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In Guizhou Province, China, the worlds largest radio telescope is almost complete, measuring 500 metres across.

I am aware that todays largest optical telescope require very accurate figuring and that the longer wavelengths of radio waves allow more leeway in the figure of the dish, but I don't know what degree of tolerance we can "get away with" and still obtain useful data.

My question is: I am sure there a wavelength dependent formula for the accuracy required of the surface and I wonder what it is? Bearing in mind that the:

dish is 500 metres in diameter and the aim of the the telescope will be to search for ancient signals of hydrogen, 21 cm, one of the building blocks of the early Universe - to try to understand how the cosmos evolved. It will also be hunting for new stars - in particular a rapidly rotating and extremely dense type of star called a pulsar - and it will even join the hunt for extraterrestrial life.

In the comments below, CuriousOne was good enough to provide the answer (am I kicking myself? Yes) so if I could refine this question to ask: how great an increase in resolving power does this new telescope potentially have over the 305 m Arecibo telescope? Or is comparing their performance more subtle than that?

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  • $\begingroup$ I would venture to guess that since they are not trying to actually form a diffraction limited image, the requirements are not nearly as strict as on an optical telescope, which would be about $\lambda/20$ for high quality mirrors and maybe $\lambda/4$ for really crappy ones. Now, how hard is it, really, to achieve maybe 5cm accuracy over 500m? A person with a tape measure and a cheap laser pointer can probably do that. $\endgroup$ – CuriousOne May 30 '16 at 6:57
  • $\begingroup$ @CuriousOne that's my curiosity sorted, thanks very much. So the hard part is building it, even then basically, given enough chicken wire..... $\endgroup$ – user108787 May 30 '16 at 7:12
  • $\begingroup$ I was told that when the Chinese built their German designed Transrapid Maglev from the Shanghai airport to the city they were told by the Germans that each part of the track had to be adjusted individually to achieve the required evenness. The Chinese though that this was a wasteful and expensive system and decided to forgo the procedure. Rather than pour the parts individually, it's said, they poured large fractions of the entire track at the same time, achieving a superior result. Whether it's true... who knows, but I don't think they will have trouble getting this thing even. :-) $\endgroup$ – CuriousOne May 30 '16 at 7:43
  • $\begingroup$ @CuriousOne that's the trouble with being self taught, and having absolutely no experimental experience, I have basic physics knowledge gaps wider than this dish, as illustrated in this post. $\endgroup$ – user108787 May 30 '16 at 8:03

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