When Polaris is no longer the "pole star", what will be?

Polaris has not always been, nor will it always be, the Pole Star. This is because the direction that Earth�s axis points slowly changes with time. Like a spinning top whose axis slowly wobbles, the Earth exhibits a similar wobble (called precession), caused by the combined gravitational influences of the Moon and Sun.

Polaris has not always been the Pole Star (it only became so in about 500 AD) and it won't always be the Pole Star (it hands over that job to Gemma Cephei in about 3000 AD).

Over a 26.000 year cycle, the precession of the earth's axis means that a number of stars take it in turns to be the star that is nearest to the celestial North Pole and thus get designated as the Pole Star, before being superceded by another one moving closer. It is a job-share not a job for life.

NINE POLE STARS

Theta Boötis (magnitude 4.04) is approximately 47 light years from Earth. From about 4300 BC until 3942 BC, it was the closest star to the celestial north pole visible to the naked eye, although it was still too far away and too dim to be regarded as a pole star.

Thuban (Alpha Draconis) Magnitude: 3.65 (binary star). It was Pole Star from 3,942 BC, when it moved farther north than Theta Boötis, until 1793 BC, when it was superseded by Kappa Draconis. In 20,346 AD, it will again be the pole star, that year

Kochab (? Ursae Minoris) (Magnitude: 2.07) and its neighbour Pherkab (? Ursae Minoris) (Magnitude: 2.1) are both naked-eye stars. They served as twin pole stars, Earth's North Pole stars, from 1500 B.C. until 500 A.D. Neither star was as proximitous to the pole as Polaris is now.

Polaris (Alpha Ursa Minorae) Magnitude: 1.97 (Triple star) 48th brightest in the sky. In about 3,000 AD Polaris will be replaced by first Gamma Cephei and then by Iota Cephei as Pole Star.

Vega (Alpha Lyrae) Magnitude: 0.03 and 5th brightest in the sky. Was Pole Star in 12,000 BC and will be again in 14,000 AD.

POLARIS IS A CEPHEID VARIABLE

Polaris is a Cepheid variable. Since Cepheids are an important standard candle for determining distance, Polaris (as the closest such star) is heavily studied.

If it died, the opportunity to study and understand it would die with it.
http://astropixels.com/stars/Polaris-01.html

Because of changes in the axis of the Earth's rotation relative to the plane of the elliptic, within a few tens of thousands of years Polaris will no longer be the star closest to the northern celestial pole.

Five thousand years from now, the North Star will be Alpha Cephei. Seven thousand years after that, it will be Vega. Nine thousand years after that, Thuban will be the North Star again. At these dates, the various stars will be at the closest to absolute north. For some time before, the relevant star will be approaching due north and it will be receding for some time after the time listed. In these interim times, the North Star is whichever star is closest to north.

http://www.wisegeek.com/what-is-polaris.htm