50 people). Northern Canada, Greenland, Scandinavia and Siberia might be more practical, but will not be as good locations as the poles.

Any remaining difference in temperature after we've gone as far north as possible and adjusted the atmosphere can be dealt with via AC. Now if we're unlucky and the rocks are 80 degrees C and we need to reduce the air temperature to 25 C that's going to be an enormous energy output,^[2] but since the temperature will rise very slowly underground over many years, there will be time to ramp up power supply - and over the medium term this can be mitigated by digging deep underground to find still cold rocks to use as heat dumps.

Overall though, our biggest hope will have to be in geoengineering.

Meteorites

Under the ground we'd be safe from all but the largest of meteorites. Alas the book implies there's a fair number of them, enough to erode land masses, and even break through the crust at some points to trigger volcanoes.

Once again, the further towards the poles we are the better - both because there'll be fewer meteors, but also because those that are will have to go through more of earths atmosphere, and so are more likely to break up before they hit the earth.

As the moon orbits the earth from west to east^[3] I believe the meteorites will almost exclusively come from a westerly direction. This means it would be sensible to shelter on the eastern slopes of steep mountains. For example, Greenland's Watkins range on its east coast is regularly over 2000 metres - It would be possible to dig horizontally in from the coast and gain significant protection.

When sufficiently underground we'd have to be unlucky to be taken out by a direct hit, and there's not much we can do about them.^[4] But even a hit at some distance will cause powerful shockwaves to travel through the earth. Fortunately tunnels are naturally more earthquake resistant than above earth structures, and can be designed to be more so.

The best approach then would seem to be dig shelters in the eastern side of large polar mountains. At first these shelters would be however big we could manage in two years, but over the next 5000 years they could be expanded. The new digging should slope gently down into the mountain, and be earthquake resistant, so that over time the shelter becomes more secure.

Energy And Food

Over the short term, industrial scale energy isn't needed to stay alive underground. Over the long term it will be needed to grow food, to provide AC, and to maintain a modern technologically advanced society.

So how much are we talking about?

Let's assume that we need approximately however much we already use per-capita plus the AC and food costs. We don't need to provide US quality of life so lets pick a poorer but still modern country as our baseline. The UK will do and is similar to much of Europe at 30,000 KWH per capita per year.

I've seen estimates for energy required to grow a kg of wheat using light bulbs ranges from 30 KWH to 400 KWH. A kg of wheat provides enough energy for 1 person for about a day. So per year we're going to need an extra 10,000 - 150,000 KWH per capita. The difference between those two is massive, and possibly critical to the survival of this endeavour, so definitely an area worth investigating more.

AC costs will be much larger if we can't cool the planet using SO2, and I don't really know how to calculate them. If anyone else can, let me know, thanks.

So what can be used for energy? Nuclear power seems enticing, but might not be a long term solution: the largest known uranium reserve in Greenland (and the second largest in the world) contains enough uranium to provide 100,000 KWH per capita per year for 10,000 years to 1,000,000 people. We want to support hundreds of millions of people.

But a ton of ordinary sea water has about 2 million KWH of energy available as fusion energy from deuterium. For 10,000 years we would need 50 tons of water per person - or an area 2 metres high by 5 metres by 5 metres, about the same as we would need living space per person. Even if the seas dry up, storing enough water underground for energy would thus at most double our space requirements. Even though sea levels will fall over time, they'd do so slowly, meaning if needed we could dig enough space to store the sea water over a hundred years, then pump it all up an extra hundred metres. So if we can survive just long enough to invent practical fusion, we should be OK. Let's aim for a hundred years. Then our uranium mine gives us enough energy for 100,000,000 people! Woohoo!

What about solar power? Probably not a great option if we're in Greenland and blotted out the sun with SO2. Reverse geothermal, where we expose water to the boiling heat from meteorites hitting the atmosphere, then cool them using the glacier might work if we don't manage to control the temperature. It's also possible we could directly use hydroelectric power from the melting glacier. Oil and gas should be fine, but are difficult to transport. There's probably some other novel ideas I haven't thought of, but nuclear seems best.

The Plan

Given all that, what's the plan?

The most important thing is location. We want somewhere polar, in the safety of mountains, yet practical to deliver people and materials to en-masse in the next couple of years. It should have an abundance of different materials we're going to need, since from now on we only have whatever's available locally. In fact we probably want lots of locations. And we need to decide fast. Let's give it a month.

Note that it should still be possible to transport rare materials using expensive methods, so we don't have to pick somewhere right next to a uranium mine. f-35Bs can take off and land vertically without the need for a runway, carry a few tons of weight, survive extremely high temperatures, and have a range of a few hundred kms. They could bring enough equipment to sustain whatever a small mining and enrichment colony near a uranium source can't produce themselves, and transport back enriched uranium to the main population centre. Similarly, nuclear submarines should be a pretty effective form of transport for hundreds of years, at least until the entire sea heats up above the operating temp of the submarine, or the sea level falls so low that there's no practical way to make it from the sea to the population centres without excessive risk.

Once the location of any main population centres is decided, it becomes imperative to move as much digging equipment there as possible. Military engineers can build an airport and dock in a matter of weeks. In parallel we want to dig the deepest, longest tunnel into the side of a mountain as fast as we can. As soon as enough space is made, we start moving the digging equipment factories there too, and begin building a nuclear plant.

The fastest nuclear plant ever built took just over 3 years, and the average is over double that. We don't have that long. We need to sacrifice safety for speed. We'll build a number of nuclear plants a good few KMs distance from the main tunnel, with their own separate living and working quarters. Connection with the main population centre will be via a long small tunnel with lots of blast doors and airlocks. Even if something goes wrong in one of the nuclear plants it should mostly go unnoticed by everyone in the main tunnel, and there's plenty of other plants as backups. So we can afford to remove essentially all safety restrictions that usually hold up nuclear plant construction.

As the tunnel gets larger, we can move more material, population, and factories there, which with good planning will in turn increase the rate at which the tunnel gets expanded. Solar power + small nuclear reactors taken from ships can provide energy till the power plants are ready. As the time ticks down we'll eventually reach a point where we're just dumping as much people, supplies and equipment as we possibly can into the tunnel, without necessarily sorting out living and working areas. That will all come later.

We also need to set up the SO2 releasing facilities. These should be located near a large sulphur deposit, which are usually in volcanic regions. Iceland is close to Greenland, had a large sulphur mining industry till the 19th century, and still has extensive deposits. A mining colony should be established there whose job is to mine sulphur, make balloons, and release them into the stratosphere. They will have to be supplied by air or sea, much like the uranium miners.

An initial system of government, police, and financial institutions should also be established.

At some point the rate of meteorites will shoot up along with the outside temperature. At the point the blast doors of the tunnel close, and the sulphur dioxide injection program begins. Inside the tunnel there's a huge number of people, equipment and supplies, mostly disorganised. There's electricity and enough food for everyone to survive for a year. Some factories are already up and running, but most are still in pieces. The immediate aim will be to expand the tunnel^[5], organise everything, start the economy running, fully transition to the new government, and most importantly start food production at scale using vertical farming.

Once food production is working, we now have a period of say 10 to a 100 years where we can prepare for the long term. What resources are we going to run out of, and how do we ensure that we can get a fresh supply of them? What will we do once difficult to repair equipment (e.g. VTOL aircraft, nuclear submarines) starts breaking down? When one of our mining colonies gets struck by a meteorite, what's our backup plan? What's our alternative source of energy once our uranium runs out? How's progress on fusion reactors coming along? Is our SO2 injection program working? What is the rate at which dangerously large meteorites are hitting this latitude? Can we communicate or trade with other population centres? etc.

Eventually long term solutions will be needed for all of these problems, and the tunnel should end up in a self sustainable situation. Once the rate of meteor fall reduces sufficiently it will need to start working on a terraforming plan to return to the surface.

Conclusion

Will any of this work? Is this really survivable? I don't know, but I am absolutely certain that there's no way this is less workable than trying to build a self sustaining population in space in the space of 2 years, and this obvious plot hole annoyed me enough to write this.

Also, I don't actually know much about any of the topics touched upon here, and am basically speculating based on my poorly done research. I'm sorry! If you have ways to make any parts of this more concrete, please let me know in the comments. Thanks!

^{^}
Where to? Presumably the atmosphere expanded as a result of the increased heat and water vapour, and was stripped away by the weaker gravity at the higher orbits. The water vapour couldn't have all stayed in the atmosphere, or the pressure at sea level would be more than 200 times what it is now - which in turn would have prevented most of the water evaporating.
^{^}
Energy required to cool via AC is roughly linear in temperature of the heat sink, but gets less efficient as the difference in temperature increases. At 80C current systems would be capable of cooling to 25, but very inefficiently.
^{^}
The earth rotates much faster than the moon orbits the earth, which is why the moon appears to travel from east to west. But as the orbit of some moonfall collapses its period should decrease, which I expect should easily become faster than the earths rotation.
^{^}
Maybe it would be possible to use nuclear bombs combined with existing ballistic missile defence technologies to break up large incoming meteors? If a meteor splits into several pieces their trajectories will change, which might turn a certain hit into a near miss.
^{^}
A mechanism will need to be included to allow safely and efficiently dumping waste material out of the tunnel.