🚀 go-pugleaf

In reply to Dale Amon's questions "What are the theoretical limits to
the distance at which they [planetary details] can be seen by an optical
scope? What is the relationship between the scope size and the distance
to the interesting surface feature?"
The theoretical limits for optical telescopes:

resolution size = distance/(diam * 46000)
where telescope diam is in inches, and the distance and size are in any
units, so long as they are the same units.

A single object has to be at least the resolution size to detect that it
has any size at all.  A smaller object that is bright is easily seen
(otherwise the night sky would be blank except for the moon), but is
seen as a dot that appears the size of the theoretical resolution.  An
object would have to be twice the resolution size to see the grossest
detail (for example that the left side is black and the right white).
Two objects of equal brightness have to be separated by the resolution
size to even see that they are not a single object.  If one object is
much brighter (as in a star with an orbiting planet), then the
separation may have to be tens or hundreds of times greater, else the
brighter one swamps the dim one with a spread-out overexposed image.

Putting real numbers in, say the largest optical telescope on earth and
the nearest star, we get resolution of 2.4 million miles.  But no
telescope of substantial size on the ground achieves its theoretical
resolution (because the atmosphere messes it up), and we haven't
launched anything of substantial size above the atmosphere.  The space
telescope will be 2.5 times worse than these numbers (because its size
is 2.5 times smaller than the big Russian telescope), but will achieve
essentially the theoretical resolution, much better than the achieved
resolution of bigger telescopes on earth.

So what we are talking about with the space telescope is possibly seeing
very bright planets hundreds of millions of miles from the very nearest
few dozen stars.  To be in the ballpark of seeing continents on planets
of only the nearest star requires a telescope mirror of tens of miles
diameter, something not likely in our lifetimes (historically, since
Galileo, we have taken roughly 40 years for each doubling of the size of
the largest telescope, and there is no indication yet that this rate is
changing even with our present technology explosion).  Remember that a
mirror has to be VERY stiff; no point on it can move more than a few
millionths of an inch from the correct curve, or you lose the
resolution.  The only outside hope I see is some form of interferometry,
in which you use two or more mirrors, and use their separation in place
of the diameter in the above formula.  

Or we could take a reasonable sized telescope and send it closer to the
star in question; but it would require thousands of times closer, which
is essentially a visit to that star.  A visit to a star is energy-wise
roughly 100,000 times harder than the TAU mission, the latter being
barely within our technology soon.

Other questions:
"Are there quantum effects that will limit resolution?"
No, the above formula is an effect of the wavelength and wave properties
of visibile light.

"How much effect does intersteller dust and gas between us and the
object have on theoretical resolution?"
Essentially no effect at the distance of planets of the nearby stars,
which are already beyond our observing limits.  These nearby stars are
in a neighborhood that comprises less than 1/1000 the size of our
galaxy.  At a substantial fraction of the way across our galaxy, in the
dirtiest directions, dust and gas become a problem.  Also, there are a
few small pockets of stuff at distances of hundreds of light years, but
these are still beyond the nearby stars.  Dust and gas do not degrade
resolution, just contrast, and eventually completely block any view.

In conclusion, optical detection of planetary detail is MANY orders of
magnitude beyond what we can do.  So don't hold your breath.  I would
guess rocket probes to stars will happen first, and I don't think we are
close to doing that.  Then we could always try finding the radio signals
of some civilization that might be happy to describe their planets to
us.

/Don Lynn