An Extremely Luminous Panchromatic Outburst

HEAT TRANSFER TYPES

I want to start off by looking at different ways to move heat. In classical physics, there are basically three ways: conduction, convection, and radiation and you can find the relevant math here.

Conduction is when two solid objects are touching. Different objects transfer heat differently and a lot depends on the quality of surface contact, but the basic idea is that if you get your object to touch an object at a different temperature that is good at transferring heat, this is a very efficient way to change the temperature of your object. Obviously, though, we don't have that option in space because, well, your spacecraft isn't generally touching other objects and, if it does, they're usually not large enough to absorb all of the heat transfer and will quickly become saturated.

Convection is when a fluid flows over a solid object. Again, this varies depending on the fluid and the quality of contact, but we usually use air or water and both can be very effecient at transferring fairly large amounts of heat if they can contact a significant surface area. Again, this isn't really an option for a spacecraft because they're in a vacuum and, thus, not in contact with any fluids except those inside the spacecraft itself which, while they are useful for moving heat around the spacecraft, don't help with heat going into or out of it.

That only leaves radiation, the least efficient method of transferring heat. Which isn't great! Honestly, making sure that you can get rid of enough heat to prevent your spacecraft from overheating is a major problem in spacecraft design and that's before you add a whole bunch of hardware whose main function generates a metric crap-ton of heat!

HOW MUCH WOULD IT TAKE?

Okay, so let's start breaking down the problem. First off, how much heat are we going to need to radiate away? I found a source that indicates that a leading data center can contain 45 million chips, which seems like a decent place to start. Looking a bit more, it seems like the newest chips generate about 1 kW of heat. Putting these together, it looks like, just for the chips, we're going to need to be dissipating about 45 GW of heat for our space-based datacenter.

Secondly, let's look at our heat equation. Taking the net radiation loss rate equation from this site, we've got most of the variables, but we still need the temperatures. For simplicity I'm going to assume that we need to keep the temperature of the chips below 80 C (353 K) which seems like a high estimate for max temperature, but it should mean we're being conservative in our assumptions, so I'm okay with it. As far as the outside temperature, the environment in earth orbit, either LEO (Low Earth Orbit) or MEO (Middle Earth Orbit) is extremely variable depending whether you're in direct sunlight or not. I'm using this temperature profile and taking the average outside temperature of about -32.5 C or 241 K.

Calculating with those numbers, what I'm getting is that you'd need a radiator area of over 65 million cubic meters to cool all of this. For reference, that's over 9,000 football fields.

Now, according to this presentation from two years ago (shout-out to CalPoly, my alma mater!), current radiator technology generally comes in at a density of about 19 kg/m^2 but there is a stated goal to get that down to 6 kg/m^2 for long-range missions. Running both numbers, I come up with a weight of over 1.2 billion kg for the current density and almost 391 million kg for the lower goal density. A Falcon 9 has a payload capacity of 22,800 kg to low earth orbit, so it would take over 54,000 launches just for the radiators needed to cool the datacenter chips at current densities, though that drops to a little over 17,000 launches if we can get down to the goal density. A Falcon 9 launch costs about $45,000 per kg to LEO, so that puts your cost of launch somewhere between $55.7 trillion and $17.5 trillion.

Also, how long would that take? Well, I found a timeline of SpaceX launch missions each year (https://spacexnow.com/stats) and it looks like, starting in 2021, the trend line is pretty linear. If the number of launches keeps increasing at that rate and if all launches were dedicated just to launching radiator panels for datacenters, they could launch enough of the current radiator panels to cool the chips of one datacenter by 2065, though it could be done by 2046 with the lower density panels they're working on.

Keep in mind, that's just the radiators to cool the chips, that doesn't include the rest of the spacecraft or the datacenter itself. I'd also note that I didn't even really consider solar heating or the reflected heat from Earth or any other heat generated by the spacecraft (including the heat generated by generating the power for the chips in the first place!), I only considered the heat generated by the chips themselves, so this is probably way smaller than what would actually be needed.

THAT'S CRAZY!

Right? Look, I don't doubt that we'll have orbital infrastructure at some point in the future, probably including computational datacenters, but the amount of problems that need to be overcome before that is a possibility are immense. I've only detailed out one of them and it's already completely prohibitive with current technology and even with reasonably projected technology.

For comparison, if you were to try to cool all of that here on Earth with water, as they're often doing, you'd need a surface area of about 49 million square meters (about 6,800 football fields) assuming water at 10 degrees C and you'd need to run absolutely epic amounts of that water through it to maintain the temperature. But that's something that you can do on Earth! Don't get me wrong, there are all kinds of negative externalities in terms of the way that excess heat affects the environment, but even if all of those were priced in it doesn't approach nearly the multi-trillion dollar price tag of cooling a space-based datacenter.

Also, caveats again, keep in mind that I only looked at the amount of radiative capacity that would be necessary to cool the chips themselves. I didn't consider the cost of launching the datacenter or all of the heat that would be generated by all of the other components necessary to run it or issues with maintenance and longevity, all of which are much worse in space than on the ground. I'd also note that I tried to make every assumption in a way that would reduce the size of the radiative capacity necessary, so even just my estimate for this one thing is probably too low.

Long story short, I don't think that datacenters in space are a near-term possibility and they're definitely iffy in the medium term as well. Long-term? Sure, I think it'll probably happen, but I think that space-based datacenters are unlikely to happen anywhere near in time to justify SpaceX's current sky-high stock valuations.

CONCLUSION

Look, I'm a big space guy and I absolutely think that, in the future, there will be lots of things in space, even datacenters. That said, the economics and just the pure physics of what it looks like today are so monumentally, over-the-top bonkers that anyone trying to sell you something premised on the idea that it's just around the corner, say, SpaceX shares at today's valuation of $132 which would make the whole company worth $1.786 trillion when it generated only $4.7 billion in revenue last quarter for a net loss of $4.3 billion, is probably selling you the modern equivalent of seaside property in Nebraska.