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Our latitude in Shawnee is 35 degrees north, and we find Polaris 35 degrees above the northern horizon. Similarly, to sail west at a constant latitude Columbus kept the north star at a constant altitude above the horizon.
Polaris, located almost exactly at the north celestial pole, the center of spin, stays in the same place, while stars farther away from the north celestial pole can be seen to move in a wider circle around Polaris as viewed from Earth during its daily rotation. Polaris actually lies just a short distance away from where Earth's axis points. Polaris is located about 1 degree off to the side of the north celestial pole, so Polaris does move a little, tracing a very small arc in the night sky ...