Much larger.

The compute part may be a rack or a cabinet worth of GPUs (though TBH the public designs are currently vague to the point of being artistic impressions), but they also need to come with a PV array big enough to power that, plus a cooling array that's going to be close to 25% as big as the PV array regardless of what unit size they go for in the end.

If they settle on making e.g. 120 kW satellites, that would be about 400 m^2 for the PV and another 100 m^2 for the radiator.

Have you seen Real Engineering's analysis? https://www.youtube.com/watch?v=_qpdUNMt2yg

Yes; their video pertains to two specific proposals for the data centres, unfortunately I am finding that *all* the various proposals fail to make sense but for different reasons.

Yes but would these need to be in LEO? I would imagine that they would aim for farther orbits to spend a smaller percentage of their time in Earth's shadow

Perhaps there will be communications nodes in LEO with high bandwidth directional links to heavy compute nodes in higher orbits? At some point I would assume that the jurisdiction of the FCC no longer applies? Or maybe you use laser links?

I still cannot believe it's economical to have "data centers in orbit" but I guess the truth will be seen in whether or not it actually happens.

> At some point I would assume that the jurisdiction of the FCC no longer applies?

The FCC has regulatory jurisdiction for communications on US objects in space, regardless of distance from earth.

Depends how cheap they can launch them.

Even very optimistic estimates (by people who aren't Elon Musk) say it will take a decade to get the costs low enough to be worthwhile for LEO; higher orbits are much more expensive.

They would be as large as your average hyperloop capsule.