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Event horizon achieved earth-size telescope by using seperate telescopes around the world to interpolate an image of a black hole at resolution of 60 arcmicroseconds.

What resolution could we get if we built radio telescopes on the moon and used earth-moon orbit to interpolate an image? What could we see with it?

What if we used earth-moon-mars telescope?

Would it make sense to go even bigger?

This is all assuming we would have possibilities to build local telescopes like ones on earth in future.enter image description here

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According to Wikipedia, the angular resolution is inversely proportional to the baseline (the separation between the telescopes). The order of magnitude of the baseline of the Event Horizon Telescope is 10,000 km; the Earth-Moon distance is about 40 times larger, and Earth-Mars at its maximum 25,000 times larger. That means we could theoretically reach 1.5 arcmicroseconds (at this wavelength) with an additional telescope at the Moon, and 2.4 arcnanoseconds with Mars.

However, to obtain proper interferometry we need (regardless of the baseline size) to know the telescopes' precise location with the precision of a quarter of the wavelength. For 230 GHz radio waves, the wavelength is 1.3 mm, so the precision needs to be 0.3 mm. I suppose that this is incredibly difficult to reach for bodies moving through space.

I am not well-versed enough in the matter to say what the effect of arranging the telescopes in a line (on Earth-Moon or Earth-Mars scale, it's a line, unless you add space telescopes at e.g. L4 and L5 Lagrange points) vs. a grid like the Event Horizon Telescope is. But interferometry does work for two telescopes already.

Note that angular resolution is not the only metric you should consider; objects become fainter when you enlarge them, so you'll need more telescopes (and/or a longer exposure time) to get the same level of brightness in the pictures.

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A space based radio telescope has been tried, although I can see little evidence of it being successful.

To get an image you do need baselines at multiple angles, not just a single line. This can be achieved on Earth with just two telescopes by combining measurements made at different times as the Earth rotates, and an Earth-Moon baseline could be treated similarly over a month, although this would require the image not to change over that time and be limited to objects in the Northern or Southern parts of the sky.

You could probably get direct line-of-sight high-bandwidth laser and microwave communications between the telescopes for a significant part of each day, so some of the synchronisation problems would actually be easier than for Earth-based VLBI.

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