Right up to the radiation limit and then you'll either have to throttle your precious GPUs or you'll be melting your satellite or at least the guts of it. You're looking at an absolutely massive radiator here, many times larger than the solar panels that collect the energy to begin with.
> > absolutely massive radiator here, many times larger than the solar panels
> A_radiator / A_PV = ~3;
Seems like you're in agreement. There's a couple more issues here--
1. Solar panels are typically big compared to the rest of the satellite bus. How much radiator area do you need per 700W GPU at some reasonable solar panel efficiency?
2. Getting the satellite overall to an average 27C temperature doesn't necessarily keep the GPU cool; the satellite is not isothermal.
My back of the envelope estimate says you need about 2.5 square meters of radiator (perhaps more) to cool a 700W GPU and the solar panel powering the GPU. You can fit about 100 of these GPUs in a typical liquid-cooled rack, so you need about 250 square meters of radiator to match one rack. And, unfortunately, you can't easily use an inflatable structure, etc, because you need to conduct or convect heat into that radiator.
This assumes that you lose no additional heat in moving heat or in power conversion.
And they’re going to mass a -lot-. Not that anyone would use a pyramid— you would want panels with the side facing the sun radiating too. There are plenty of surfaces that radiate more than they absorb at reasonable temperatures in sunlight.
First of all a note on my calculations: they appear very simple, and its intentional, its not actually optimized, its intended to give programmers (who enjoyed basic high school physics but not more) the insight that cooling in space while hard, is still feasible. If you look around the thread you'll find categorical statements that cooling in space is essentially impossible etc.
The most efficient design and the most theoretically convincing one are not in general the same. I intentionally veer towards a configuration that shows it's possible without requiring radiating surface with an area of a square Astronomical Unit. Minimizing the physics and mathematics prerequisites results in a suboptimal but comprehensible design. This forum is not filled with physicists and engineers in the physical sciences, most commenters are programmers. To convince them I should only add the absolute minimum and configure my design to eliminate annoying integrals (for example the heat radiated by earth on the satellite is sidestepped by simply sacrificing 2 of the triangular sides of the pyramid to be mere reflectors of emissivity ~0, this way we can ignore the presence of a nearby lukewarm earth). Another example is the choice of a pyramid: it is convex and none of the surfaces are exactly parallel to the sun rays (which would result in ambiguity or doubt, or make the configuration sensitive to the exact orientation of the satellite), a more important consequence of selecting a convex shape is that we don't have to worry about heat radiated from one part of the satellite surface, being reabsorbed by another surface of the satellite (in view of the first surface), a convex shape insures no surface patch can see another surface patch of the satellite. And yes I pretend no heat is radiated by the solar panel itself, which is entirely achievable. So I intentionally sacrifice a lot of opportunities for more optimal design to show programmers (who are not trained in mathematical analysis, and not trained with physics textbook theorem-proof-theorem-proof-definition-theorem-proof-...) that physically it is not in the real of the impossible and doesn't result in absurdly high radiator/solar panel area ratios.
To convince a skeptic you 1) make pessimistic suboptimal estimates with a lot of room for improvement and 2) make sure those estimates require as little math and physics as possible, just the bare minimum to qualitatively and quantitatively understand the thermodynamics of a simple example.
You are asking the right questions :)
Given the considerations just discussed I feel OK forwarding you to the example mini cluster in the following section:
It describes a 230 kW system that can pretrain a 405B parameter model in ~17 days and is composed of 16x DGX B200 nodes, each node carrying 8x B200 GPUs. The naive but simple to understand pyramid satellite would require a square base (solar PV) side length of 30 m. This means the tip of the pyramid is ~90m away from the center of the solar panel square. This gives a general idea of a machine capable of training a 405B parameter model in 17 days.
We can naively scale down from 230 kW to 700 W and conclude the square base PV side length can then be 1.66 m; and the tip being 5 m "higher".
For 100 such 700 W GPU's we just multiply by 10: 16.6 m side length and the tip of the pyramid being 50 m out of the plane of the square solar panel base.
Why bother with all this crazy geometry? Why not just area as I've done above? You can design a radiator so that barely any of the light shines back on the spacecraft.
Your differences from my number: A) you're working based on spacecraft average temperature and not realizing you're going to have a substantial thermal drop; B) you're assuming just one side of the surface radiates. They're on the same order of magnitude. Both of us are assuming that cooling systems, power systems, and other support systems make no heat.
You can pick a color that absorbs very little visible light but readily emits in infrared-- so being in the sun doesn't matter so much, and since planetshine is pulling you towards something less than room temperature, it's not too bad either.
None of these numbers make me think "oh, that's easy". You're proposing a structure that's a big fraction of the size of the ISS for one rack of GPUs.
I don't really think cooling in space is easy. The things I have to do to get rid of an intermittent load of 40W on a small satellite are very very annoying. The idea of getting rid of a constant load of tens of kilowatts, or more, makes me sweat.
Datacenter capacity (and thus heat) grows by the cube law, but the ability to radiate heat grows by the square law, so it seems like it would be advantageous to have a bunch of smaller satellites, if you were concerned about cooling them.
> it would be advantageous to have a bunch of smaller satellites, if you were concerned about cooling them.
...That's only relevant if you start from the position that your datacenters have to be space.
You could already make smaller datacenters on earth, and still have better cooling, if you were concerned about that. We don't do that because on earth it's more efficient to have one large datacenter than many small ones.