No, Polaris would not be overhead if you were at the South Pole. The North Star -- Polaris -- is not visible from the Southern Hemisphere.
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Well, isn't that a lovely thought! If Polaris is directly overhead, that means you are standing precisely at the North Pole on our beautiful planet Earth. How delightful it would be to look up and see the North Star shining down right above you in the vast night sky. Just picture it and let that feeling of wonder fill your heart.
They're called the celestial poles and they move over time (due to Earth's precession).If the axis of the Earth were extended into space, the North Pole would point almost exactly at the giant star appropriately called Polaris, in the tail of the Little Bear or handle of the Little Dipper. The South Pole doesn't have so convenient a marker; it would fall several degrees away from the long axis of a small bright asterism known as Crux, the Southern Cross. The nearest visible star to the south celestial pole is a very dim star called Sigma Octantis, and even it's not really all that close to the pole (about a degree away).By 4000 AD, the celestial south pole will be very near the significantly brighter (though, at about magnitude 4, still quite a bit dimmer than Polaris) Gamma Chameleontis. At that time the north celestial pole will be very close to Gamma Cephei, a magnitude 3.2 star (also dimmer than Polaris, which is magnitude 2).Unfortunately, between now and then, the celestial poles won't point to any stars in particular. By about 3000AD, there will be no notable stars very near either of them.
You would be pretty darn close to the north pole. _______________________ Specifically, you would be within about 40 miles of the north pole. Polaris is about 2/3 of a degree away from being directly above the north pole.
The celestial pole is directly above Earth's geographic poles, so to place a celestial pole at your zenith you would need to be at either the North Pole or the South Pole. At these locations, the celestial pole would be directly overhead, making it appear as if the axis of Earth's rotation extended into the sky.
Your location must be located on the Earth's axis, specifically at the North or South Pole. At these locations, the stars appear to move in circles around the celestial pole that is directly overhead.