If, for instance, Hubble's camera was a $10^{300}$ times better, could it see a distant star in details, or is there a limit to the amount of light that reaches the Earth's orbit or perhaps does the light get distorted on its way so you must come closer?

Is there a limit to the number of light beams that hit a telescope camera's "eye" or if you built a huge telescope would you then be able to see that distant star in high detail (for instance, see an earth size satellite around Betelgeuse's orbit).

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    $\begingroup$ This is a really interesting question. First guess is that for an arbitrarily large, arbitrarily excellent telescope this may be possible for nearby starts (that there be no limit to the diffraction limit). But for stars very far away, there may be blurring along the way due to effects we don't normally think about. $\endgroup$ – uhoh Jan 8 '19 at 5:28
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    $\begingroup$ We're already trying to do this kind of thing. Here's a link to a story of one experiment using the ESO's Very Large Telescope Interferometer (VLTI). I doubt anyone will try doing this with a single telescope. The key word here is interferometer. $\endgroup$ – StephenG Jan 8 '19 at 9:36
  • $\begingroup$ It would be helpful if you could quantify "distant". In human terms, any star other than the Sun is pretty distant, but in fact the distances to stars we know about vary by factors of billions. A @StephenG said, we are already trying to image (as points of light) Earthlike planets around relatively near stars, but if you wanted to detect, let alone examine in detail, such a planet in one of the more distant galaxies we have observed, there might be dust and gas in the way that would make it impossible, no matter how large or good your telescope. $\endgroup$ – Steve Linton Jan 8 '19 at 15:36
  • $\begingroup$ @SteveLinton for instance Betelgeuse, could you see in detail a satellite around Betelgeuse? Or is the "information" lost on the way? $\endgroup$ – Guy Jan 8 '19 at 16:15
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    $\begingroup$ xkcd.com/1276 may or may not be relevant. At some point, I think angular size would be a limiting factor. $\endgroup$ – user21 Jan 8 '19 at 18:02

The only limitations would be related to building an instrument large enough.

There's a limit to the size of the finest detail a telescope can see. "Size" here is angular size, the angle that the detail is covering in the visual field. For a given wavelength of light, the smallest angular size depends on the aperture (diameter) of the telescope in a linear fashion: double the aperture, and you cut the angular size in half.

Rule of thumb: 100 mm aperture has a resolving power of 1 arcsecond, for visible light (not exactly, close enough). Therefore 200 mm aperture has 0.5 arcsec resolving power, etc.

By building larger and larger telescopes, the angular size of the smallest details becomes smaller and smaller. But are there any limits here?

There aren't any cosmologic mechanisms that I'm aware of that would prevent telescopes from operating at arbitrarily large resolving powers (arbitrarily small angular sizes). But we can't build arbitrarily large instruments.

The biggest monolithic (single mirror) telescope has an aperture of 8.4 meters. Using segmented mirrors, the aperture aim of the current largest project is 30 meters - the Thirty Meter Telescope, still in a very early stage, completion date unknown.

Beyond that size, large scale interferometers are the only option, with synthetic aperture varying from dozens of meters to kilometers, and larger projects are being discussed.

In theory, very large scale interferometers could be built in space. But there might be inherent limits for the aperture of such systems. Anyway, this is hypothetical.

EDIT: Giant telescopes in general do not require a continuous surface of glass. Interferometers almost by definition do not use a single reflector. You could build a gigantic telescope or interferometer where the active reflective surfaces are just these tiny chunks at the periphery of a huge perimeter. Most of the area in between is empty / unused.

EDIT2: The performance of the "tiny chunks" reflector is not the same as the performance of the full size mirror, as mentioned in the comments.

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    $\begingroup$ oddly, almost related to a recent question - astronomy.stackexchange.com/questions/29082/… $\endgroup$ – Carl Witthoft Jan 8 '19 at 20:39
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    $\begingroup$ Very clear and detailed answer. So basically the visual "information" is around us but it is hard to capture because of the inverse proportion between angular size and aperture. So if a 1 meter^3 satellite is orbiting Betelgeuse and has a license plate, the light radiating from Betelgeuse (0.05 arcsecond, 1.4*10^8 m diameter) will hit the plate and travel 640 years in the space-time continuum and according to the rule of thumb, if we had a telescope with an aperture of 2.8 million kilometers we could read the license plate, right? :-) $\endgroup$ – Guy Jan 8 '19 at 23:40
  • $\begingroup$ Now I understand the frustration of being a scientist... information (aka "the truth" about the nature of things) is all around us but is inaccessible... $\endgroup$ – Guy Jan 8 '19 at 23:40
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    $\begingroup$ @Guy I made an edit addressing one of your observations. $\endgroup$ – Florin Andrei Jan 9 '19 at 0:19
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    $\begingroup$ There are 9 telescopes Wikipedia link with monolithic mirrors in the 8.1 to 8.4 meter range (the two Gemini telescopes, four ESO VLT's, Subaru and the Large Binocular Telescope) so I wouldn't say they are "very difficult to make and operate" (You may be referring to the Soviet BTA-6 meter which is a much older telescope and which did indeed cause a lot of problems) $\endgroup$ – astrosnapper Jan 10 '19 at 0:04

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