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.
It probably increases Elon's share of the combined entity.
It delivers on a promise to investors that he will make money for them, even as the underlying businesses are lousy.
A Starlink satellite uses about 5K Watts of solar power. It needs to dissipate around that amount (+ the sun power on it) just to operate. There are around 10K starlink satellites already in orbit, which means that the Starlink constellation is already effectively equivalent to a 50 Mega-watt (in a rough, back of the envelope feasibility way).
Isn't 50MW already by itself equivalent to the energy consumption of a typical hyperscaler cloud?
Why is starlink possible and other computations are not? Starlink is also already financially viable. Wouldn't it also become significantly cheaper as we improve our orbital launch vehicles?
Aside from the point others have made that 50 MW is small in the context of hyperscalers, if you want to do things like SOTA LLM training, you can't feasibly do it with large numbers of small devices.
Density is key because of latency - you need the nodes to be in close physical proximity to communicate with each other at very high speeds.
For training an LLM, you're ideally going to want individual satellites with power delivery on the order of at least about 20 MW, and that's just for training previous-generation SOTA models. That's nearly 5,000 times more power than a single current Starlink satellite, and nearly 300 times that of the ISS.
You'd need radiator areas in the range of tens of thousands of square meters to handle that. Is it theoretically technically possible? Sure. But it's a long-term project, the kind of thing that Musk will say takes "5 years" that will actually take many decades. And making it economically viable is another story - the OP article points out other issues with that, such as handling hardware upgrades. Starlink's current model relies on many cheap satellites - the equation changes when each one is going to be very, very expensive, large, and difficult to deploy.