You might need space for radiators, but there is plenty space in space.
Radiators in space are extremely inefficient because there's no conduction.
Also you have huge heat inputs from the sun. So you need substantial cooling before you get around to actually cooling the GPUs.
EDIT: people continue downvoting and replying with irrelevant retorts, so I'll add in some calculations
Let's assume
1. cheap 18% efficient solar panels (though much better can be achieved with multijunction and quantum-cutting phosphors)
2. simplistic 1360 W/m^2 sunlight orthogonal to the sun
3. an abstract input Area Ain of solar panels (pretend its a square area: Ain = L ^ 2)
4. The amount of heat generated on the solar panels (100%-18%) * Ain * 1360 W / m ^ 2, the electrical energy being 18% * Ain * 1360 W / m ^ 2. The electrical energy will ultimately be converted to computational results and heat by the satellite compute. So the radiative cooling (only option in space) must dissipate 100% of the incoming solar energy: the 1360 W / m^2 * Ain.
5. Lets make a pyramid with the square solar panel as a base, with the apex pointing away from the sun, we make sure the surface has high emissivity (roughly 1) in thermal infrared. Observe that such a pyramid has all sides in the shade of the sun. But it is low earth orbit so lets assume warm earth is occupying one hemisphere and we have to put thermal IR reflectors on the 2 pyramid sides facing earth, so the other 2 pyramid sides face actual cold space.
6. The area for a square based symmetric pyramid: we have
6.a. The area of the base Ain = L * L.
6.b. The area of the 4 sides 2 * L * sqrt( L ^ 2 / 4 + h ^ 2 )
6.c. The area of just 2 sides having output Area Aout = L * sqrt( L ^ 2 / 4 + h ^ 2 )
7. The 2 radiative sides not seeing the sun and not seeing the earth together have the area in 6.c and must dissipate L ^ 2 * 1360 W / m ^ 2 .
8. Hello Stefan-Boltzmann Law: for emissivity 1 we have the radiant exitance M = sigma * T ^ 4 (units W / m ^ 2 )
9. The total power exited through the 2 thermal radiating sides of the pyramid is then Aout * M
10. Select a desired temperature and solve for h / L (to stay dimensionless and get the ratio of the pyramid height to its base side length), lets run the satellite at 300 K = ~26 deg C just as an example.
11. If you solve this for h / L we get: h / L = sqrt( ( 1360 W / m ^ 2 / (sigma * T ^ 4 ) ) ^ 2 - 1/4 )
12. Numerically for 300K target temperature we get: h/L = sqrt((1360 / (5.67 * 10^-8 * 300 ^ 4)) ^ 2 - 1/4) = 2.91870351609271066729
13. So the pyramid height of "horribly poor cooling capability in space" would be a shocking 3 times the side length of the square solar panel array.
As a child I was obsessed with computer technology, and this will resonate with many of you: computer science is the poor man's science, as soon as a computer becomes available in the household, some children autodidactically educate themselves in programming etc. This is HN, a lot of programmers who followed the poor man's science path out of necessity. I had the opportunity to choose something else, I chose physics. No amount of programming and acquiring titles of software "engineer" will be a good substitute for physicists and engineers that actually had courses on the physical sciences, and the mathematics to follow the important historical deductions... It's very hard to explain this to the people who followed the path I had almost taken. And they downvote me because they didn't have the opportunity, courage or stamina to take the path I took, and so they blindly copy paste each others doomscrolled arguments.
Look I'm not an elon fanboy... but when I read people arguing that cooling considerations excludes this future, while I know you can set the temperature arbitrarily low but not below background temperature of the universe 4 K, then I simply explain that obviously the area can be made arbitrarily large, so the temperature can be chosen by the system designer. But hey the HN crowd prefers the layers of libraries and abstractions and made themselves an emulation of an emulation of an emulation of a pre-agreed reality as documented in datasheets and manuals, and is ultimately so removed from reality based communities like physics and physics engineering, that the "democracy" programmers opinions dominate...
So go ahead and give me some more downvotes ;)
If you like mnemonics for important constants: here's one for the Stefan Boltzman constant: 5.67 * 10^-8 W / m^2 / K ^ 4
thats 4 consecutive digits 5,6,7,8 ; comma or point after the first significant digit and the exponent 8 has a minus sign.
On Earth, you can vent the heat into the atmosphere no problem, but in space, there's no atmosphere to vent to, so dissipating heat becomes a very, very difficult problem to solve. You can use radiators to an extent, but again, because no atmosphere, they're orders of magnitude less effective in space. So any kind of cooling array would have to be huge, and you'd also have to find some way to shade them, because you still have to deal with heat and other kinds of radiation coming from the Sun.
It's easier to just keep them on Earth.