Circumpolar means to circle around the pole. Circumpolar star is a star that never sets (that is, it never disappears below the horizon at all times, irrespective of day and night or year), as seen from a given latitude, due to its proximity to one of the celestial poles. They move in a counterclockwise direction. However it is not visible during the day because of sunshine. Designation of a star as circumpolar depends on the observer's latitude. At either of Earth's poles all stars of that hemisphere are circumpolar, whereas at the equator none are, since only one half of the celestial sphere can ever be seen. For an observer (with a latitude ϕ), a star whose declination is greater than 90∘−ϕ will be circumpolar, appearing to circle the celestial pole and remaining always above the horizon. However, there will be some stars which can never be seen beyond a certain latitude.
Fig 1: The nautical triangle for deriving transformations between the horizontal and equatorial frames.
Using spherical trigonometry and transformations between the horizontal and equatorial frames, the relation between various relevant positions can be found to be:
where =altitude,=hour angle of the star,=declination of the star,=observer's latitude. These are shown in Fig. 1. Any object's altitude is greatest when it is on the south meridian (the great circle arc between the celestial poles containing the zenith). The hour angle isat that instance and it is called upper culmination, or transit. When it is called lower culmination. Using previous relation, for , we find,
So the altitude at the upper culmination is,
The altitude is positive for objects with . Objects with declinations less thancan never be seen from the latitude Using the relation between various relevant positions, for , we get
Likewise, at the lower culmination, the altitude is. Stars with a declination will never set.
Fig 2: The altitude of a circumpolar star at upper and lower culmination.