Space is a vacuum. i.e. The lack-of-a-thing that makes a thermos great at keeping your drink hot. A satellite is, if nothing else, a fantastic thermos. A data center in space would necessarily rely completely on cooling by radiation, unlike a terrestrial data center that can make use of convection and conduction. You can't just pipe heat out into the atmosphere or build a heat exchanger. You can't exchange heat with vacuum. You can only radiate heat into it.
Heat is going to limit the compute that can be done in a satellite data centre and radiative cooling solutions are going to massively increase weight. It makes far more sense to build data centers in the arctic.
Musk is up to something here. This could be another hyperloop (i.e. A distracting promise meant to sabotage competition). It could be a legal dodge. It could be a power grab. What it will not be is a useful source of computing power. Anyone who takes this venture seriously is probably going to be burned.
Next up in the equation is surface emissivity which we’ve got a lot of experience in the automotive sector.
And finally surface area, once again, getting quite good here with nanotechnology.
Yes he’s distracting, no it’s not as impossible as many people think.
It's not physically impossible. Of course not. It's been done thousands of times already. But it doesn't make any economic sense. It's like putting a McDonald's at the top of Everest. Is it possible? Of course. Is it worth the enormous difficulty and expense to put one there? Not even a little.
Same with datacenters in space, not today, but in 1000 years definitely, 100 surely, 10?
As for the economics, it makes about as much sense as running jet engines at full tilt to power them.