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How about something to do with sun spots. e.g. clusters, or the speed with which they traverse (determine the sun's speed of rotation?), maybe at different latitudes of the sun, etc (I'm thinking friendly daylight hours; observations made over a reasonable time frame, etc.)
Or, keeping it simple, what about Eratostenes' classic experiment, measuring the length of a stick's shadow at different latitudes at noon on the same day to estimate the diameter of the earth. An oldie but a goodie.
I don't suppose there any easy and accessible astronomical objects that can use the Earth's movement to establish parallax effects??
Good luck, anyway.
Brian.
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