I hear this a lot without actual calculations backing up the claim.

First of all, orbital data centre doesn't mean a monolithic 500MW monstrosity orbiting Earth. That's not what the companies actually investigating the idea (Google, Amazon, SpaceX, ...) have in mind.

The real-world implementation would use constellations of Starlink-sized satellites, so we're talking about a ~10kW power envelope. Under ideal orbital conditions (sun synchronous near polar orbit, ~250-450km), you can get away with as little as 40m² of radiator area depending on engineering margins, provided you allow your radiator/coolant temps to be 70°C and above (70°C is what I used for my estimation plus an ideal 400km SSO and a reasonably efficient radiator similar to the improved ETCS on the ISS - no ammonia for the coolant, though see below as to why).

People often cite the ISS and its ~100m² radiators for comparison. The problem with that is that for one, the design operating temperature of the ISS' EATCS is 4°C on the low temp loop and 17°C on the moderate temp loop. That little known fact aside, the current improved ATCS is capable of rejecting 70kW of waste heat - way more than the thermal output a realistic satellite would produce. The active temperature control system (ATCS) of the ISS is designed around humans and science experiments in a 400km 52°N to 52°S orbit, not silicon chips that are allowed to run much hotter than 25°C and sit in SSO.

In short the *actual* thermodynamics work out just fine if you consider real satellite designs instead of sci-fi monstrosities, use realistic operating temperatures for the coolant loop designed around silicon chips, and the desired target orbit.

So when you say "unless we learn how to change those rules the problem will be unsolvable" I'd honestly like to know why my 25+ year old literature on satellite mission and hardware design, Boeing's numbers from "Active Thermal Control System (ATCS) Overview" document, the formulas from NASAs "Guidelines for thermal analysis of spacecraft hardware", this gem from DLR https://doi.org/10.1016/j.asr.2024.11.024 and my calculator are all wrong at the same time.

Sure, I only did some napkin math (still took nearly 45min) using some simplified formulas and crude estimates for the required parameters (I was curious, but not THAT curious), but I always rounded up and used a healthy 2x margin on top of the estimated result.

So please tell me why I'm wrong.