Among stars you can see (which depends on latitude on earth, sky conditions, and power of your telescope if any), which has the largest proper motion?
Lifetime scale project: document a star moving over the course of your life. Perhaps choose a star close to the celestial equator in case you move hemispheres (though that'll still be a problem if you move close to the poles). Mark where the star was on important dates of your life.
Or, communal telescopes could periodically photograph a star and make the pictures available to everyone. This is probably already being done.
Documenting the movement in the sky of Uranus (orbital period 84 Earth years) or Neptune (165 years) would be less difficult projects.
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