Moreover, you can easily calculate how big of a radiator you need for a given power level and temperature. You can use the Stefan–Boltzmann law:
A ~ (1000 P) / (2 e k T^4)
Where A is the radiator area in square meters
P is the power in kilowatts
e is emissivity (usually 0.9)
k is the constant 5.67e-8
For a 1 kW test like Googles, you just need 1 square meter of radiators (assuming two-sided).For SpaceX's 175 kW satellites, they will need ~170 square meters of radiators.
None of this is impossible or even difficult to calculate. That's why I think this is the laziest argument against space data centers. There are so many other more reasonable arguments (like whether they will be economically competitive) but people love to latch on to this one for some reason.
That's like a quarter of a rack of modern AI hardware. Modern AI datacenters are now in the multi-GW range.
Now the argument is, what, you can't launch that many satellites?
How can anyone be certain of any of those numbers without (a) knowing how the technology will evolve, and (b) doing the math?
I'm just astounded that people can have such confidence.
They are showing that space-based DCs only make sense for criminal enterprises. Which probably IS what's going on here.
The 15-minute figure is what they currently designed for because they have mass constraints. If they wanted a different figure (like forever) they could do it with a larger radiator.
As you said, the physics is solved! We know exactly how much heat a surface radiates in space--there is literally an equation for it. We know how to cool stuff in space. Will the price be low enough to make a profit? That's the real question. But stop worrying about cooling in space.
If you have something useful to contribute regarding how to actually reasonably put up enough mass to make this remotely a feasible idea then please contribute. We have the technology to prevent global warming, and doing that is far easier than this, and yet even that is apparently not feasible for humanity.
What's unfeasible about that? SpaceX has already launched 10,000 Starlink satellites. Falcon 9 launches 150 times per year.
People use that argument because it takes zero thought to make and significant effort to refute.
"Space is cold" is classic zero effort to make, significant effort to refute stuff: proponents imply complete nonsense about vacuums being optimal for cooling and anyone who understands why this is a lie to gull retail investors ends up getting bogged down in "sure, but Boltzmann equations proving it's prohibitively expensive doesn't prove it isn't possible"...