What are the upper physical resolution limits on telescopes?

[BWV]

So if we become a Kardashev type II civilization, able to harvest all the energy and matter in the solar system what could we see through the massive telescopes that would be possible to construct? (say with a lens the size of Saturn). Could you get surface detail on extrasolar planets, for example?

 

[phyzguy]

Theoretically, yes. The theoretical angular resolving power of a telescope is given by θ = 1.2 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. The angle subtended by an object of size S at a distance d is just S/d. So with a telescope of size D, you could resolve an object of size S = 1.2 λ / D * d at a distance d. If you plug in the numbers, in visible light with a telescope the size of Saturn, on a planet 10 parsecs away you could resolve an object about 1.5 km across, so you could see surface detail nicely. Of course the technical challenge of building a telescope the size of Saturn are pretty huge.

 

[newjerseyrunner]

Size would not be the only consideration. The reason we launch sensitive telescopes into space is because the atmosphere distorts images. Software can help with that, but it's not as good as being above the atmosphere. Space isn't empty, gas, dust, warped space... all would limit the theoretical resolution of a telescope.

 

[BWV]

Cool, thanks. I do wonder if a few hundred years from now this kind of telescope is less of a challenge than interstellar travel. In theory, you could have the same kind of knowledge of our local area of the Milky Way as we do today of our solar system

So playing with this a more realistic 100 meter diameter lens in a space telescope could resolve a Jupiter-sized object at 1 parsec and a 1KM lens could see an Earth sized object at that distance

 

[russ_watters]

Size actually is not limited that way. With interferometry, it would likely be feasible with existing or near-term technology to use Earth's orbit as the baseline.

 

[newjerseyrunner]

What @russ_watters is referring to: https://en.wikipedia.org/wiki/Aperture_synthesis ... (I think.)

 

[litup]

The only thing you lose with aperture synthesis is light gathering power. You give that up using small telescopes placed far from one another where you gain the resolution of a mirror roughly the size of the distance between them. The light gathering power is then just the sum of the area's of the telescopes used. So you could theoretically make a telescope aperture the size of the solar system if you had one say at the distance of Pluto and another on the opposite side, then you would have a telescope with the resolving power of a scope about 10 billion kilometers across but with the light gathering power of just the scopes. That would give a resolution of one MICRON at one parsec:)

 

[Chronos]

Resolution is strongly related to angular diameter of the target vs aperature diameter. For extraterrestrial bodies it is hopelessly tiny. Even our best telescopes cannot resolve anything smaller than a few hundred meters on the moon.