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Which model is used to define the polar axis?

To realize one promising adjacent problem (self-manufacture of a grid for a pole finder), I need the exact coordinates of the Polar Star. I decided to use data from Sky Safari 6.8.6.15 Pro. A friend has a Stellarium. I asked to see the coordinates of this star for different eras (today in 2022 and in 30 years at 2052). Found that the coordinates do not match for the same time and differ by several tens of seconds. As a result, I doubt that the correct model of the sky and celestial equatorial coordinates was chosen for both programs. What do you take and from what sources? How is precession calculated? I bring a screenshot. Above the coordinates of Stellarium, and below - SkySafari and differences. What can I believe?

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    Michael Grehov

    There has been no response from developers for more than a month. Sad. Can you appoint several moderators for community?

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