Because the practical ability to travel to distant star systems is
limited by the speed of light a possible alternative would be to
inspect these places using space based telescopes. As technology
improves in the coming centuries the human race may be able to
construct some very large space based telescopes. This question is not
about how this will be done but about how big these telescopes must be
to achieve sufficient resolution to see distant star systems. What I
would like to have from your researches is a chart with the following
information:

Y-axis = distance from our spaced based telescope in light years

x-axis = telescope diameter (assume a reflecting type telescope) in feet.


Plot on this chart the following points:


Diameter of telescope needed to resolve disk of nearest star.

Diameter of telescope needed to resolve disk of earth size planet in
orbit around this star.

Diameters of telescope needed to resolve surface features of varies
sizes on this planet.

Don't have time to build the chart right now so I'll leave this open
to another researcher, but as a quick note I will mention that you
would need a 40 meter diameter mirror to resolve any details on the
surface of Proxima Centauri which has an angular diameter of about 1.8
millionths of a degree from this distance.

But what you have missed is that this size scope isn't necessary -
large mirrors are needed to gather more light, not achieve greater
resolution.

Since nearby stars are bright enough to see easily you would actually
use two relatively small mirrors placed 40-50 meters apart which would
give the resolution you need without the impossibly large size of a
single mirror.

Hello,

   siliconsamurai, you said:

"large mirrors are needed to gather more light, not achieve greater
resolution"

   This isn't correct. Large aperture is required for high resolution.
The reason why multiple smaller mirrors can be used in place of a
single large one is that the larger aperture can be "synthesised" by
carefully interfering the simultaneous signals from the smaller ones.
A tradeoff is that the total light collecting area of the smaller
mirrors will be less than that of a single uninterrupted mirror,
having a diameter equal to that of the separation (baseline) of the
smaller ones, and so longer exposure times are necessary.

   Synthetic large apertures have been used commonly in radio
astronomy for several decades. The largest one of course is the Very
Large Array (VLA), near Socorro, New Mexico. Optical bandwidth
interometers are more demanding due to the smaller wavelengths, and
only in recent years have any gone online.

   Also, there are ongoing plans to deploy a very large baseline
space-based interferometric optical telescope in a few years, which
will be capable of resolving images of extra-solar planets.

excerpt from an article in New Scientist recently;

----------------

Turn off the star to see the planet
 

ALMOST every extrasolar planet discovered so far has been detected
indirectly by measuring the wobble it induces in its host star.
Spotting a planet directly is a huge challenge because the star is at
least 10 million times brighter and completely overwhelms any light
from the planet. But a simple device called an optical vortex could
help astronomers blot out the starlight and bring planets into focus.

So far, attempts to see planets directly have involved positioning a
small opaque disc in a telescope so that it blocks out the star's
light. But light from the star can still bend round the edges of the
disc, creating bright diffraction bands that swamp signs of the
planet.

Now Grover Swartzlander, Gregory Foo and David Palacios from the
University of Arizona in Tucson think that the starlight could be
removed using a helical mask with a series of steps etched into a
transparent material (see Diagram). Light travels more slowly through
the mask than it does through air. And because some parts of the mask
are thicker than others, it creates a phase difference between the
light that travels through the various sections. When the phase
difference between the thickest and the thinnest parts is exactly two
full waves, something unexpected happens: light in the central core
destructively interferes, creating an "optical vortex" that has a dark
core with light spinning out into a bright ring around it.

The mask can block out the starlight, leaving a dark core that acts as
a window through which a planet's light can pass (Optics Letters, vol
30, p 3308). The vortex will work only with powerful telescopes
capable of resolving the star from its planet, so that the light from
the planet and star come in at different angles. In laboratory trials
using lasers to mimic a star and planet, the vortex mask cut the
"starlight" by factors of between 100 and 1000 without blocking any of
the planet's light.

But there are limitations. The pitch of the helical mask determines
the wavelength of light that it will block out. Essentially each mask
works for only one colour. For the technique to be practical,
Swartzlander says that the mask would have to work over a wider range
of wavelengths. Also, the mask's optical quality must be improved.
"But these are the first experiments to demonstrate the basic idea,"
Swartzlander says. "Theoretically, our technique would make an
arbitrarily dim planet visible."
?The mask blocks the starlight, leaving a dark core that acts as a
window through which a planet's light can pass?

His team hopes the vortex might be useful for projects such as NASA's
Terrestrial Planet Finder (TPF). But Steve Kilston of Ball Aerospace
and Technologies in Boulder, Colorado, a company contracted by NASA to
work on the TPF design, says the mask's single-colour results do not
come close to demonstrating the performance needed to see the
multicoloured light from a faint planet.
From issue 2529 of New Scientist magazine, 10 December 2005, page 19

here is an article from Scientific American that uses a similar
technique to improve resolution.

http://www.scientificamerican.com/article.cfm?chanID=sa003&articleID=000DAB63-D062-13A9-906283414B7F0000

the idea being it is not so much the size of the scope any more but
the technology behind it. Of course a larger scope would gather more
light and improve results but no longer are the results contrained to
the light gathering capabilities of scopes, we can now see much
farther using yesterday's scopes and today's technology. There is no
reason to think that the trend wont continue.

Elí

Large mirror "surfaces" such as large diameter round mirrors are used
to gather more light. Higher resolution can be obtained by a line of
small mirrors which generate almost the same resolution as an entire
mirror of that full diameter.

If this weren't true then the VLA wouldn't work.

"Large mirror "surfaces" such as large diameter round mirrors are used
to gather more light. Higher resolution can be obtained by a line of
small mirrors which generate almost the same resolution as an entire
mirror of that full diameter."

   Yes, that's what I said, with the exception that arrays are
connected interferometrically. Otherwise they'd just be a bunch of
smaller independent mirrors.

I figured someone asking such a question would understand that - I
don't go into extensive detail unless I am actually answering.

Check out the latest issue of the Discover magazine.