Well, it can’t use more than it can get from the sun that hits it. So it can’t need to radiate more than that away. So it’s radiator size needs are in proportion to its solar panel size needs, and no worse than that.

> Well, it can’t use more than it can get from the sun that hits it. So it can’t need to radiate more than that away

You are correct that the first law of thermodynamics dictates the energy, but anyone who has parked a car in the sun will tell you, the temperature where the absorption/radiation equilibrium is achieved is often ill-suited for normal operation.

The average temperature of a rock or the ISS in earth orbit is about -18C.

It's this huge misconception that space is super cold. A better mind model is that space doesn't have much of a temperature at all just cause there's nothing there. Vacuum doesn't have a temperature.

You won't immediately freeze if you enter space without a suit. You'll die almost immediately, but it will be because your blood will begin to boil because of the lack of pressure kinda like an extreme form of divers sickness - it's just not the cold that'll get you first.

That’s all true. But stuff in space has a temperature, and once I’d been dead a while in LEO, mine would be -18C.

> mine would be -18C

FYI; that's not how it works, you and the rock you mentioned in a different comment cannot have the same temperature of -18C. This is due to differences in material, and geometry to a lesser extent.

Even if you were rock-shaped, the rates of energy absorption and radiation is what determines your remains' temperature, this ratio differs for different materials, and thus difference fiilnal temperatures.

Sure it varies a bit. ISS average skin temp is 10C, for example. A difference that doesn’t matter.

Why keep pushing back on this point? The total available energy from the sun in LEO averages about 1.36KW/m^2, and more than this can be radiated away by current deployed technology.

Solar powered space data centers probably make no economic sense. But not because we can’t cool them. We wouldn’t be able to run them very hot because there isn’t enough power there to do so.

> Sure it varies a bit

No, not just a bit. It varies by hundreds of degrees depending on the materials α/ε ratio.

Your mental model is off: materials that good absorbers but poor emitters will get very hot, and the flip-side stay cool, and are used to make the cooling elements in the ISS . The temperature of ball of black nickel at 1 AU will settle at balmy 239C - not -18C. Polished Aluminum -> roughly 145C.

I’ve made a note not to make my space data center a black nickel sphere, and instead to make it like we generally make satellites.

My nickel guy is gonna be so disappointed.

Again, just to remind you, I didn’t claim space datacenters are economically rational.

My original claim, in its entirety, was "You'll also get much better cooling for free via convection."

You sure will. My contribution is that you don’t need much better cooling.

Well yes, but what matters is how hot that rock gets. Some rocks melt or vaporise in space (see comets).

An object in low earth orbit has an average temperature of -18C.

That’s right, and it’s not very hot: -18C on average.

The Earth and moon have rock crusts and don’t melt.

There is the additional problem that the GPUs are not in the panels, so to radiate the heat you must first transport it from the GPUs, then distribute it uniformly over the entire surface of the radiators, otherwise some parts will overheat.

Without gravity, it is likely that this can be done only by pumping continuously a lot of liquid, which will increase the power consumption and it will reduce reliability.