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Centering The North Star

Once pointed at it it should stay there for tens of thousands of years at least.
Earth's axis of rotation wobble (precession - a 25,770 year cycle) and Polaris is just a star we can see at this point in time that is close to the point in the sky Earth's rotation is pointed at. The point in the sky Earth's rotation axis points to will soon start moving away from Polaris.

The star Alrai (Gamma Cephei) will be the 'north star' 100 or so years from now.
Some 3000 years ago the star Thuban in Draco was the 'north (or pole) star'.

By the way - the 2 stars that form the back of the Big Dipper dipper - Megrez and Phecda - point to Thuban in the same way Dubhe and Merak at the front of the dipper point to Polaris.
 
It would help to know what camera model you are using. Both Canon and Sony support "exposure simulation" when in "live view" mode. So you pu the camera in live-view mode, crank the ISO to max, crank the shutter speed to longest exposure (it's usually 30 seconds before going to "bulb" mode) and lowest possible aperture (based on the attached lens). This will usually brighten the stars enough that you can see them.

Use the live-view zoom feature to zoom in to 5x or 10x and help put the star where you want.

If you want star trails, then it doesn't much matter where Polaris is located within your frame -- that's "fielder's choice" ... wherever you think you want it. If, on the other hand, you're trying to use a tracking head for a long exposure of the sky without star trails, then the alignment of the tracking head does matter -- but it really just matters that the tracking head is aligned and not the camera (you can point the tracking head at the pole but point the camera elsewhere.)

BTW, Polaris is roughly 2/3rds of a degree off the north celestial pole -- it's technically not true north. That 2/3rds of a degree may not seem like much... but the width of the moon is typically 1/2 degree from edge to edge. That means if you could move the position of the moon in the sky then it would fit rather comfortably between Polaris and the true north celestial pole.

If you were to draw a line from Polaris to Kochab (Kochab is the name of the star at the opposite end of Ursa Minor - aka the "little dipper" -- at the end of the "bowl" of the dipper) then the true NCP is located on that line, 2/3rds of a degree away. It's getting closer to the true pole and at the end of this century it will only be about 1/2º away... and then it'll start moving away again.

Tracking heads intended for astrophotography use typically include some type of alignment scope with a reticle marked to help you find the "true" north celestial pole.
 
I've heard about these mounts that can track things across the sky but isn't the thing about the north star is that it doesn't change position. Once pointed at it it should stay there for tens of thousands of years at least.

I think the telescope mount is probably best especially if you're trying to get it exactly lined up. To be clever, (you can find it anyway) but can't you point north and then based on your latitude go up a certain number of degrees maybe with a tripod that has degree markings. Likely not as exact as eyeballing it or being able to line it up on the dot or even hip firing.

Lastly zooming apparently doesn't help? and maybe the little lights inside the view finder with your settings are enough to prevent you seeing the stars, can they be turned off?

Assuming you don't want star trails (some people want them) then you could use an equatorial telescope mount (with appropriate dovetail bar to mount to the bottom of your camera), or you can use a tracking head that can mount to any photographic tripod. The tracking heads are typically more "portable" because equatorial telescope mounts that are motorized tend to be bulky and require their own tripod -- which tends to be much larger and heavier than a photo tripod.

If you use a telescope mount then it MUST be an "equatorial" mount (this is very important... you cannot use a alt/az tracking mount because they experience field-rotation and that will smear/blur the image. Such mounts are great for visual use with a telescope but no good for astrophotography.)

In "tracking heads", probably the favorite with respect to value for the money is the Sky Watcher "Star Adventurer" -- but you would want the "astro" package that includes the declination plate, counterweight bar and weight, and the tripod wedge. The whole kit will cost around $400. This is a fairly new product on the market (probably within the last year).

For around $300 there's the iOptron SkyTracker but the quality isn't as good as the Star Adventurer. The iOptron used to be the favorite based solely on price. The "Star Adventurer" is about the same price for the "photo" package, but a bit more for the "astro" package ... but this package is so much better that it would be foolish not to get it (if what you intend to do is astrophotos) and the quality is better (it can handle heavier loads, it's easier to use, it's got a better design, etc.)

At the high end there's the Losmandy StarLapse (that'll run around $600) and there are some accessories that could take that cost up to $900. Losmandy is a machine shop so this is a machine-tooled head and very high quality -- nothing is plastic or mass-produced (well... the handbox is plastic, but the head itself is all machined metal.) It can handle the most weight of all of the trackers. The StarLapse is technically just the "right ascension" drive for a Losmandy GM-8 telescope mount but Losmandy adapted it as a star tracker by eliminating the declination motor and replacing the normal telescope wedge with a design that can be mounted to a photo tripod. I have the Losmandy. It's rock solid.

You do need a sturdy/beefy photo tripod for these heads. This is not the time to skimp on tripod cost or try to get the lightest tripod you can find. You want something rock-solid that can handle the heavy load.
 

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