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As David (AstralTraveller) mentioned, variable stars are a great avenue for study. Picking a variable star with a relatively short period (say a week or so) is one way to introduce you to star magnification determinations and they can be studied both via imaging or visible observation. Lots of physics involved in regards to orbital rates and inclinations.
Peter Williams of the Sutherland Astronomical Society is a wealth of information about observing variables if you decide to go this route.
Cheers,
Simon
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