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Name: JP Reed
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I am doing a project on astronomy and positions of the stars/constellation. My question is how accurate are the formulas that we use to figure out the positions of the stars when they are applied to 2 or 3 millennia into the future. Are those positions that we say they will be in 2500 or even 3500 (if we are still around) as accurate as those that we predict for next year?

What you are asking about is the "proper motion" of stars. Only the closest stars have appreciable proper motion; the largest known is for Barnard's Star with a proper motion of: "an excep- tional 10 arcseconds per year" (60 arcseconds = 1 arcminute, 60 arcminutes = 1 degree, both the Sun and the Moon subtend about one half a degree in the sky as seen from the surface of the Earth [which is why we have such spectacular total solar eclipses!]). So, Barnard's Star will move about 3 degrees in a thousand years. Most stars have a proper motion much less, and their change in position in the night sky over one or two thousand years will not be noticeable to the naked eye.

To actually answer your question (finally!), the formulas used to predict a stars position are very accurate over time scales of a few thousand years.

The reference for the quote in the previous response is: "Introductory Astronomy and Astrophysics" by Smith and Jacobs, 1973


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