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I want to try confirm my thoughts on the position of Thuban (Alpha Draconis) in relation to the Northern Ecliptic Pole (NEP). I have been asked to specify how many degrees Thuban is from the NEP today and then 5000 years ago (when it was earths north star).

From everything I have read it seems to me that the ecliptic and NEP is fixed in relation to the stars, as it corresponds to the plane in which the earth travels around the sun. So would I be right in saying in my answers that the distance from the NEP to thuban hasn't changed in 5000 years?

I am aware that the position of the stars change in relation to the Northern celestial pole, but was specifically asked about the ecliptic pole.

Also as mentioned before, I am being asked how many degrees from the NEP thuban is, I am tempted to say zero as the NEP lies in Draco which thuban belongs to, so it can't be that far? Or is there a way of knowing how many degrees it is from the NEP that I am not quite understanding?

Would appreciate anyone leaving their thoughts. Thanks

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    $\begingroup$ I do not know which constellation is the smallest, but I do know that even the smallest constellation is larger than 0 degrees. To assume the distance from Thuban to NEP is 0 just because they are in the same constellation is flawed. $\endgroup$
    – JohnHoltz
    Feb 1, 2022 at 17:27
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    $\begingroup$ yes I knew this was flawed really, it was just a stupid approximation relative to the grand scheme of things. I will try work it out properly $\endgroup$
    – v_ecila
    Feb 1, 2022 at 18:09
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    $\begingroup$ Not that I can add much, but the smallest constellation is Crux Australis. $\endgroup$
    – Jim421616
    Feb 3, 2022 at 1:36
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    $\begingroup$ The ecliptic plane isn't fixed, but the variation in its inclination is ~1% of the Earth's axial precession. See astronomy.stackexchange.com/a/19594/16685 $\endgroup$
    – PM 2Ring
    Oct 30, 2022 at 1:54

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Answering your third question: look up RA and declination for the North Ecliptic Pole and Thuban. Then solve the spherical triangle with vertices at those points and the Earth's North Pole. The angle at the pole is equal to the difference in their RAs, and the two sides meeting at the pole are equal to 90 degrees minus their declinations. Having done that, I found Thuban and the North Ecliptic Pole to be 23.64 arc degrees apart.

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    $\begingroup$ 53 degrees sounds too large to me. 23.5 sounds more realistic. $\endgroup$
    – JohnHoltz
    Feb 1, 2022 at 18:27
  • $\begingroup$ You're right. I'll edit my answer. I didn't follow my own method, I used declinations rather than 90 degrees minus declinations. $\endgroup$
    – stretch
    Feb 1, 2022 at 22:48
  • $\begingroup$ @JohnHoltz do you have a shortcut method for the calculation? Your saying "sounds more realistic" sounds like you were using a rule of thumb. $\endgroup$
    – stretch
    Feb 1, 2022 at 23:04
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    $\begingroup$ As expected, this value is close to the inclination of the ecliptic which also measures the Earth's axial tilt from the line perpendicular to its plane of revolution. $\endgroup$
    – Barry Carter
    Feb 2, 2022 at 14:39
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You probably want to consider the proper motion of the star - it's easy to think of the night sky as just a big, static image, but since stars are moving at various speeds and directions relative to us, they move at an angular speed known as "proper motion". This is usually quite slow, but can be as high as 10.3 arcseconds/year in the case of Barnard's star. Thuban has a proper motion of −56.34 milliarcseconds/year RA, and 17.21 milliarcseconds/year declination. So, over 5000 years, that's a move of -281.7 arcseconds RA, 86.05 arcseconds declination. Of course, that assumes proper motion is constant over 5000 years.

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