Finding the position of an object 1800 years ago?

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The discussion focuses on the capabilities of the planetarium program The Sky, which can simulate the night sky from 4,700 years ago to 10,000 years into the future. The methodology behind this simulation involves using proper motions for each star, allowing for accurate positioning over time. Users are encouraged to explore the concept of proper motion, particularly in relation to familiar constellations like the Big Dipper, to understand changes over millennia. The program likely employs a combination of small incremental adjustments and a final leap to reach specific historical dates. Overall, the use of proper motion is essential for accurately determining the positions of celestial objects in the past and future.
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I use the planetarium program The Sky quite a bit. It's capable of showing the sky from -4700 years ago to 10000 years into the future. What's the methodology behind this? One giant leap, or small leaps of say 100 years to get there, with some last jump to the final date?
 
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I believe the answer is that proper motions are used for each star seen in the virtual sky.

Google proper motion big dipper. One of the first hits shows what happens to the big dipper over something like 10K years.
 

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