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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.

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Have you seen Real Engineering's analysis? https://www.youtube.com/watch?v=_qpdUNMt2yg
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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.
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They would be as large as your average hyperloop capsule.
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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
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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.

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> 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.

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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.

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