Here me is the emissivity of the object – its effectiveness as a radiator (0 me < 1), P is the Stefan-Boltzmann constant, AND is the surface, and T is the temperature (in Kelvin). Since we have temperatures up to the fourth power, you can see that hotter things radiate A lot more power than cooler stuff.
OK, say you want to play Red Dead Redemption in space. Your computer will heat up – maybe up to 200 F (366 Kelvin). For simplicity, let’s assume that it is a cube-shaped computer with a total area of 1 square meter and equipped with a perfect radiator (ε = 1). The thermal radiation power would then be approximately 1000 watts. Of course your computer NO the radiator is perfect, but it looks like everything will be fine. As long as the output power is greater than the input power (300W), it will chilly down.
Now say you want to run some modest AI stuff. This is a bigger task, so let’s make our cubic computer bigger with edges twice as long as before. This would make the volume eight times larger (23) so that we can have eight times as many processors, which means we need eight times more power consumption – 2400 watts. However, the area is only four times (22) larger, so the radiation power will be approximately 4000 watts. You still have more outputs than inputs, but the gap is narrowing.
Size matters
You can see where this is going. If you scale up, the volume will grow faster than the surface area. So the larger a space computer is, the more challenging it is to chilly it. If you imagine an orbiting structure the size of a Walmart, like data centers on Earth, that simply won’t happen. It would melt.
Of course, external radiant panels can be added. The International Space Station has them. How substantial would they have to be? Let’s assume your data center runs on 1 megawatt. (Existing AI data centers on Earth consume between 100 and 1,000 megawatts.) Then you would need a radiating area of at least 980 square meters. This is getting out of control.
Oh, and these radiators are not solar panels connected by wires. They need systems to dissipate heat from the processors to the panels. To do this, the ISS pumps ammonia through a network of pipes. This means even more material, which makes it much more steep to put into orbit.
So let’s summarize. Even though we made this with favorable assumptions, it doesn’t look too good. We don’t even take into account the fact that solar radiation will also heat up the computer, which will require even more cooling. Or that intense solar radiation will likely damage electronics over time. How do you make repairs?
One thing is clear, however: because cooling in space is ineffective, your “data center” would have to consist of a swarm of petite satellites with better surface-to-volume ratios, rather than a few huge ones. This is what most proponents like Google Project Suncatcher suggest. Elon Musk’s SpaceX has already asked the FCC for permission to launch a million petite AI satellites into orbit.
Hmm. Low Earth orbit is already crowded with 10,000 energetic satellites and approximately 10,000 tons of space debris. There is a risk of collisions, and perhaps even catastrophic Kessler cascades already real. And we add a hundred times more satellites? All I can say is Look below!
So what is the answer to our question? Theoretically, you could probably create an off-planet computer system with lots of petite satellites, although the launch and construction costs would be astronomical. Whether this is a good idea is a completely different question.