The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere. The north and south celestial poles appear directly overhead to an observer at the Earth's North Pole and South Pole respectively.
At night the stars appear to drift overhead from east to west, completing a full circuit around the sky in 24 (sidereal) hours. (Of course, exactly the same motion occurs during the day, except that the stars are not visible because of the sun's glare.) This apparent motion is due to the spinning of the Earth on its axis. As the Earth spins, the celestial poles remain nearly fixed in the sky, and all other points seem to rotate around them.
The celestial poles are also the poles of the celestial equatorial coordinate system, meaning they have declinations of +90 degrees and −90 degrees (for the north and south celestial poles, respectively).
The celestial poles do not remain permanently fixed against the background of the stars. Because of a phenomenon known as the precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. The Earth's axis is also subject to other complex motions which cause the celestial poles to shift slightly over cycles of varying lengths; see nutation, polar motion and axial tilt. Finally, over very long periods the positions of the stars themselves change, because of the stars' proper motions.
An analogous concept applies to other planets: a planet's celestial poles are the points in the sky where the projection of the planet's axis of rotation intersects the celestial sphere. These points vary because different planets' axes are oriented differently (the apparent positions of the stars also change slightly because of parallax effects).
Finding the north celestial pole
The north celestial pole currently is within a degree of the bright star Polaris (named from the Latin stella polaris, meaning "pole star"). This makes Polaris useful for navigation in the northern hemisphere: not only is it always above the north point of the horizon, but its altitude angle is always (nearly) equal to the observer's geographic latitude. Polaris can, of course, only be seen from locations in the northern hemisphere.
Polaris is near the celestial pole for only a small fraction of the 25,700-year precession cycle, and the fact that it is currently so is purely a coincidence. It will remain a good approximation for about 1,000 years, by which time the pole will have moved to be closer to Alrai (Gamma Cephei). In about 5,500 years, the pole will have moved near the position of the star Alderamin (Alpha Cephei), and in 12,000 years, Vega (Alpha Lyrae) will become our north star, but it will be about six degrees from the true north celestial pole.
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