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In the future, personal Cryonics (in the hope of cure or immortality on re-awakening)) have become enormously popular. However there is a storage problem. There just isn't enough space for all the bodies. Also the equipment that keeps them cool itself generates heat and requires enormous amounts of electricity.

We really need unlimited storage in a constant low-temperature. It would seem that space is the ideal environment.

The question is, with early 21st century-type technology, where can we safely and economically store the customers?

(a) In orbit around Earth

(b) In orbit around the Moon

(c) On the Moon

(d) In orbit around another planet

(e) In Sun orbit

(f) Somewhere else

It is enormously expensive to ship them to the outer reaches of the solar system and bringing them back is worse. Placing them on the Moon has the obvious problem of alternate heating and cooling.

Where in space should the customers be stored?

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    $\begingroup$ With 21st century technology is enormously expensive sending mass into space. And protecting a corpse in space from radiation, vacuum and extreme heat is going to take a lot of mass. Sending corpses into space is a bad idea. $\endgroup$ – L.Dutch Dec 27 '18 at 13:05
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    $\begingroup$ We are in the early 21st century and there are companies that offer that service, storing in special cemeteries. You should see how they solve their problems and what they charge. $\endgroup$ – Renan Dec 27 '18 at 14:05
  • $\begingroup$ Actually the vaccum isn't cold, but the best isolator you can have. Only leaving particles 'cool' a spaceship. There is a german wiki entry about this (unfortunatly not in english, maybe you can translate it with google translator). If you have something that produces heat in the spaceship, much heat, you need good cooling systems $\endgroup$ – user55267 Dec 27 '18 at 14:18
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    $\begingroup$ "Space is cold" is a very common misconception. It's a vacuum which, by definition, has nothing in it to have a temperature. The only way to reject heat is via infrared radiation, which is very, very slow - hence why the ISS is painted white (to avoid too much heating from sunlight) and has a very large set of radiators to reject waste heat. $\endgroup$ – UIDAlexD Dec 27 '18 at 14:26
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    $\begingroup$ Why was this closed as too broad? It's not like you need to write an entire book to rationalize why one spot would be better than all others. It's not even POB since the reality-check tag requires people to back up their answers with a justification. The early 21st century tech (aka, right now) is a bit of a problem, so my vote is "(f) Somewhere in the antarctic," but otherwise I'm having trouble understanding why this was closed. VTR. $\endgroup$ – JBH Dec 27 '18 at 22:43
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TLDR: space is expensive, and not as cold as you want it to be. Without major technomagical change, it's going to be far cheaper just to store them on Earth.

Let's suppose you want to store 10 billion people-popsicles, a bit more than the current population of Earth.

A human body has volume of approximately 1 cubic metre, but since humans don't tesselate neatly, let's allow about 2 m^3 and 100 kg per person, including a frugal allowance for the structures that will contain them. So you need to store a total of 20,000,000,000 (2e10) cubic metres of peepsicles with a total weight of 2e12 kg.

Current cryo technology generally uses liquid nitrogen, which requires maintaining a temperature of around −196°C.

Currently, SpaceX are quoting \$90m for a Falcon Heavy launch, with a payload of 64 tons to low Earth orbit. That works out at about \$1500 per kilogram to LEO (more if you want to get anywhere else in the solar system), or about \$3000 trillion (\$3e15) for ten billion people. This is about forty times the GDP of the entire world. Put another way, it's about \$150k per person.

That's at current prices. Technological improvements and economies of scale might achieve some savings, but a large chunk of the cost is kerosene-based fuel, which is a limited resource and likely to become more expensive with increasing use.

Unfortunately, even when you get to LEO, space isn't actually that cold... on average. While most of the "sky" is at a nice frosty three Kelvin, there's a great big fusion reactor in one corner of the sky radiating heat at six thousand degrees. If it can keep Earth warm, it can keep a nearby satellite warm too - it won't be quite as warm, because of the lack of a greenhouse-effect-inducing atmosphere and tidal/radiothermal heating, but the black-body temperature for an object in LEO is a few degrees above freezing.

This means that if you want to keep your peepsicles at liquid-nitrogen temperatures in anywhere near LEO, you're going to need a lot of refrigeration... which is really hard to achieve in space. You can't conduct or convect heat away, so your only option is to radiate it. Black-body radiation varies with the fourth power of temperature, so an object at −196°C (77 Kelvin) will radiate about 1/160th as much as the same object at room temperature.

You can improve things a bit by keeping a reflective shield between your space station and the Sun, but even a small amount of heating through the shield is going to be very difficult to counteract. To stay at cryo temperatures purely by passive means, you're going to need to go a long way out, and as you've noted, that steeply increases costs.

Next consideration: how are you getting those people back from wherever you choose to keep them? If you want to retrieve them from anywhere other than LEO, then you need to expend a lot more energy (rocket fuel/etc.) to recover them... and unless you have a convenient fuel supply located near your storage facility, you need to spend even more energy to get the fuel out there.

Retrieval from LEO is a bit easier, because you can take advantage of the Earth's atmosphere for braking. However, that tends to be a rough ride, and cryo-frozen humans are fragile things (a friend of mine who used to work in the industry used the term "meatglass"), so you're going to want some good shock absorbers... which ups the weight.

Unless your setting includes some developments that drastically reduce launch costs, it's hard to see how this would be cheaper than storing people on Earth. If you're willing to stack people ten high, you can fit them all in a footprint approximately 30 x 30 km; that's probably less than you'd need for the launch pads and kerosene refineries required to launch them into space.

Sorry to be a downer here!

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on Earth

There is plenty of space on Earth. If each capsule takes 2 m^3 then storing 5e9 capsules will take 1e10 m^3. If you stack them in ten layers that's only 1000 km^2 of area. The Antarctic has an area of 14e6 km^2. Your cryo plant will not even take 1% of the area. Plenty of free cooling. Constant solar for half a year, small nuclear plant will be enough for another half. I wouldn't be surprised to find a deep geothermal power plant there by the time you start building your cryo.

in Space

Not really. As others explained space is really poor coolant. There is a reason why thermal flasks have a layer of "space" between two walls, also called vacuum flasks. If you really want to get them out of Earth you could potentially use Moon, with the caveat it is not going to be nearly as effective as on Earth. Depending on your technology level you would probably want to move to some solid body with cool atmosphere, like Mars (210K, -63C, 0.006 atm) or maybe even Titan (94 K, -180 C, 1.45 atm).

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Assuming a bit of a handwave (we won't discuss the cost of sending objects into space), the best place would actually be on the Moon.

Placing the storage units beneath the surface of the Moon provides protection from radiation, micrometers and other potential dangers for objects in free space or even on the lunar surface. In addition, the mass of rock surrounding the storage units will act as a massive heat sink, moderating the temperature swings on the surface and protecting against the direct rays of the sun. During the lunar night, heat pipes can be raised to the surface to bring down the temperature in the cavern, if needed. The cavern itself will be i vacuum, in order to provide the insulation needed to keep the storage units at liquid nitrogen temperatures.

While this will be very expensive in terms of 21rst century technology (the cost to bring construction equipment, the storage units and the people to the moon will be extremely high), and of course we don't actually know how to revive frozen people.

So this is going to be something of a niche market, and only viable for the extremely wealthy. The only way to bring the costs down to any sort of reasonable level would be that this is a sideline to some large scale lunar industrial development (for example 3He mining), so digging tunnels and storage chambers is just something they can do as a sideline to the main business on the Moon.

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