Amateur astronomers have observed satellites and other space craft since the dawn of the Space Age. Video Astronomy is a rapidly growing segment of the amateur astronomy community and is yielding impressive results. Indeed, dedicated amateurs have even succeeded in obtaining high power telescopic images of the ISS and its predecessors with excellent resolution using home camera/video equipment and software.

When the Space Shuttle Columbia reentered the Earth's atmosphere during the STS-107 mission, amateurs astronomers were on hand to record its troubled flight. Photometric analyses of the better videos of the reentry were able to establish the timing of early spacecraft failure and provide data allowing for the calculation of sizes of some of the early debris pieces prior to the Columbia’s final breakup. This information helped to understand and confirm the early events leading to breakup. The STS-107 work is documented in the Columbia Accident Investigation Board report, volume 3, part 2, section 6.

Apparently, amateur video of Columbia breaking up was invaluable in the post mortem analysis. Here are some tips that they gave for shooting future reentries.

I'd also recommend looking at the section of the CAIB report linked
from here. The level of imaging science here is pretty amazing.

NASA - Space Shuttle Re-entry Video Procedures for Space Enthusiasts