Mmm, quite pleased with answers which are placed already, seems WB does better those days, nice to see. Here my own 2 cents on your problems(and solutions).
As for the reasons, it not necessary to introduce some unobtanium at this point in time. Unobtanium is more suitable for small scale like it is now, there are examples of producing fiber optic in 0g, and thanks to the absence of weight it turns to be of better quality for some reasons.
Proposes by SpaceX network of satellites can be a significant driver for expansion, and servicing them in orbit can be a start for having production capabilities in orbit, which can serve as a seed for further expansion and scaling up. Having them being serviced in orbit solves few challenges - one is a more relaxed choice of materials used in those satellites, as a strategy of their disposal is not anymore a burning of them in the atmosphere but refurbishment or scraping for materials for the production of something useful in orbit(for that production facility or for energy collection or else). So it's a natural extension to reuse materials which you already send in orbit. And it basically half'ing the price - whatever it is cheap or expensive.
Cleaning orbit maybe another activity which primes the bigger things, as there about 8000t(around that number, may remember it wrong) debris in orbits, it is scattered but, there are proposals of different mini space crafts which goal is to service present satellites in orbit in terms of repair, and moving them in a graveyard - thus extending their operational lifespan. You can scavenge for some bits on Robots In Space LLC site/blog the guy has some good ideas, but there are more out there.
ESA announced few years ago about air-breathing electric thruster which can be nicely combined with ideas of servicing satellites.
Both thruster and servicing incentives can be combined with in orbit refurbishing of those electric engines and their energy-producing setups, by some production station, and then it may not matter that much how scattered debris is - one can collect it all(but timewise(reasonable time), more like a good portion of it).
so that servicing fleet can be expanded using the debris, if it half of it then 10 times of that ISS station we have, by mass. And it quite a significant portion of the material to work with and it may be capable of different kinds of things.
Here is quite an extensive article on in orbit air scooping. And that air can be used to refuel some stations(current or future ones) so it may be useful as for now(making some profits here) so as for your stations and their air loss.
the same air can be used as reactive mass for those ion engines as a reactive mass in transits between Moon and Earth. This may be a significant expense slashing solution for all programs connected with the moon, which you mention in some of your comments.
I'm not the fan of unimaginable expenses positions, so as the unifying goal, it more likely some enterprise or smart gov(if there is some - china is that you?)
Combining technologies and business as which are mentioned earlier and more, it possible to create some specific in orbit solution that may prime further expansion, in form of some production platform of 10x ISS, which we may operate remotely, so no humans there, and which may be an integral part of solving current demands and which on its own providing additional options and possibilities.
If we take that Starlink proposal from SpaceX, I'm a firm believer it will be a cash cow with a good yield, as it is way too convenient for many applications to have a good connection in all the places. So it will pay itself off easily. Even smaller satellite servicing startups if they would hold a bigger picture and path in their view they have a chance to prime that 4000-8000t production station in orbit. And make that cheap connection between earth and the moon.
So do not fix on great capital investment at the start, it more about will, vision and some money not trillions one trows in the project. Thanks to the sci-fi will and opportunity and negotiations are those you can easily handwave by the power of your letters, which in reality is slower and more painful to achieve. One has money there are easier places to invest, one has ideas but didn't the homework in being wall street wolf.
There are really more tricky and crazier options, to prime stuff with small scale rockets like the scale of Electron (rocket), and there are even more out of ordinary proposals(still rocket-based, with some tech and support of that production orbital base that Electron rocket could deliver up to 10x what it can do now).
Looking at the Moon, you do it right.
Besides supporting our current space activity by cleaning orbit, by extending the lifespan of satellites with the same launch expenses, by providing air supply, by recycling space trash flying and produced by stations, by producing something which may be done better in 0g(it not only optics, chemistry, crystals, electronics etc) - participating in all or some of those can provide some pocket money, but the real deal is sure the moon as a source of materials - not necessarily some specific materials but any materials which can be used in construction for space structures.
By coincidence and magic of 0g, any material you scoop from the surface of the Moon can be used in construction, as one of the main things, there is no weight so it has just to not fly apart. So glass fiber(or more likely basalt) fiber, so as sintered "bricks" can be used pretty much as is to build habitable volumes aka space stations for humans.
Even with current or projected prices from SpaceX, the price of any dirt you may deliver from moon to earth orbit is quite high, if you may sinter it to some usable construction. Sintering process for producing and using for moon bases is an actual topic that is researched by different people, and it is possible and maybe even easier in 0g as it does not need to be that high grade, to begin with. More you can do on that in orbit seed production platform more you can produce from it, including extraction metals and our usual tech for use of those.
So that link Earth-Moon-Earth is essential for making more profits and do more.
Even with your mentioned 20 bucks per kilo, it means 20 thousand per tonne, and with relatively simple means you can massdrive from the surface of the moon millions of tons. 2019 article this
- For a SpaceX Falcon 9, the rocket used to access the ISS, the cost is just $2,720 per kilogram.
So the main trick is what you do on the moon, how you do it, I guess you have your own ideas about that, but there are also ways in line with that production seed station. But being delivered on proper orbit, any dirt costs around 2 million per tonne(as of now) if you can shape use it in some useful way, and it(shaping in a useful way) can be done with moon dirt.
Economical reasons, real money
Having a link between Moon and Earth this creates the opportunity for having real money flow, if you need it, as at that point you need more technologies and improving technologies to achieve your stations or orbital rings whatever. But okay, for the shake of those technologies be developed by people you hire, one needs money, where to get them.
There are several ways and Energy from space maybe another cash cow. There are plenty(several) of project proposals of that kind, and some are studied in depts by NASA-related folks. The main problem of those as it seen from all those studies, and as it is seen now is the cost of launching stuff in space from the Earth. And that part is covered if you have Earth-Moon link.
Energy is essential for all parts of our technological life, so as the energy from space is all green(almost) and cool, it does no run out ever, no fuel of any kind is required it already there and will be for next few billion years, and you merely redirect it.
Data processing is another very essential and somewhat money earing direction that has broad application/use/list of consumers. Training AI's for different fields may be expensive as I have read from OpenAI guys which made their bots for Dota competition year a few years ago and for AlphaGo, they would like to run mass training more often but it costs them 10's of thousand for a single deep run session. And that problem of teaching AI's networks as for now it does not require top-notch processors it requires many many of some good enough processors, so it a venue which can be explored - by producing them in space and having data centers in space, in similar ways as that Starlink project. And some huge huge setups which dwarf the whole Top500 list, in some of Lagrange points. There is a proposal of cheap grid computing using solar energy for free, no sms - the direction of thinking is actually quite good.
At that point, some planet-scale moves may be possible - cooling the planet starting from dusting atmosphere(like vulcanos do) to make manageable sunshades which more fine-tuning who and how much energy gets on the surface of the planet. And it has a direct connection to another essential - food production, weather, temperature, CO2 consumption speed, AC usage in cities, the habitability of some countries in general which may be(or may not) a problem in the future because of the peak temperatures(they are on the threshold already).
So there are broad and deep money wells to tap into if one can deliver stuff from the Moon.
Thanks to all that, actual living in space on a great scale may be made possible so as the price of delivering stuff from the planet into space maybe not that much relevant, as that energy from space may work on the rocket making business supply enough energy for them to produce one rocket per hour in the middle of pacific as an example.
Making Research and Development cheap. For our technological society, it is a core being able to develop new stuff and fix problems etc. This necessity permeates the whole society - all the needs are connected to some RD done. And space resources can make it cheap, pay 10 times less, get 10 times the result. So some remote labs rented, sold whatever - and customers are whoever develops technologies, basically everyone. Sure it hard to provide everything for all at once, but it is a big market to be consumed by a combination of different means.
Quite skeptical on Bezos statements of moving production from the earth, he is far behind the current wagon with this one, we do not need that, we just need more energy to recycle the waste, but moving RD processes in space - that a totally different deal, making something from Top500 as your desktop PC for your lab or fiddling with the artificial intelligence of game server, a similar transition which happened in 70's - that's a deal which is not possible(almost, fusion) on earth, but which can be done just by scaling in space.
Back to station
as for the size of the station, I may suggest looking this answer of mine, even if cylinder design has its problems, stresses induced are calculated in an okayish way, so km's sizes are achievable. In general look at Kalpana one design, it quite reasonable, and good enough for starters.
In general, the diameter isn't that limited by materials used, if you imagine it like some sort of bearing which one part is rotating and another is not and that no rotating part of the construction takes all required loads. And you can make that external part as big as it needs to be. Sure there are still some limitations and challenges, but they far beyond a few km's sizes.
One can easily place a hundreds of them even on the same orbit, km's apart like a cluster of those or 100's km apart. Yes sure you need some monitoring orbit correction system for those, but not a big deal as of today, and if you have air scoop then you do not have any shortage of reaction mass for corrections.
where it's a pain to pour water into a glass. - guess it is a joke all isn't that bad.
Power is solved with solar farms - yeah, a way to go, and you do not need SMES for energy storing, in rotating of the station itself or similar structures plenty of energy can be stored.
Cooling - as mentioned in one of the answers it has better options, in general it is not a much bigger problem than cooling a station itself. It isn't a big problem if you do not do huge huge things in one solid piece by casting - but there no heatsink can help you to solve that, and it needs just different ways of making stuff.
Atmosphere ... resupplies - not such a big problem with scooping, and in general, it should hold and easily can do much more than 3 months without resupply. IDK I guess your plot may require that, so just noting that. Volume grows proportional to a cube and surface proportional to square and that creates a big reservoir of those gases, for any big enough station.
Food is partially supplied from the surface - you need only branded stuff, the rest can be produced locally relatively easy and it is a way to close cycles by air water and stuff.
we built a really cool Orbital Ring - yeah, why not, mine Moon well, and you will have it.
Inter-station trade and travel is done through shuttles - idk, maybe focus more cyberpunk style, more on immaterial digital goods - technologies of production. Still, there is a place for cool drivers transporting expensive cool handmade one of its kind stuff, it more elite and cool than transporting toilet paper between stations in space trailers.
Here it needs to focus more on the aspect. Production on stations can be fully self-sufficient. Reason being - cheap and abundant energy supply. It way cheaper to get energy in space than here on earth, there are many reasons for that, but consider one of them - a thin foil shaped in a spherical way is all you need in space to heat something to stunning 5000-6000K temperatures, so your steam or CO2 or Na-steam turbines will work like a charm. (in orbit, especially at LEO, it may be bit trickier but not by much). So it simple as technology, as the production of those etc etc, and it weighs less as there is 0g so fewer materials required in places which are wasted on supporting structures, protecting them from the atmosphere, rain, wind etc.
So big factories which we build here on earth are for efficiency - energy efficiency of processes and other benefits of scale. But if you have cheap energy, if one is 10 times more wasteful in terms of using the energy it does not matter as you may have as much as you need. Sure there are more reasonable and less reasonable ways to do things.
You aren't constricted by flat area, so a by territory limitations in general. So, in general, you may have all the technologies we have today on some smaller scale, as big as you need it to be and to not worry about being a few times less efficient in production as those surface bigger counterparts are. So your cost more in RD, and here you can tap for the earth and send the plans via email and such. I mean if there is some stuff you need and if it can be produced in a lab(and basically all stuff we do is produced in a lab for the first time) if it does few times 10 times less efficient than big factory you still can stick to lab way of doing stuff. And scale the process according to your demands.
- To avoid collisions, orbital lanes are taken by "first come first served" - no need for that really. You can easily have a million crafts swarming near the station waiting for their time or just hanging there. So as orbits are big, a single plane LEO orbit is about 40000 km, so there plenty of space considering every 100 meters is basically a new orbit. Some unified system which guides the crafts sure is needed, so as the preferred direction of the orbit may be useful, because 2 space crafts separated by 100m orbits, they move very slowly relative to each other if they move in the same direction.
So limits are high, you basically can launch a million of spacecraft from your ring, each minute and still easily manage them in orbit +72km.
- Health effects of 0G are mostly hand waived by Centripetal habitats - no problem here, as for me.