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Suppose an astronomer gave a 1 m radio dish to 500 people scattered over the face of the Earth and connected them to the internet. The people are directed to set their radio antennae up in their backyard per given instructions. The astronomer would then control the array of radio antennae remotely via the internet.

Could such an array of radio dishes be used to do any kind of meaningful astronomical interferometry? If so, what kind? If not, why not?

I fully expect that the radio dishes wouldn’t hold a candle to the sensitivity other radio dish networks (EVT, VLA, EVLA, etc.) due to the tiny dish size. I expect time synchronization would be an issue, but perhaps they could find a clever way to synchronize. I imagine this array would have very high resolution due to the large number of large and small baselines — extended further by the Earth’s rotation. Between low dish sensitivity, large numbers of dishes and a huge baseline count, I’m curious what such a network could be capable of.

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Partial answer:

I imagine this array would have very high resolution due to the large number of large and small baselines

and

I expect time synchronization would be an issue, but perhaps they could find a clever way to synchronize.

The 1 meter dishes are small and so for the dish to have any relevance to the project the wavelength has to be a lot smaller.

To do interferometry your synchronization will have to be extremely good; a 3 cm wavelength would be 10 GHz and the period is 0.1 nanosecond. You'll need to have all kinds of expensive and sophisticated electronics to maintain a stable and drift-free timebase at that level of accuracy.

You might be able to leverage your long baselines but fairly wide fields of view for these small dishes by using timing somehow. If you had ten distant dishes each pointed in 50 different directions and there was a sudden event, you might be able to localize it by arrival time differences, a bit like how lightning detectors work.

I don't know anything about it, but there is also something called intensity interferometry but it's not clear if that's actually helpful at all. See Hanbury Brown and Twiss effect and (paywalled) R. Hanbury Brown, R.Q. Twiss (1954) LXXIV. A new type of interferometer for use in radio astronomy

A new type of interferometer for measuring the diameter of discrete radio sources is described and its mathematical theory is given. The principle of the instrument is based upon the correlation between the rectified outputs of two independent receivers at each end of a baseline, and it is shown that the cross-correlation coefficient between these outputs is proportional to the square of the amplitude of the Fourier transform of the intensity distribution across the source. The analysis shows that it should be possible to operate the new instrument with extremely long baselines and that it should be almost unaffected by ionospheric irregularities.

See Boffin : a personal story of the early days of radar, radio astronomy and quantum optics

See also Dainis Dravens' 2010 BOSON INTERFEROMETRY From astronomy to particle physics, and back especially the radio part.

Only somewhat related, with some discussion of the effect before going on to discuss the optical implementation (but using electronic correlation): Intensity interferometry: Optical imaging with kilometer baselines

I wrote a related answer here: https://astronomy.stackexchange.com/a/42131/7982

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