computational amateur astronomy?

I've been thinking about getting started in amateur astronomy. However, I'm from the computer science area, and as such I love computing/calculation. I've been disappointed because most amateur astronomy books just focus on looking at things. I would also enjoy calculating things. Is it possible with amateur equipment to make any sort of meaningful calculations? Distances, speeds, anything? I imagine so, since Kepler and Newton probably had less equipment and was able to determine the laws of planetary motion. Anyway, I was curious if anyone knew of a good beginner book or website that shows how to re-make such classic calculations or do any other kind of computational astronomy.

Thanks!

Jon
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