https://taranis.ie/datacenters-in-space-are-a-terrible-horri...
I don't have any specialized knowledge of the physics but I saw an article suggesting the real reason for the push to build them in space is to hedge against political pushback preventing construction on Earth.
I can't find the original article but here is one about datacenter pushback:
https://www.bloomberg.com/opinion/articles/2025-08-20/ai-and...
But even if political pushback on Earth is the real reason, it still seems datacenters in space are extremely technically challenging/impossible to build.
Figuring out how to radiate a lot of waste heat into a vacuum is fighting physics. Ordinarily we use a void on earth as a very effective _insulator_ to keep our hot drinks hot.
Currently SpaceX have managed to land the booster only, not the rocket itself, if you are thinking about Starship. And reusability of said rocket is also missing (collecting blown up pieces from the bottom of the ocean doesn't count!).