Here ε is the emissivity of the object—how effective it is as a radiator (0 < ε < 1), σ is the Stefan-Boltzmann constant, A is the surface area, and T is the temperature (in Kelvin). Since we have temperature to the fourth power, you can see that hotter things radiate much more power than cooler things.
OK, say you want to play Red Dead Redemption in space. Your computer is gonna get hot—maybe 200 F (366 Kelvin). To keep it simple, let’s say this is a cube-shaped PC with a total surface area of 1 square meter, and it’s a perfect radiator (ε = 1). The thermal radiation power would then be around 1,000 watts. Of course your computer is not a perfect radiator, but it looks like you’d be fine. As long as the output (1,000 watts) is greater than the input (300 watts), it’ll cool down.
Now say you want to run some modest AI stuff. That’s a bigger job, so let’s scale up our cubical computer with edges twice as long as before. That would make the volume eight times larger (23), so we could have eight times as many processors, and we need eight times as much power input—2,400 watts. However, the surface area is only four times (22) larger, so the radiative power would be about 4,000 watts. You still have more output than input, but the gap is narrowing.
Size Matters
You can see where this goes. If you keep scaling it up, the volume grows faster than the surface area. So the larger your space computer, the harder it is to cool. If you were picturing an orbiting Walmart-size structure, like the data centers on Earth, that’s just not going to happen. It would melt.
Of course, you could add on external radiation panels. The International Space Station has these. How big would they have to be? Well, say your data center runs on 1 megawatt. (Existing AI data centers on Earth use 100 to 1,000 megawatts.) Then you’d need a radiating area of at least 980 square meters. This is getting out of hand.
Oh, and these radiators aren’t like solar panels, connected by wires. They need systems to conduct heat away from the processors out to the panels. The ISS pumps ammonia through a network of pipes for this. That means even more material, which makes it that much more expensive to hoist into orbit.
So let’s take stock. Even though we set this up with favorable assumptions, it’s not looking very good. We’re not even taking into account the fact that solar radiation will heat up the computer as well, which will require even more cooling. Or that intense solar radiation will likely damage the electronics over time. And how do you make repairs?
However, one thing is clear: Because cooling is inefficient in space, your “data center” would have to be a swarm of small satellites with better area-to-volume ratios, not a few large ones. That’s what most proponents, like Google’s Project Suncatcher, are now suggesting. Elon Musk’s SpaceX has already requested FCC permission to launch a million small AI satellites into orbit.
Hmm. Low Earth orbit is already congested with 10,000 active satellites and some 10,000 metric tons of space junk. The risk of collisions, maybe even catastrophic Kessler cascades, is already real. And we’re going to add a hundred times as many satellites? All I can say is, “Look out below.”
