Theoretical limits of telescopes

[Rainalkar]

Hello everyone, 

I have a question maybe you could help with. I was wondering what are the theoretical limits of telescope zooming, especially in visible wavelengths? 

For instance, is it possible to magnify the surface of a hypothetical planet in the Alpha Centauri system to about 100 km resolution? Or more? And if no, why? Assume that the media is always interstellar space, a few atoms per cubic metre, disregard the possible asteroid belts etc. Like the telescope is placed outside the heliopause.

I've read a bit about the Focal proposal. Should such a telescope be made, what would it's limits be? 

And lastly, I assume that there has to be some hard limit based on what we know? Telescopes cannot be artificially big; at least not that big that there own gravity comes into the picture.

Thanks

[cantab]

It's referred to as the Rayleigh criterion or as Dawes' limit, the former being theoretical while the latter's an empirical figure. It depends on the size of the scope and the wavelength being observed.

If we could build a big enough interferometer - a network of telescopes spread out - we could have as small a resolution as we wanted. The Rayleigh limit applies as though the aperture was the area the network spans. We've built radio interferometers spanning the Earth, but everything needs to be so much more precise for visible light.

FOCAL is a quite different approach, using gravitational lensing, and the capabilities are extensively discussed here: http://www.centauri-dreams.org/?p=785

[Rainalkar]

I've read into the article explaining FOCAL and the criteria but they do not offer practical explanations relating to my questions. You said that there is no limit. Perhaps you could provide figures what kind of a telescope (array) we need to make to be able to, for instance:

1. distinguish relief on a hypothetical planet in the Alpha Centauri system

2. same thing, but a planet is in the Andromeda galaxy

And lastly, what is the best resolution we can get at the moment when looking at the a) Moon Mars (when it is closest)? Use the figures for the most powerful optical telescope on Earth or in Earth's orbit.

I am really interested in these things, but my background isn't sufficient to deduce the answers to my questions.

[acey]

a = Distance to Alpha Centauri = 4.4 light years = 4.1 x 10¹⁶ m approx.

b = Diameter of Earth  = 1.3 x 10⁷ m approx.

c = Angle subtended (at Earth) by an Earth-sized planet at the distance of Alpha Centauri = 2tan^-1(b/a) = 1.3 x 10^-4 arcseconds approx.

D = telescope aperture in inches such that c is the Dawes limit = 4.56/c = 34862 = roughly half a mile.

That's just to resolve the planet as a disc, never mind see relief on it. Move the planet to the Andromeda galaxy and you need to multiply the aperture by about half a million.

I don't know what the best current telescope resolution is: for ground-based telescopes the atmosphere limits it to just under an arcsecond but adaptive optics can improve on that. Suffice to say that no optical telescope on Earth or in orbit can resolve e.g. the Apollo moon lander.

Apparently the Hubble Space Telescope could theoretically resolve lunar features down to about 40 metres.

http://www.spacetelescope.org/about/faq/

[Cath]

If we could build a big enough interferometer - a network of telescopes spread out - we could have as small a resolution as we wanted. The Rayleigh limit applies as though the aperture was the area the network spans. We've built radio interferometers spanning the Earth, but everything needs to be so much more precise for visible light.

Just to add. We do gain angular resolution with the method, but we don't gain the same amount of increase on the magnitude scale. This is due to their being no photon/RF collection in the space between the nodes (telescopes). But that's not a problem if what you're looking at has enough brightness/emission.

[Cath]

Apparently the Hubble Space Telescope could theoretically resolve lunar features down to about 40 metres.

Their is a method called SuperResolution (also known as drizzling) that I guess could be used to extract fine sub-pixel detail, but it requires lots of images and actual physical dithering of the optics/camera.

[Rainalkar]

Really interesting. For instance, say that we take the telescope you described and point it to Mars. What would our resolution be?