Colatitude
Encyclopedia
In spherical coordinates, colatitude is the complementary angle of the latitude
, i.e. the difference between 90° and the latitude.
because it refers to the zenith distance of the celestial pole
s. For example, at latitude 42°N
, Polaris
(approximately on the North celestial pole) has an altitude of 42°, so the distance from the zenith
(overhead point) to Polaris is 90 - 42 = 48°.
Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star (its angle from the horizon
at culmination
or upper transit). For example, if Alpha Centauri
is seen with a latitude of 72° north (108° south) and its declination is known (60°S), then it can be determined that the observer's colatitude is 108 - 60 = 48 (i.e. their latitude is 90 - 48 = 42°S).
Stars whose declinations exceed the observer's colatitude are called circumpolar
because they will never set as seen from that latitude. If an object's declination is further south on the celestial sphere than the value of the colatitude, then it will never be seen from that location. For example, Alpha Centauri will always be visible at night from Perth, Western Australia
because the colatitude is 90 - 32 = 58, and 60 is greater than 58; on the other hand, the star will never rise in Juneau because its declination of -60° is less than -32° (the negation of Juneau's colatitude).
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
, i.e. the difference between 90° and the latitude.
Astronomical use
The colatitude is useful in astronomyAstronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
because it refers to the zenith distance of the celestial pole
Celestial pole
The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere...
s. For example, at latitude 42°N
42nd parallel north
The 42nd parallel north is a circle of latitude that is 42 degrees north of the Earth's equatorial plane. It crosses Europe, the Mediterranean Sea, Asia, the Pacific Ocean, North America, and the Atlantic Ocean....
, Polaris
Polaris
Polaris |Alpha]] Ursae Minoris, commonly North Star or Pole Star, also Lodestar) is the brightest star in the constellation Ursa Minor. It is very close to the north celestial pole, making it the current northern pole star....
(approximately on the North celestial pole) has an altitude of 42°, so the distance from the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
(overhead point) to Polaris is 90 - 42 = 48°.
Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star (its angle from the horizon
Horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...
at culmination
Culmination
In astronomy, the culmination of a planet, star, constellation, etc. is the altitude reached when the object transits over an observer's meridian....
or upper transit). For example, if Alpha Centauri
Alpha Centauri
Alpha Centauri is the brightest star in the southern constellation of Centaurus...
is seen with a latitude of 72° north (108° south) and its declination is known (60°S), then it can be determined that the observer's colatitude is 108 - 60 = 48 (i.e. their latitude is 90 - 48 = 42°S).
Stars whose declinations exceed the observer's colatitude are called circumpolar
Circumpolar star
A circumpolar star is a star that, as viewed from a given latitude on Earth, never sets , due to its proximity to one of the celestial poles...
because they will never set as seen from that latitude. If an object's declination is further south on the celestial sphere than the value of the colatitude, then it will never be seen from that location. For example, Alpha Centauri will always be visible at night from Perth, Western Australia
Perth, Western Australia
Perth is the capital and largest city of the Australian state of Western Australia and the fourth most populous city in Australia. The Perth metropolitan area has an estimated population of almost 1,700,000....
because the colatitude is 90 - 32 = 58, and 60 is greater than 58; on the other hand, the star will never rise in Juneau because its declination of -60° is less than -32° (the negation of Juneau's colatitude).