Circumpolar stars always reside above the horizon, and for that reason, never rise or set. All the stars at the Earth’s North and South Poles are circumpolar. Meanwhile, no star is circumpolar at the equator.
Anyplace else has some circumpolar stars, and some stars that rise and set daily. The closer you are to either the North or South Pole, the greater the circle of circumpolar stars, and the closer you are to the equator, the smaller.
From the Northern Hemisphere, all the stars in the sky go full circle around the north celestial pole once a day – or more precisely, go full circle every 23 hours and 56 minutes. And from the Southern Hemisphere, all the stars in the sky go full circle around the south celestial pole in 23 hours and 56 minutes.
We in the Northern Hemisphere are particularly lucky to have Polaris, a moderately-bright star, closely marking the north celestial pole – the point in the starry sky that’s at zenith (directly overhead) at the Earth’s North Pole.
At the equator (0o latitude) the star Polaris – the stellar hub – sits right on the northern horizon, so no star can be circumpolar at the Earth’s equator. But at the North Pole (90o) Polaris shines at zenith (directly overhead), so from the North Pole every star in the sky stays above the horizon all day long every day of the year.
The circle of circumpolar stars in your sky is determined by your latitude. For instance, at 30o North latitude, the circle of stars within a radius of 30o from Polaris is circumpolar. In the same vein, at 45o or 60o N. latitude, the circle of stars within 45o or 60o, respectively, of Polaris would be circumpolar. Finally, at the North Pole, the circle of stars all the way to the horizon is circumpolar.
At 41o North Latitude (the latitude of New York City), and all latitudes farther north, the famous Big Dipper asterism is circumpolar. That’s because the southernmost star of the Big Dipper, Alkaid – the star marking the end of the Big Dipper handle – is 41o south of the north celestial pole (or 49o north of the celestial equator).
Bottom line: Every star rises and sets as seen from the Earth’s equator, but no star rises or sets at the Earth’s North and South Poles. Instead, as viewed from the poles, every star is circumpolar. Between the equator and the poles … you’ll see some circumpolar stars and some stars that rise and set daily.