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