How much detail can telescopes actually provide?

For example, could the numbers / letters on a postage stamp in a randomly specified location be clearly visible from space.

This is to settle a discussion with a friend that piqued my curiosity.

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Here's a practical test, but it might be a bit too conservative: cloudynights.com/item.php?item_id=1354 – Florin Andrei Feb 22 '12 at 1:01
If you build a Dyson sphere-sized reflector, can you image a postage stamp from another solar system? – endolith Apr 17 '14 at 14:11

2 Answers

Two major issues here. Well, maybe three...

• Optical limits of the instrument. Think Rayleigh Criterion, but beware of the existence of interferometric methods (hard to do in the optical for now, but...). It's going to take a big lens to image the a postage stamp even from low Earth orbit, and you might expect to find a spy satellite a bit higher up than that.
• Stuff in the way. The "twinkle" you see in stars is related to atmospheric interference. There are methods to compensate. Trying to look through clouds in the optical is a lost cause.
• Is the platform stable? If your optics are not well isolated from any vibration of your platform the camera will jump around.
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Under excellent conditions, a telescope on Earth can see details with an angular size as small as 1 arcsec. This tells us that the greatest distance at which you could see a detail as small as a postage stamp (0.02 m or 2 cm) is about 4,126 m or around 4 km. So I infer that a telescope that is 4 km above Earth's surface could resolve the postage stamp (in excellent viewing conditions.) Now, I am guessing that the number on a stamp might be as big as 1/5 the width of the stamp, so the telescope would need to be 5 times closer, about 0.8 km. I used the small-angle formula to determine this. Reference: Universe (2010) Freedman, R.

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I'm not sure the analogy holds. When a ground-based telescope looks up, the thickest and most turbulent part of the atmosphere is close to the telescope, where small angular deviations are more important than angular deviations close to the target and far from the detector. A space-based telescope looking down is in the opposite (i.e., more favorable) configuration. So the diffraction limits of the optics may be a better metric of how good an earth-based scope can do. – Larry Gritz Feb 27 '12 at 18:14