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A moon-sized asteroid approaches Earth in the near future, where space tourism has become normal. The Earth has a few satellite structures above Mars conducting research, as well as successful terraformed farmland on the surface. Going into a suborbital space to experience zero gravity for a few minutes costs about as much as a plane trip across country today. In this scenario we have developed the technology to support megastructures in space, and need for farm land has pushed artificial farming to where we only need 1/4 the amount of land to grow the same amount of food.

The world comes together and decides that they should make an attempt to save at least one million people by migrating them into an orbital space station. The space station should be able to travel from orbit to Mars where it could link up with the Martian Base, in a worse case scenario where the asteroid causes variance to the gravity of the planet.

Accounting for fuel, engines, rockets, farmland, water, living spaces, hospitals, waste management, etc. how large would this space station have to be? I am looking for an estimate, I realize an actual square footage is next to impossible.

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  • $\begingroup$ Are we restricted to today's technology, or can assume it will be more advanced? $\endgroup$ – Alexander Aug 30 at 22:48
  • $\begingroup$ You can assume more advanced $\endgroup$ – Alex Sep 4 at 19:45
  • $\begingroup$ Building farmland in space sounds like incredible luxury. Isn't it easier to use advanced biotechnology to grow most food in microgravity (no bulk support structure needed) and without soil (less material necessary)? Especially in these exceptional cimrcumstances, so if you want it it's good to justify it in-story somehow (or ask a question here). $\endgroup$ – Juraj Sep 4 at 20:32
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    $\begingroup$ I don't think you can accomodate people forever in a space station. Even a planet cannot provide "forever", and your space station is bound to be much more fragile. So i think you may want to limit "indefinitely" to something more reasonable $\endgroup$ – Burki Sep 5 at 14:32
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    $\begingroup$ You say "indefinitely" but you also talk about your station hooking up with the Martian base. How long do you need those million people to actually be on the station? $\endgroup$ – Monica Cellio Sep 6 at 3:31
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For the sake of convenience let’s start with the assumption that your population will desire a North American urban population density and a globally averaged diet.

The city of Austin TX has approximately 1,000,000 residents and a surface area of approx. 800 km^2, for a density of about 1,250/km^2. The City of New York (5 boroughs) NY also has a surface area of approx. 800 km^2 but a population of approx. 8.5 million, for density of about 10,500/km^2. However the density of the Manhattan borough is close to 28,000/km^2. That is the highest density population center in North America with a population of at least 1 million and possibly near the limit of Western cultural tolerance (or we could reasonably expect it would be even higher by now). For our purposes let's say a few more people can be squeezed in to conveniently round the figure to 30,000/km^2.

So the station would need at least 1,000,000/30,000 km^2 of surface area (assuming living structures are approx. as multidimensional and compacted as Manhattan), or 33.3 km^2. Since much of the surface of Manhattan is pavement for cars, and we'll assume that citizens of space will have learned to do without that kind of freedom, let's then shave 10% off of the requirement for a nice rounded living space of: 30 km^2.

For food production usage, let's take the conservative approach of using globally averaged statistics since they're easy to find. According to one source (https://ourworldindata.org/yields-and-land-use-in-agriculture) approx. 50% of habitable land on earth, or 104M km^2, is used for agriculture. Of that 77% is used for livestock and 23% for crops. Let's now take the somewhat controversial liberty of assuming that 0% of your station's residents will derive calories/protein from livestock simply because farming livestock is so incredibly inefficient and, generally, sufficient non-livestock alternatives exist. 23% (crops only) of earth's agriculture equates to 11M km^2.

Now let's assume that the earth's population is a rounded 8,000,000,000 (in the near future). Let's also assume (quite ridiculously - this is a fictional model) that all of earth's population has equal access to earth's total yield of crops and there is 0% wastage. That means it takes 11M km^2 of crop surface area to feed 8,000,000,000 people, or approx. 725 people per km^2.

So a population of 1,000,000 would need close to 1,400 km^2 of crop surface area, using modern terrestrial practices of course.

As you can see the ratio of this area to living space of 30 km^2 makes the latter insignificant.

However I believe it's reasonable to assume that necessity would be the mother of invention when it comes to occupying space and crop yields / km^2 could be greatly increased over terrestrial norms. Let's be incredibly inventive and say efficiency could be increased by a full order of magnitude. Then you're down to 140 km^2. Much more plausible.

So at this point we have:

140 km^2 for crop production and 30 km^2 for living space, for a total of 170 km^2.

That means if your station's structure was a cylinder 2 km wide it would have a height of 26 km. To put this in perspective Manhattan is about 22 km long.

Now consider this. What if the station wasn't divided into urban/rural areas like on earth but was instead all rural with the residents living "off the land". In that scenario the station could be significantly smaller and perhaps even a more pleasant habitat.

[Corrected cylinder calculation.]

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  • $\begingroup$ for your human population, you assume that they can be stacked, but you don't do the same for your crops. I think that kind of invalidates your result. That said, i still think you did good work for your answer. $\endgroup$ – Burki Sep 5 at 14:21
  • $\begingroup$ Did you consider available office space when calculating the population density of Manhattan? Unless I messed up the square feet to km² conversion (which is not unlikely at all), Manhattan has something like 41 km² of office space (450 million square feet). You could convert this office space to living quarters, thus probably boosting the population density quite a bit beyond your assumed maximum of ~30,000/km². $\endgroup$ – Schmuddi Sep 9 at 15:18
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There are two general requirements - power and space.

Power

1,000,000 humans need about 2,000 calories per day each plus energy for day-to-day functions. Total up the calories and convert it to something workable, and we have a total of 96.85 MW. That is a lot, but that pales in comparison to energy. The average US household uses 900 kWH per month, giving us a princely total of 480.8 MW. Add them up and we need 577 MW.

Now you said 'indefinitely' so instead of using something like a nuclear powered core, I've elected to use solar panels, because the Sun lasts longer than the core. Judging from the answers here at 40% efficiency you'll only needs about 1,068,518 square meters of solar panels. Incidentally, a small nuclear power reactor can achieve the same output. So, uh, your choice, more or less.

Space

Now for space. Food storage and preparation wouldn't use traditional Earth means of growing food - that's time consuming and takes up too much space, even with your method of cutting it down by a quarter. Instead, the garbage would be sorted and all organic waste would be broken down by bacteria strains and then cultured or synthesized into nutrients. Disgusting - yes. Efficient - also yes.

It sounds like this is going to be boosted into place, so I'm assuming that the main boosters are more of less external, and the only boosters within the design are for corrections.

Since I'm just approximation everything, I'm not going to go through careful lists. Instead, I'll just instead assume that everyone would get a 5 by 10 by 5 box for living space, personal effects, and utilities. That seems to be to be the bare minimum required. May be a tight fit on taller people, but they can just ask for their box to be upright.

In addition, every 100 people could probably use the space to organize together in some assembly room, as well as having it function for several recreation purposes so add another 20 x 20 x 5 area. For larger assemblies, just have people assemble in their personal ones and use wall screens to link them together.

That's a total of 270 million cubic feet. There will be more things required because you always need more space/time/money etc., so I'm just going to round that number up to 300 million cubic feet. In terms of design, I'd argue for as large of a superstructure as possible, so things can be safely ejected in case of an emergency or contamination. In fact, I'd actually recommend that you don't even make this one giant station, instead make this a fleet of colony style ships with a few thousand on each one. That will, of course, require a bit more space, but I stand by my estimates - 300,000,000 cubic feet, and 1,000,000 square meters.

(Sorry for using both square meters and cubic feet. You can use 8.5 million cubic meters instead.)

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  • $\begingroup$ 1 Calorie = 1000 calories. $\endgroup$ – Jasper Sep 10 at 1:13
  • $\begingroup$ @Jasper The calculations were done using kcals, I just wrote calorie with a lower case because that's the more common vernacular and if I'm doing Fermi estimations, I'm not meticulous about correct SI usage. I mean, half the calculations are in metric and the other half are in American. $\endgroup$ – Halfthawed Sep 10 at 1:47

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