Definition of Circumpolar Stars
Whether a star is circumpolar depends upon the observer's latitude. Since the altitude of the north celestial pole (NCP) or south celestial pole (SCP) (whichever is visible) is the same as the absolute value of the observer's latitude, any star whose angular distance from the visible celestial pole is less than the absolute latitude will be circumpolar. For example, if the observer has latitude +50°, any star will be circumpolar if it is less than 50° from the north celestial pole. If the observer's latitude is −35°, then all stars within 35° of the south celestial pole will be circumpolar. Stars on the celestial equator are not circumpolar when observed from any latitude in either hemisphere of the Earth.
Whether a given star is circumpolar at the observer's latitude (θ) may be calculated in terms of the star's declination (δ). The star is circumpolar if θ+δ is greater than +90° (observer in northern hemisphere), or θ+δ is less than −90° (observer in southern hemisphere).
Similarly, the star will never rise above the local horizon if δ−θ is less than −90° (observer in northern hemisphere), or δ−θ is greater than +90° (observer in southern hemisphere).
Some stars within the far northern constellations, such as Cassiopeia, Cepheus, Ursa Major, and Ursa Minor, roughly north of the Tropic of Cancer (+23½°), will be circumpolar stars that never rise or set.
For British observers, for example, the first magnitude stars Capella (declination +45° 59) and Deneb (+45° 16') do not set from anywhere in the country. Vega (+38° 47') is technically circumpolar north of latitude +51° 13' (just south of London); taking atmospheric refraction into account it will probably only be seen to set at sea level from Cornwall and the Scilly Isles.
Some Stars within the far southern constellations, such as Crux, Musca, and Hydrus, roughly south of the Tropic of Capricorn (-23½°), will also be circumpolar stars.
Stars (and constellations) that are circumpolar in one hemisphere are always invisible in the high latitudes of the opposite hemisphere, and these never rise above the horizon. For example, the southern circumpolar star Acrux is invisible from most of the Continental United States, likewise, the seven stars of the northern circumpolar Big Dipper asterism are invisible from most of the Patagonia region of South America.
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