[jacquesm]

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.

[DoctorOetker]

not really, for A_radiator / A_PV = ~3; you can keep the satellite cool to about 27 deg C (300K) check my example calculation (Ctrl-F: pyramid)

[mlyle]

> > 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.

[DoctorOetker]

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:

https://news.ycombinator.com/item?id=46867402

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.

[mlyle]

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.

[DoctorOetker]

As I said, my geometry and properties are chosen to be easy to understand with a minimum of knowledge and mathematics.

Yes, I could make more optimistic calculations: use the steradians occupied by earth, find and use the thermal IR emissivities of solar panels place many thin layers of glass before the solar panel allowing energy generating photons through and forming a series of thermal IR black body radiators as a heat shield in thermal IR, the base also radiates heat outwards and at a higher temperature, use nonsquare base, target a somewhat higher but still acceptable temperature, etc... but all of those complicate the explanation, risking to lose readers in the details, readers that confuse the low net radiative heat transfer between similar temperature objects and room walls in the same room as if similar situation applies for radiative heat transfer when the counterbody is 4 K. Readers that half understand vacuum flasks / dewars: no or fewer gas particles in a vacuum means no or less energy those particles can collectively transport, that is correct but ignores the measures taken to prevent radiative heat loss. For example if the vacuum flask wasn't mirror coated but black-body coated then 100 deg C tea isolated from room temperature in a vacuum flask is roughly 400 K versus 300 K, but Stefan Boltzmann carries it to the fourth power (4/3) ^ 4 = 3.16 ! That vacuum flask would work very poorly if the heat radiated from the tea side to the room-temperature side was 3 times higher than the heat radiated by the room temperature side to the tea-side. The mirroring is critical in a vacuum flask. A lot of people think its just the vacuum effect and blindly generalize it to space. Just read the myriad of comments in these discussions. People seriously underestimate the capabilities of radiative cooling because the few situations they have encountered it, it was intentionally minimized or the heat flows were balanced by equilibrium, not representative for a system optimized to exploit radiative heat transfer.

Some small corrections:

>Both of us are assuming that cooling systems, power systems, and other support systems make no heat.

I do not make this assumption! all heat generated in the cooling, power and other support systems stem from electrical energy used to power them, and that energy came from the solar panels. The sum of the heat generated in the solar panel and the electrical energy liberated in the solar panel must equal the unreflected incident optical power. So we can ignore how efficient the solar panel is for the rest temperature calculation, any electrical energy will be transformed to heat and needs to be dissipated but by conservation of energy this sum total of heat and electrical energies turned into heat must simply equal the unreflected energy incident on the solar panel... The solar panel efficiencies do of course matter a lot for the final dimensions and mass of the satellite, but the rest temperature is dictated by the ratio of the height of the pyramid to the square base side length.

>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.

emissivity (between 0 and 1) simultaneously dials how well it absorbs photons at that wavelength as well as how efficiently it sheds energy at that wavelength. A higher emissivity allows the solar panel to cool faster spontaneously, but at the cost of absorbing thermal photons from the sun more easily! Perhaps you are recollecting the optimization for the thermal IR window of our atmosphere, the reason that works is because it works comparatively to solar panels that don't exploit maximum emissivity in this small window. The atmospheric IR window location in the spectrum is irrelevant in space however.

> A) you're working based on spacecraft average temperature and not realizing you're going to have a substantial thermal drop;

of course I realize there will be a thermal gradient from base to apex of the pyramidal satellite, it is in fact good news: near the solar panel base the triangular sides have wider area and hotter temperature, so it sheds heat faster than assuming a homogenous temperature (since the shedding is proportional to the fourth power of temperature). When I ignore it it's not because I'm handwaving it away, it's because I don't wish to bore computer science audience with integral calculations, even if they bring better news. Before bringing the better news you need to bring the good news that its possible with similar order of magnitude areas for the radiator compared to the solar panels, without their insight that its feasible first, its impossible to make them understand the more complicated realistic and better news picture, especially if they want to not believe it... Without such proof many people would assume the surface of the radiator would need to be 10's to 100's of times the surface area of the solar panels...

> B) you're assuming just one side of the surface radiates.

No, I even explicitly state I only utilize 2 of the 4 side triangles of the pyramid (to sidestep criticisms that earth is also radiating heat onto the satellite). So I make a more pessimistic calculation and handicap my didactic example just to show you get non-extreme surface ratios even when handicapping the design. If you look at history of physics, you will often find that insights were obtained much earlier by prior individuals, but the community only accepted the new insights when the experimental design was simplified to such an extent that every criticism is implicitly encoded in the design by making it irrelevant in the setup, this is not explicitly visible in many of the designs.

[jacquesm]

You won't be able to make up for a lack of physics grounding by using more words.

[mlyle]

> I do not make this assumption! all heat generated in the cooling, power and other support systems

Nah -- when we're talking about how much it takes to power 70kW of GPUs, we need to include some kind of power utilization efficiency number. If 70kW is really 100kW, then we need to make this ridiculously big design 40% larger.

> >You can pick a color that absorbs very little *visible light* but readily emits in *infrared*-

> how well it absorbs photons at that wavelength as well as how efficiently it sheds energy at that wavelength.

Yes. Planetshine is infrared, 290K-ish; sunshine is 5500K-ish and planetary albedo is close enough to this, with a very small portion of its light being infrared. You are being long winded and not even reading what you reply to.

So, for example, white silicate paint or aluminized FEP has a equilibrium temperature in full sun, with negligible heat conducted to or away from it, somewhere in the span of -70 to -40C depending upon your assumptions. It will happily net radiate away heat from above-room temperature components while facing the sun.

It will also happily net radiate away heat when facing the planet because the planet is under room temperature and the planet doesn't subtend a whole hemisphere even in LEO.

I don't really like argument from authority, but... I will point out that I am the PI for multiple satellite projects and have owned thermal design, and that the stuff I've flown in space has ended up at very close to predicted temperatures. I don't feel like this is an easy thermal problem.

I mean, it's easy in the sense of "it takes a radiator area about the same as the floor area of my house". It's not easy in the sense of "holy shit I need to launch a radiator that's bigger than my house and somehow conduct all that heat to it while keeping the source cool."

> of course I realize there will be a thermal gradient from base to apex of the pyramidal satellite

No, there will be a thermal gradient from the hot thing -- the GPU -- to the radiator surface. S-B analysis is OK for an exterior temperature, but it doesn't mean the stuff you want to keep cool will be that average temperature. This is why we end up with heat pipes, active cooling loops, etc, in spacecraft.

If this wasn't a concern, you could fly a big inflated-and-then-rigidized structure and getting lots of area wouldn't be scary. But since you need to think about circulating fluids and actively conducting heat this is much less pleasant.