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Imagine: A Kardashev Type I civilization mainly resides on a planet analogous to Earth, with one moon, analogous to Earth's moon. Eventually, the society grows so complex that machines filling space becomes a serious problem: the world's growing population needs food more than it needs machinery, but it still wants to balance both with the space it has.

Their solution: Building a Death Star like object, roughly the size of their existing moon, in orbit. Its function will be doing all computations required for the civilization, and then some; it will handle all storage of data, and other things that the planet can access wirelessly, to preserve space for farmland and residential areas at home.

Let's ignore unless necessary:

  • How such an object will be constructed. Let's just assume at this point in the civilization's life, building this is plausible.
  • Where the resources to build it will come from. Assume that all necessary materials can be procured and transported from the inner asteroid belt with relative ease. Somehow.
  • Why it needs to be so large. Assume this civilization plans to rely on this object for centuries or millennium to come, so they are building it with far more processing power than they currently need.

But let's not ignore the following:

In this scenario how would such an object realistically receive power?

Note that this method should be on or inside the satellite, that it should power the entire volume of the sphere, and that if it produces heat, there should be a way to reduce its effect on the machinery.

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    $\begingroup$ “why would a civ contrive to build such a ting” is not a good question for this site. For future reference see the sandbox on the Worldbuilding Meta site. $\endgroup$ – JDługosz Oct 17 '16 at 4:45
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    $\begingroup$ You've got several questions here, some of which may not be directly answerable. Such as how it would be constructed. We don't know. An object large enough to have its own surface gravity is not something we have the engineering solution for: all known construction materials behave as liquids on those scales (tldr: that's why Earth is roundish). $\endgroup$ – Draco18s Oct 17 '16 at 5:09
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    $\begingroup$ @Draco18s Thank you for the feedback, but that is not what I asked. That is under "things I am not concerned about", and the actual question is much different. $\endgroup$ – Zxyrra Oct 17 '16 at 5:42
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    $\begingroup$ So, FTL communication is possible or no computation ever needs to be done in (near) real time? $\endgroup$ – Alexander Kosubek Oct 17 '16 at 9:30
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    $\begingroup$ Does your civilization possess FTL communications technology? Earth's Moon is roughly 1.2 light-seconds from the Earth. That's some pretty significant latency. I certainly wouldn't want to have to wait 2*1.2 seconds to get the results for all computational operations on my computer. $\endgroup$ – Ajedi32 Oct 17 '16 at 15:15
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I like your original formulation more, as it shows some of your thoughts about such construction.

a) Prevent Collisions

  1. You can build this structure on the moon itself.

  2. If you build it in lower or higher orbit it will take ages for a collision, to happen if any. There is a lot of space between planet and moon where such construction will be perfectly fine.

  3. Build it in the same orbit as the moon, but on opposite side of the Earth. It will need some positional corrections, but as far as materials go, it should be not a problem. (Do it same way as you would haul materials to the moon-station.)

b) Power

Solar power is not a bad choice actually, since you are primarily concerned about interior temperature. Solar power will provide the same order of magnitude of power as the waste heat you can radiate away from your station.

Solar is reliable; it will work for long time, will not blow up your station, and is a constant steady flow of energy.

You are wrong saying that the station - will be at an angle too acute or too obtuse to use effectively with stationary solar panels. The station should rotate with angular velocity 2$\pi$ rad per year so it faces the Sun with one side (there will be small perturbations, parallax, not perfectly circular earth orbit, and construction should avoid earth's shadow by choosing orbit->orbital period).
For most orbits(for orbits with inclination more then few grad) there will be 2 times per year when shadow of earth covers small section of that orbit, and station should not be there for that time. So we just should avoid Sun eclipses, but that is actually rare situation and no very long lasting one as we may see on moon examples, and it is possible to avoid it, in case when we choose orbit and phase angle of our station on that orbit and have some means to correct orbit a little.

If you have thermonuclear power - great, but to exceed amount of power you get from solar you need to have big radiator, almost the same size as you would need solar collectors for same power production. Thermonuclear may be more efficient allowing radiators to work at higher temperatures (because hot end of thermonuclear reactor is millions of Kelvin).

  • hot end temperature of thermonuclear reactor is millions of Kelvin, temperature of plasma where reaction is happening, so if cold end will be 10000K, so potentially efficiency may be 99.99%, and 10000K of radiator (plasma ball contained by magnetic field) will radiate away 10000 more energy then 1000K radiator. Efficiency of TR will not be 99.99%, mostly because we are not capable to convert all sorts of energy released in the process - neutrons, gamma, muon's, at that temperature(million's of kelvin), as we can do it with plasma. And energy released in the ways which we can't efficiently to utilize may be significant portion of total energy, it differs for different reactions but it counts by 10's of percent of it.

c) Temperature and Power

  • Generator: The temperatures of the hot and cold reservoirs of your power generation system define Carnot efficiency: $\small\text{Efficiency}=\frac{T_{hot}-T_{cold}}{T_{hot}}$

  • Radiator: The heat radiator works using black body radiation. Power emission from a black body follows the Stefan-Boltzmann law, $Q=\sigma T^4$, where $σ = 5.67×10^{−8} W m^{−2} K^{−4}$, where $T$ is radiator temperature.

  • Assume desired internal temperature of 300K

For solar power generation $T_{hot}$ is about 6000K as maximum; If the cold reservoir is 1000K, then maximum efficiency is about 83 percent.If 1000K is the temperature of radiator, then it will emit 56700W from each square meter of surface. For each 1MW produced electricity you should have about 3.62 $\text{m}^2$ of radiator, and about 245 $\text{m}^2$ of collector.

A second set of radiators is used to dissipate heat and cool down the internal structures of the system, where we use this 1MW of electricity (which eventually generates 1MW of heat) to do some computation work. Assume coolant temperature is about 300K (same as internal temperature) on the input of radiator and 250K coolant on the output end from radiator back in to internal system, then average energy flow from radiator will be: $j^*=\frac{\sigma}{5}\frac{300^5-250^5}{300-250}\approx 330W/m^2$

  • 1/5 comes from integration $\frac {\int \sigma T^4}{\Delta T}$, it is kinda average flux from radiator over surface of that radiator, because of temperature changes from 300K to 250K on radiator surface. We pump heat carrier in to radiator at 300K, and return it at 250K. Radiator will have hotter zones and cooler zones. And if we have radiator divided in 50 zones(for each 1K) with equal surface for each zone, average emitted energy will be that integral divided on temperature difference between heat carrier we pump in and pump out.

  • Result is just approximation and do not includes other effects which maybe good to consider there - like Heat capacity is not strictly a constant, and if heat carrier changes phase gas-liquid-solid. Heat carrier can be solid object, which you just physically move as solid object. Those details depend on particular implementation and construction of that radiator and heat carrier(s) used.

  • also I use 1 side of radiator here and in other calculations below, but for flat radiator it is possible to use both sides(both sides emit energy, it is kinda my error, because I'm used to spherical emitting surfaces), so for flat radiators 1/2 surface of my calculations is possible.

  • kindly added by kingledion upper limit for thickness of radiator shell made of aluminum.

    To support this heat transfer, you need sufficient heat flux in your radiator. Assuming an aluminum heat sink (thermal conductivity $k = 205 \frac{\text{W}}{\text{m}\cdot\text{K}}$), then using 1-d Fourier's law $330 \frac{\text{W}}{\text{m}^2} = 205 \frac{\text{W}}{\text{m}\cdot\text{K}} \cdot \frac{dT}{dx}$, $\frac{dT}{dx} = 1.6 \frac{\text{K}}{\text{m}} = \frac{50 \text{K}}{x}$, so radiator can be no more than 31 meters thick or heat flux will be too low. Heat flux is no problem.

For each 1MW of electricity used inside the station you will need about 3030 additional square meters of radiator. You can use active cooling and have higher radiator temperature and thus less surface area. 600K will get you 16 times reduction of radiator surface, but overall energy efficiency of the system will drop.

The heat radiation efficiency of this system is already a problem. With 1000K of radiator temperature, the surface of a station the size of the moon can dump 56700 $\small W/m^2$. And for each square meter of surface there is 580000 cubic meters of volume in a 'death star'-like sphere where this 1MW of energy can be used. 56700W used there is literary nothing as one 1x1x2 meters box of servers can consume 10kW easy. So to use that volume efficiently -- lets say 1kW per cubic meter of volume -- the surface of your radiator should be about 10000 times more then whole surface of your moon station.

This volume efficiency is the reason why building on the moon itself isn't a bad idea, because you would barely need all the volume a spherical station would have. You could utilize a 50-100 meter thick layer with hot radiator (1000K), and something like 1 meter thick layer with 300K radiator - covering moon.

You could still solve that problem, and pack 1kW per cubic meter of volume, but the radiator size will be huge. In case, if it is another sphere, then it should have a 173000km radius (which would stretch halfway from the moon to the earth; or 2.5 the size of Jupiter). If it is a disk then the radius must be 2 times bigger: 346000km. And that is when the radiator temperature is 1000K, when it is 300K it will be 13 times bigger, for both the sphere and the disk.

d) Self Repair

The station would be repaired with the same technology you built it with. If we consider the radiator to be moon size, it will be 37.6 million square kilometers of 1-100 meter thick structure. So you probably should use some replacement for human labor there, probably 100% of it have to be replaced with sort of automatic building producing system. Because even if you use automatic construction machinery for 99% of work(including teleoperation), and there is still 1% of work you can't do remotely, it is kinda similar to situation when people have to build 376000 km$^2$ by them self and it is kinda equivalent to build 300 cities size of 5 million people each, it needs lot of work force(labor) hundreds of million people, they will need life supporting and all kinda stuff humans need, so they have to live there by hundreds of millions. And this situation will be incompatible with reason of freeing space on earth, as obviously shows that humans can live with that technology level in space.

Just use blocks, produce them, and replace them when they are broken and recycle broken ones. Using human there will ruin all your idea of doing that thing in first place.

There are other options possible, but you will still have to have some program for maintenance and repair (aka software and hardware solutions): it will not repair itself, if developer did not developed this process to be part of the system. The designer must choose which technologies to use to repair. Nanomachines, micromachines, macrofabrics and robots could all be used, but these would be the same technology you used to build the station.

Simplest algorithm to repair, just demolition of old block and build in new one on that place.

e) Own gravity

I will recommend Isaac Arthur youtube channel, Megastructures playlist, first 6 videos(as they numbered in titles) or 5th one Shell Worlds if I recall correctly.

Pay attention to active supporting structures, what are their capabilities. So gravity of the body is not a big problem there (body as moon).

  • In short, one can build layered structure, supported by active supporting structures(they work same way as Launch loop can be suspended above the atmosphere of Earth). So any stress which comes from gravity of body itself, can be compensated by those means.

  • These active structures may be used to transfer energy in the station, and transfer heat from the station.

  • technology used in this answer may be used to solve problems with your station (as it capable to implement an active supporting structure and actually it is used in answer).

    Problem with that solution is that by using it, you do not need to build your station explicitly, for the reasons you mention: as for future use and to free space on earth. But such station may exists for other reasons, as example - we just need a big computer. (Ed note: unclear, please clarify - overpowered solutions for op's needs/reasons: same way it is possible to move everything from earth in to space(manufactures, people, animals), build new earth each year using Jupiter matter, etc. Problem will not exists, or will have completely different solution. But having Raw computing power is always good reason, where to use is not a problem, problem is to have enough)

Motivation is a big problem in your question, but I consider that also as a thing to ignore, along with problems like where to get materials, where to get energy, which technologies used for building etc.

Regarding gravity and system effects - if earth has 2 moons of the same mass it will have no effect on solar system, and not big effects on earth(there will be some, tides will be reduced significantly, how behave atmosphere(wind maps may change)).

However, if you move the station to L1, and solve L1 instability problem (as example by releasing and contracting counterweights that may be part of the station itself like cores and radiators), then gravity forces from that body will be 4% compared to moon forces, with will significantly reduce any effects this body may have on earth, including tidal problems.

But considering the radiator problems, if the size of the structure is limited by the size of the radiators being equal to the moon's surface area, then the mass of the whole construction will be an insignificant, 0.00X% of the moon's mass - and it will have no effects on earth.

Critique

In short, if you have the problems stated in the original post, it is very hard to both stay on earth and be able to build this station. It will need considerable amounts of energy generated in space, materials moved, etc. If you can already do that, it might be easier just to build space habitats which will free from lot of constrains, including those you have mention.

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  • $\begingroup$ I am impressed and taken aback by the thought put into this. This is very, very helpful! Thank you @MolbOrg $\endgroup$ – Zxyrra Oct 17 '16 at 9:45
  • $\begingroup$ @Zxyrra no problem, big construction in space are my sweet spot. $\endgroup$ – MolbOrg Oct 17 '16 at 9:54
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    $\begingroup$ @Zxyrra and probably take look at "Diskworld", this is 6th video in play list - it may be better form for your station, then sphere, as you will need more surface then volume, spheres are good for opposite situation. $\endgroup$ – MolbOrg Oct 17 '16 at 10:17
  • $\begingroup$ I edited this post heavily for clarity, let me know if I changed anything incorrectly. I left some notes for things I did not understand. I also took the liberty of adding Fourier's law for heat flux: an aluminum radiator would easily accomplish all your heat removal needs in the 250-300K range. $\endgroup$ – kingledion Oct 17 '16 at 15:55
  • $\begingroup$ @kingledion thanks, your edits are very appreciated by me and are useful for me. I added some clarifications, and reversed bullet lists in few places(prefer to keep side notes as bullet lists, they are used as notes and clarifications, but not as important or main part of answer, so they can be easily skipped). $\endgroup$ – MolbOrg Oct 18 '16 at 3:18
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Let's focus on the "how does it recieve power" question, as you wish :)

I suggest using a Dyson Sphere. It's the one single most reliable and powerful source of energy you can obtain in our solar system. If that's not what you are looking for, why not put a few fusion powerplants into your death star? If that tech is not available, nuclear power plants will also do. And if they are also not what you require, nuclear batteries can produce low levels of energy for a loooooong time (iirc there are radioactive materials that can provide energy for 17.000 years+). you will need a lot of those, though.

Whatever you do, no source of power comes without maintenance, and given things like Moores Law, your computer will require upgrades all the time, anyway. Also, radiation in space is not friendly to computer parts, requiring extensive shielding and exchanging broken parts. So i am pretty sure your moon will be full of people maintaining and working on the computer.

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  • $\begingroup$ A Dyson Sphere would normally be great, but seeing as this is a satellite in orbit around a planet it would be hard for energy from said sphere to reach its destination. Fusion, on the other hand, would be ideal, but wouldn't the thermal energy from a plant that large melt the machines? In other words can it be controlled on that scale, even with advanced technology? $\endgroup$ – Zxyrra Oct 17 '16 at 7:49
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    $\begingroup$ @Zxyrra fusion plants use strong magnetic fields to keep the super hot plasma in place. currently, those fields are up to 10 tesla strong, so naturally, you need some distance between the power plants and the computers. Heat management is going to be a problem, but i think in your moon-sized computer, there is more than enough space to separate power plants from calculations. Also, do not underestimate the power consumption and resulting heat of computers. In space, getting rid of heat is a problem, and your system will need very elaborate cooling systems anyway :) $\endgroup$ – Andreas Heese Oct 17 '16 at 8:01
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    $\begingroup$ On the topic of heat dissipation, you might be better off putting your computer quite far from the sun. No need to unnecessarily handicap it by making it the same temperature as earth. I'm assuming 1. you'll be running high compute jobs on it that don't mind a few mins of latency and 2. since you have the tech to mine asteroids, you'll have tech to get people to the station for maintenance. $\endgroup$ – csiz Oct 17 '16 at 8:37
  • $\begingroup$ @csiz Wouldn't the distance slow the transfer of data back to the planet? And what if it were obscured by the sun if it revolved faster than the civilization's planet? etc $\endgroup$ – Zxyrra Oct 17 '16 at 8:55
  • $\begingroup$ @csiz but if you move it further away - let's say to mars distance, you already get several minutes of signal delay. I would assume that pretty much beats the purpose of external calculations altogether, making it faster to just do the calculations on earth for 99% of all cases. The OP, as far as i got it, wanted everything to be stored inside the "moon". Talking about the moon - you might hide your computer in earth's or the moons shadow to reduce the heat problems with the sun. $\endgroup$ – Andreas Heese Oct 17 '16 at 9:09
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The entire paradigm of massive scale, dealing with enormous amounts of power and dissipating heat really leads to the conclusion that you don't want a moon sized object at all. Rather, you need to take the volume of the computing devices you intend to build and distribute it over a large volume in space.

This has a multitude of benefits:

First off, it scales nicely. Each day your launch system can deliver an arbitrary amount of computing devices into orbit or into deep space (more on that later). Your system is available from day one, and continues to scale much like adding racks to the server farms of cloud computing companies, or massive datacenters like Amazon.com or Google.

Second, every element can be exposed to sunlight for energy. You don't have to worry about huge fusion reactors, geothermal taps, cable bundles and RF interference from the electrical system, each chip is attached to a small solar cell which provides energy.

Third, since each element is exposed to space, the Carnot efficiency (which MolbOrg talked about in his answer) is going to be extremely high. The hot end is the solar cell exposed to the Sun, while the "cold end" is pointed at deep space, and radiating to the background temperature of the Universe. In the outer solar system, you would realistically be radiating to an infinite heatsink with a temperature of 3K. In the inner solar system, the background temperature is a bit higher. (Incidentally, this is one of the reasons solar cells here on Earth have difficulties, the temperature differentials between the hot and cold sides of the cells is very limited).

Finally, the actual volume of materials will be far less than a moon or planet sized supercomputer, since there is no need for supporting structures, cabling, cooling circuits, lunchrooms for the technical staff (or charging closets for the robots), access tunnels etc. Put another way, you can subtract the volume of the supporting structure and have as much computing power on a smaller budget, or use the entire budget for computing elements and have a much greater amount of computing power.

"Wow!", you say, "where can I get such a system?"

Amazingly enough, this is based on the work of Keith Lofstrom (Inventor of the Lofstrom Loop), and he calls this idea "Server Sky". Early versions can be in orbit around the planet itself, for proof of concept and low latency (since the elements are close together and close to uplink points on Earth). Later on, these elements can be moved (or new ones launched) to the L4 and L5 points, so you can have massive clouds of elements in free space with much more computing power. The "Server Sky" in Low Earth Orbit can be maintained as the cache so users on the ground still get high speeds.

enter image description here

Conceptual design of a single Server Sky element

enter image description here

Server Sky 1.1 in GEO, hovering over a point on Earth 24/7

Lofstrom once wrote a small article about Server Sky (which I haven't been able to retrieve, unfortunately) which talked about the ultimate evolution of the system, with a Dyson swarm of trillions of elements sharing the orbit of Uranus around the Sun, utilizing the cold background of space to maintain high levels of efficiency in the computing and energy generation system. You can imagine subsidiary Server Sky clouds scattered throughout the Solar System at various Lagrange points or an artificial "asteroid belt" acting as storage and caches for the massive Server Sky cloud in the far reaches of the Solar System.

So this is a relatively simple, massively scalable, modular system to achieve the goals of massive computing infrastructure for a K1 level civilization. In its fully developed form with clouds of elements in the deep solar system, it is an analogue of Dyson Swarms to create a Matrioshka Brain, which should provide all the computing power a single solar system could need.

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    $\begingroup$ +1 for the fact that at K1, your problem is less farmland and more heat dissipation, and for giving a more realistic computronium solution. This also points the path towards moving to a K2 civilization. $\endgroup$ – Yakk Oct 17 '16 at 15:29
  • $\begingroup$ Nice answer. With 3K infinite heat sink is not so simple trough. Potentially yes, no problem. Practically not so simple. Taper ratio of shadow cone is important here. Example of that problem is in this answer worldbuilding.stackexchange.com/a/46563/20315 . If cpu field bigger then 2.3 light sec(bigger then sun) then this construction can have infinite long radiator cylinder, or probably 17 light second long cylinder in that case will be enough. Probably that is possible and for small construction, I have to think about that, but swarm of those construction should be sparse, interesting. $\endgroup$ – MolbOrg Oct 18 '16 at 5:09
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My gut feeling is that you apply a paradigm from the 1960s, the mainframe, to the far future. Projecting current trends, I imagine that data processing will look much different in the future. It will be hard to pinpoint, actually, because everything will be a computer. All human artifacts will be intelligent and networked. It's possible that self-organizing computers will extend into the earth's crust using self-replicating nano or micro technology. Low-power will be a paradigm, and everything will just use heat differentials (including geological ones) or light as energy source and thus not contribute to global warming. Computing power will be where you need it (what good is an answer from the fastest computer if it takes the eternity of 2 seconds to arrive?).

But then, I may just be applying a paradigm of the 2010s to the far future.

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The problem is not how it could receive the power (could use the internal nuclear power source like a star, seems plenty of energy for everything) but how would it dissipate the heat, much bigger problem in the modern human made machines.

Unless some advanced technology allows the computer to operate at stellar temperatures, making it a "thinking star".

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  • $\begingroup$ This is important. A death star size computer would melt itself to slag due to inability to get rid of waste heat. Conduct the following experiment: Open up your computer, play Overwatch for 2 hours, then put your finger on the CPU or GPU heat sink. Then put an ice cube on your finger for the third degree burn you just got. Now imagine how hot a death-star size computer will get with no cooling fan in sight. $\endgroup$ – kingledion Oct 17 '16 at 14:46
  • $\begingroup$ @kingledion It probably won't immediately char your flesh, so probably 2nd degree. $\endgroup$ – Yakk Oct 17 '16 at 15:27
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    $\begingroup$ @Yakk Crap, I always mix up 1st and 3rd degree burns. $\endgroup$ – kingledion Oct 17 '16 at 15:55
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I read somewhere that there are really gigantic electric currents circling around in our magnetosphere. For a machine the size you are thinking of, can there be a solution involving having a liquid iron core, a big magnetic field and capturing solar wind charge as energy? Someone with better physics than me might be able to expand on this idea.

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  • $\begingroup$ How much energy would that be, compared with the conventional solar power? $\endgroup$ – JDługosz Oct 17 '16 at 18:23
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    $\begingroup$ You just have to keep the Vogons from blowing it up for their bypass before the computation is finished. 42? $\endgroup$ – Josh King Oct 17 '16 at 19:18
  • $\begingroup$ @JDługosz en.wikipedia.org/wiki/Birkeland_current suggests 100,000 amps during quiet times, to 1,000,000 amps during solar storms. I don't have any numbers for solar power, which presumably gives zero for half the time, but using one doesn't preclude the other $\endgroup$ – Innovine Oct 17 '16 at 19:39
  • $\begingroup$ You should edit that into the answer (and then clean up these comments). $\endgroup$ – JDługosz Oct 18 '16 at 2:08
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    $\begingroup$ @Innovine It is worth noting that current does not give you power. Power is current times voltage, so 1,000,000 amps at 1V is only 1 MW which isn't really that much. This paper suggests the potential drop at the poles is more like 60 kV, so you can get 60 GW electric power, or about 15 kim^2 of solar panels in space. $\endgroup$ – kingledion Oct 18 '16 at 3:32
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Let's focus in the main question. The moon where the supercomputer would be built should have a hot core, as Earth has but not our moon, in order to exploit its geothermal energy.

If the civilization is advanced enough to be able to build a planet-sized supercomputer, it should be able to take efficiently the energy from the depth of the moon, as a first step in the design of this colossal system.

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    $\begingroup$ In this situation, the existing moon is analogous to ours; geothermal energy would be ideal and very useful but a) Our moon does not have a substantial amount of geothermal energy, and b) That amount of geothermal energy may not power the whole surface area of said moon, volume of another moon aside. $\endgroup$ – Zxyrra Oct 17 '16 at 7:53
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    $\begingroup$ Geothermal is another way of saying Natural RTG. Given that this is an artificial Celestial body the size of the moon, any natural radiation would have decayed, and any introduced radiation would be artificial... $\endgroup$ – Aron Oct 17 '16 at 10:19

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