Polaris Distance from Celestial Pole

If you've taken star trails photos facing north, or used Polaris to calculate latitude, you're probably aware that the North Star doesn't sit directly over the north celestial pole. But how far off is it?

My trails are a little wonky because my tripod was on a wooden balcony, 300mm zoom lens, field of view in this image is about 3.5°

In the above photo, Polaris is the brightest line in the center of the image. You'll notice that there are quite a few stars in between Polaris and the true celestial pole. However, none of these stars are bright enough to be reliably visible, and aren't used for naked eye navigation or basic polar alignment.

Polaris lies 0° 40' 37" from the celestial pole

Polaris' position in the sky is moving toward the pole, making it a better pole star by the day! In the year 2000, Polaris was located at 89° 15' 50.8", and is now (according to Stellarium) located at 89° 19' 23".

I thought it would be a relatively simple question to answer "how far is Polaris from the celestial pole" but now I've been looking up terms and reading about things like parallax, precession, nutation, aberration, and proper motion. Wow! So much to learn still.

So in the year 2000 at exactly noon (terrestrial time) on January 1st, the position of stars was calculated as the new standard for the next 50 years. This is called J2000.0 denoting Julian date 2451545.0 TT. I still can't find a good description of the difference between equinox and epoch, but nevertheless right ascension and declination are constantly changing, so the epoch servers as a standard starting point for calculations.

This is getting a bit heavy, so I'll wrap up by saying that since the reported "to date" position of Polaris is 89° 19' 23" all we need to do is subtract from the celestial pole 90° 00' 00", which (be sure to borrow units of 60) comes out to 0° 40' 37" (or 40 and 37/60 arc minutes = 40.6166 arc minutes).

Don't take my word for it, kids! I never took a class on this, I'm just sort of thinking out loud trying to figure all this stuff out.