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I'd flip your comment about optical surfaces: they need to be smooth, not continuous, and smoothness is actually not required either! The requirement is a consistent phase relationship, which allows the signals to add together nicely via interference. Rays coming from same direction take the same path to the detector and interfere constructively, while rays coming from different directions tend to cancel.

For optical frequencies, the phase is difficult to measure directly, so we instead polish the surfaces down to a fraction of the wavelength of light (so that it all has the same phase). For radio telescope, the frequency is a lot lower, and we actually can measure the phase directly, so we can make our sensors crazy shapes and adjust it by adding delay. If you can change the individual delays (say, via software) you can change how they interfere and therefore change the sensitive direction for your telescope. This is how phased arrays function.

Why is it difficult to measure the phase directly for optical wavelength as opposed to radio? Is it purely because the shift is smaller?

It's really fast. Visible frequencies are in the THz to PHz range, while radio frequencies are in the kHz. Modern electronics are fast enough to sample the latter but not the former.

Radio frequencies are in KHz to THz range. There is equipment already operating in sub-THz bands but not yet close to the frequencies of light.

sorry, yeah, thats a much better way of saying it and my smooth vs continuous was just confusing

Your comment was great! I'm not trying to correct you so much as adding additional context.

they would have to stay in very precise distances from each other over time

Is this necessary, or do they simply need to precisely distinguish their relative position? My understanding of the JWT's not-perfectly-smooth lens is that the ability to measure (and correct for) its distortions vastly simplified the construction, and I naively think the same principle could be used in a swarm of satellites.

So, wouldn't it still be easier to build a radio telescope from orbiting satellites than on the Moon?

This was already explained very clearly.

But it requires those different clusters of collectors to be stationary - so while you could probably build a swarm of satellites, they would have to stay in very precise distances from each other over time which would be considerably more difficult than planting them on a surface.

It sounds like the solution is to attach the satellites to some sort of frame that could be assembled in orbit by simple robots.

> difficult than planting them on a surface.

Even considering that the "surface" in question is the moon?

We know how to make thrusters. We don't know how to mine the moon and make a telescope from scratch.