Astronomy experiments for amateurs
You should visit the Astronomical League site. They have several observational programs, ranging from naked eye to detailed telescopic spotting programs. I enjoyed the Double Star series myself.
http://www.astroleague.org/
It is a long time since I do not use the internet for this, but HobbySpace has several links to projects for amateur astronomers.
Hope that helped!
I haven't done these myself, but here's a few to consider:
- Measure the mass of Jupiter from the orbital period of its satellites (Io and Europa seem natural candidates since they're closer, so their periods are shorter and the measurement takes less time). You can either assume that you already have the radius or try a different number of experiments to measure the radius (this can also be given to different "teams" in a classroom and compare the results).
- Replicate Ole Romer's measurement of the speed of light. This one should take longer, though, so it might not be what you're looking for.