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The crafts would have to contain large farms in order to sustain the immense amount of people, and they'd obviously have to be large and spacious to have good living conditions. I did some research, and ships like the Death Star from Star Wars (Which can hold a billion people at the maximum) are unrealistic in terms of how much building materials would be required to make it. Would the collection of metals from asteroids be required to construct these crafts on Earth? What type metal or alloy would be ideal for constructing the outer parts of the crafts exposed to the vacuum of space? Nanotech is present in my setting, so what applications could it have for the construction of the ships?

Their purpose is to evacuate the population off of the planet in-case some worldwide unavoidable disaster occurs. Since this takes place in the late 2100's, the population would be somewhere around 10 billion. If one ship can carry a total of 10 million people without being overcrowded, there would have to be around 1000 of these ships in order to transport Earth's population through the depths of space.

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    $\begingroup$ What technology do they have in the late 2100s? $\endgroup$ – Galactic Apr 26 at 2:18
  • $\begingroup$ @galactic_analyzer Nanotechnology is commonplace, cloning is a morally questionable activity limited to the rich, and synthetic humans do most of the difficult work for the biological humans. $\endgroup$ – Niobium_Sage Apr 26 at 2:33
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The Pixar movie, Wall-E offers a few helpful suggestions...

  • Store your humans prone in couches with entertainment built in and use robots to distribute food and maintain the ship.

  • Keep your humans fat so that they serve as calorie storage devices.

  • Don't let them exercise or even get out of their couches as that wastes calories.
  • Skip the farms! Recycle the human waste, re-energizing it from ships power into a sweet beverage which tastes like a milk shake. (Figuring out how to synthesis sugar from biologic waste products is probably easier to than building a large scale farm in space.)

Alternatively, you could follow the Matrix franchise design, using an immersion pod for your human storage and immersive full sensory VR for the entertainment system.

The idea is to get the per-human storage requirements down to an absolute minimum so that a million times those requirements don't overwhelm your ship's design potential.

In any case, the ship only has to maintain this high a population for the first generation. By taking strict control of the human passengers and locking them in gilded cages, you can keep them entertained, distracted and/or drugged for most of their lives. Allowing only a fraction of them to breed (while suppressing the urges of the rest with hormone treatments) you could quickly transition to a smaller yet genetically representative population with proportionally smaller resource needs. All while keeping the original generation happy for all of their years.

This second generation could be given greater liberties, like actually getting out of their couches. As the original population dies off naturally, the space formerly occupied by their couches can be repurposed into living quarters, parks and open spaces. This is where your nanite construction technology can really shine, making the ship's minimized space serve its newly minimized population.

As the third generation is born and the last of the first generation are recycled into communal resources, the ship can get on with its long term objective, of maintaining human culture and education levels during the long dark journey.

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Since we want to have a lot of surface area built quickly, we need to find a way to minimize the amount of time and resources to build spaceships and associated systems. To minimize energy costs most of the mining, processing and construction will take place in space. This can be done on the Moon, or using the resources of Near Earth Objects (NEOs), although for speed it may be necessary to use multiple sources of materials.

For the main bodies of the spacecraft, the formula will be simple. Two spheres of metal, with the inner one being five metres in diameter smaller than the outer one. The interspace is filled with water mined from the Moon or NEOs, which provide radiation protection, thermal buffering and basic reserves for life support. The spheres can be even as thin as heavy foil reinforces with a close knit netting to reinforce it, but this assumes the interior will always be in microgravity. A sphere provides maximum volume with minimum surface area, and thus minimal material budget.

Using mirrors to bring sunlight into the interior, and tapping into the vast reservoirs of water provides the means to grow algae. This provides a means to consume and recycle wastes, provide the basis for engineered foods and to consume the CO2 in the atmosphere and provide fresh oxygen. The algae bioreactors can be as simple as clear plastic tubes exposed to the light, although the entire suystem is obviously much more sophisticated in handling inputs and outputs.

Even propulsion can be relatively simple, using photonic laser thrusters, which essentially uses powerful lasers on the Moon or other bodies to beam at a mirror on the spacecraft, then reflecting the beam back to the base station to re reflect to the mirror - essentially a highly evolved form of solar sail.

Much of this requires building some basic infrastructure on the moon and then leveraging it. Rather than building a single huge spaceship, it would provide more security and redundancy to build multiple smaller craft. This also provides more flexibility in that you can disperse the population around multiple different moons and planets around the Solar System.

Without specifying things like the population, desired population density and so on there is no way to really quantify how much material you will need, but a series of minimalistic spacecraft built along these lines can be built quickly and cheaply, allowing you to move large numbers of people around the Solar System in an economical manner.

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