Colatitude


In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between 90° and the latitude. Southern latitudes are given a negative value and are thus denoted with a minus sign.
The colatitude corresponds to the conventional polar angle in spherical coordinates, as opposed to the latitude as used in cartography.

Examples

Latitude and colatitude sum up to 90°.
PlaceLatitudeColatitude
North pole90°0°
Equator0°90°
South pole−90°180°

Astronomical use

The colatitude is most
useful in astronomy because it refers to the zenith distance of the celestial poles. For example, at latitude 42°N, Polaris has an altitude of 42°, so the distance from the zenith to Polaris is.
Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star. For example, if Alpha Centauri is seen with a latitude of 72° north and its declination is known, then it can be determined that the observer's colatitude is .
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, 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°. Additionally, colatitude is used as part of the Schwarzschild metric in general relativity.