swa66 - 7:34 pm on Mar 17, 2009 (gmt 0)

Spy satellites use a low earth orbit, I'll presume anything up in space gets nearly superhuman care in construction (so the lens will be as good as it can be). Yet, I still think their resolution is limited by turbulence of the atmosphere, not lens quality nor diffraction limits.

The diffraction limit of e.g. the Hubble telescope (with a 2.4m main mirror) is 0.1 arcsecond (after it got its sight corrected), a 4 meter mirror would likely be possible to launch (KH-13 is rumored to have a 4 meter mirror)
The Rayleigh limit would be 138/4000 arcsecond or 0.0345 arcsecond for a perfect mirror. Similarly, the Dawes limit would be 116/4000 or 0.029 acrsecond.

On to converting arcseconds to degrees:
- 0.1" (actual hubble) is 2.77777778×10^-5 degrees
- 0.0345" (Rayleigh for 4m) is 9.58333333×10^-6 degrees
- 0.029" (Dawes for 4m) is 8.05555556×10^-6 degrees

At an altitude of 600km (to get a sun synchronous orbit) [we need to sun to shine, same angle helps as well if there's a pesky cloud to redo it the next day]
- 0.1" -> 29cm
- 0.0345" -> 10cm
- 0.029" -> 8cm

8cm is about enough to be able to tell if that's one or two baseballs sitting right next to one another in your yard.

But this discounts the turbulence of the atmosphere.

(current) Google earth images aren't satellite images AFAIK, they're made from an airplane (not flying that high), it does away with the turbulence in the atmosphere and those virtually perfect lens needs.