At some point, you look at a picture and think, it is seriously insane that we can do this. Behold: the Orbiter Discovery approaching the International Space Station, as seen from the ground:
I think I remember that scene from Star Wars!
This remarkable picture was taken by Rob Bullen on Saturday February 26 from the UK, using an 8.5" telescope. I'll note that's relatively small as telescopes go! But the ISS is now over 100 meters long, and if it's directly overhead (that is, the closest it can be to an observer on the ground) it appears large enough to easily look elongated in binoculars -- in fact, it would be big enough to look elongated to someone with good eyesight and no aid at all*! Still, images like this are difficult to obtain even with a carefully guided telescope equipped with a video camera.
Oh -- did I mention that Rob hand-guided his telescope for this shot?
This is a remarkable piece of photography involving excellent timing, good weather (it had been cloudy at Rob's location almost up until that moment), and luck. But the equation for luck is really just (hard work + preparation) x (time) x (statistical fluctuations).
Clearly, the "hard work + preparation" was the most heavily weighted factor for Rob, and it paid off for him handsomely.
[UPDATE: Another phenomenal astrophotographer, BA favorite Thierry Legault, has posted a stunning animation of an ISS/Discovery flyover on his website.]
* Here's some math for you: The minimum distance to the ISS if it's overhead is about 350 km. It's about 100 meters across, so, using the small angle formula, that means it's apparent size is about 1 arcminute (a degree is 60 arcminutes, and the full Moon is about 30 arcminutes in size). The unaided human eye, assuming normal eyesight, can resolve objects that are about that size, so as I wrote the ISS would barely appear elongated to someone with good eyesight, and would be easily resolved in binoculars. The farther it is from overhead, the smaller it would appear, so conditions have to be just about perfect to see it as more than a dot without binoculars.