Latitude

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This is about the geographical term. For its use in cinematography, see Exposure latitude.
Map of Earth
Longitude (λ)
Appear curved and vertical in this projection, but are actually halves of great circles.
Latitude (φ)
Appear straight and horizontal in this projection, but are actually circular with different radii. All locations with a given latitude are collectively referred to as a circle of latitude.
The equator divides the planet into a Northern Hemisphere and a Southern Hemisphere, and has a latitude of 0°.

Latitude, usually denoted symbolically by the Greek letter phi, \phi\,\!, gives the location of a place on Earth north or south of the equator. Latitude is an angular measurement in degrees (marked with °) ranging from 0° at the Equator (low latitude) to 90° at the poles (90° N for the North Pole or 90° S for the South Pole; high latitude). The complementary angle of a latitude is called the colatitude.

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[edit] Circles of latitude

Main article: Circle of latitude

All locations of a given latitude are collectively referred to as a circle of latitude or line of latitude or parallel, because they are coplanar, and all such planes are parallel to the equator. Lines of latitude other than the Equator are approximately small circles on the surface of the Earth; they are not geodesics since the shortest route between two points at the same latitude involves moving farther away from, then towards, the equator (see great circle).

A specific latitude may then be combined with a specific longitude to give a precise position on the Earth's surface (see satellite navigation system).

[edit] Important named circles of latitude

Besides the equator, four other lines of latitude are named because of the role they play in the geometrical relationship with the Earth and the Sun:

Only at latitudes between the Tropics is it possible for the sun to be at the zenith. Only north of the Arctic Circle or south of the Antarctic Circle is the midnight sun possible.

The reason that these lines have the values that they do lies in the axial tilt of the Earth with respect to the sun, which is 23° 26′ 21.41″.

Note that the Arctic Circle & Tropic of Cancer and the Antarctic Circle and Tropic of Capricorn are colatitudes since the sum of their angles is 90°.

[edit] Subdivisions

Each degree of latitude is further sub-divided into 60 minutes. One minute of latitude is one nautical mile, defined exactly as 1852 metres (this is approximate due to slight variation with latitude (at sea level) and is because the earth is slightly oblate). One minute of latitude can be further divided into 60 seconds. A latitude is thus specified as 13°19′43″ N. For high accuracy, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, where parts of a minute are expressed as a decimal fraction, thus: 13°19.717′ N. Degrees expressed as a decimal number (decimal degree notation) is more often used: 13.32861° N. Sometimes, the north/south suffix is replaced by a negative sign for south (−90° for the South Pole).

[edit] Effect of latitude

A region's latitude has a great effect on its climate and weather (see Effect of sun angle on climate). Latitude more loosely determines tendencies in polar auroras, prevailing winds, and other physical characteristics of geographic locations.

Researchers at Harvard's Center for International Development (CID) found in 2001 that only three tropical economies — Hong Kong, Singapore, and part of Taiwan — were classified as high-income by the World Bank, while all countries within regions zoned as temperate had either middle- or high-income economies.[1]

[edit] Types of latitude

Because the Earth is slightly flattened by its rotation, cartographers refer to a variety of auxiliary latitudes to precisely adapt spherical projections according to their purpose.
More generally, for other planets such as Mars, geographic and geocentric latitude are called "planetographic" and "planetocentric" latitude, respectively. Most maps of Mars since 2002 use planetocentric coordinates.

[edit] Common "latitude"

  • In common usage, "latitude" refers to geodetic or geographic latitude \phi\,\! and is the angle between the equatorial plane and a line that is normal to the reference spheroid, which approximates the shape of the Earth to account for flattening of the poles and bulging of the equator.

The expressions following assume elliptical polar sections with the angular eccentricity, o\!\varepsilon\,\! (which equals {}^{\arccos(\frac{b}{a})}\,\!, where a\;\! and b\;\! are the equatorial and polar radii), and that all sections parallel to the equatorial plane are circular. Geographic latitude (with longitude) then provides a Gauss map.

[edit] Reduced latitude

  • Reduced or parametric latitude, \beta\,\!, is the latitude of the same radius on the sphere with the same equator.
\beta=\arctan\left(\cos(o\!\varepsilon)\tan(\phi)\right);\,\!

[edit] Authalic latitude

  • Authalic latitude, \xi\,\!, gives an area-preserving transform to the sphere.
\xi=\arcsin\!\left[\frac{Q\left(\phi\right)}{Q\left(\frac{\pi}{2}\right)}\right]\!,\quad\!\!\mathrm{where}\quad\!\!\!Q\left(\phi\right)=\left|\frac{\sin(\phi)}{1-(\sin(\phi)\sin(o\!\varepsilon))^2}-\frac{\ln\left(\frac{1-\sin(\phi)\sin(o\!\varepsilon)}{1+\sin(\phi)\sin(o\!\varepsilon)}\right)}{2\sin(o\!\varepsilon)}\right|;\,\!

[edit] Rectifying latitude

  • Rectifying latitude, \mu\,\!, is the surface distance from the equator, scaled so the pole is 90°. Unfortunately, it involves elliptic integration:
M(\phi)=\frac{a\cdot\cos(o\!\varepsilon)^2}{\left[1-(\sin(\phi)\sin(o\!\varepsilon))^2\right]^\frac{3}{2}};\,\!
 \mu=\frac{\pi}{2}\cdot\frac{\int_{0}^\phi M(p)\,dp}{\int_{0}^\pi M(\phi)\,d\phi};\,\!

[edit] Conformal latitude

  • Conformal latitude, \chi\,\!, gives an angle-preserving (conformal) transform to the sphere.
\chi=2\cdot\arctan\left(\sqrt{\frac{1+\sin(\phi)}{1-\sin(\phi)}\cdot\left(\frac{1-\sin(\phi)\sin(o\!\varepsilon)}{1+\sin(\phi)\sin(o\!\varepsilon)}\right)^{\!\!\sin(o\!\varepsilon)}}\right)-\frac{\pi}{2};\;\!

[edit] Geocentric latitude

  • The geocentric latitude, \psi\,\!, is the angle between the equatorial plane and a line from the center of the Earth.
\psi=\arctan\!\!\left(\cos(o\!\varepsilon)^2\tan(\phi)\right).\;\!

[edit] Comparison of latitudes

The following plot shows the differences between the types of latitude. The data used is found in the table following the plot. Please note that the values in the table are in minutes, not degrees, and the plot reflects this as well. Also note that the conformal symbols are hidden behind the geocentric due to being very close in value.

Approximate difference from geographic latitude ("Lat")
Lat
\phi\,\!		 Reduced
\phi-\beta\,\!		 Authalic
\phi-\xi\,\!		 Rectifying
\phi-\mu\,\!		 Conformal
\phi-\chi\,\!		 Geocentric
\phi-\psi\,\!
0° 0.00′ 0.00′ 0.00′ 0.00′ 0.00′
5° 1.01′ 1.35′ 1.52′ 2.02′ 2.02′
10° 1.99′ 2.66′ 2.99′ 3.98′ 3.98′
15° 2.91′ 3.89′ 4.37′ 5.82′ 5.82′
20° 3.75′ 5.00′ 5.62′ 7.48′ 7.48′
25° 4.47′ 5.96′ 6.70′ 8.92′ 8.92′
30° 5.05′ 6.73′ 7.57′ 10.09′ 10.09′
35° 5.48′ 7.31′ 8.22′ 10.95′ 10.96′
40° 5.75′ 7.66′ 8.62′ 11.48′ 11.49′
45° 5.84′ 7.78′ 8.76′ 11.67′ 11.67′
50° 5.75′ 7.67′ 8.63′ 11.50′ 11.50′
55° 5.49′ 7.32′ 8.23′ 10.97′ 10.98′
60° 5.06′ 6.75′ 7.59′ 10.12′ 10.13′
65° 4.48′ 5.97′ 6.72′ 8.95′ 8.96′
70° 3.76′ 5.01′ 5.64′ 7.52′ 7.52′
75° 2.92′ 3.90′ 4.39′ 5.85′ 5.85′
80° 2.00′ 2.67′ 3.00′ 4.00′ 4.01′
85° 1.02′ 1.35′ 1.52′ 2.03′ 2.03′
90° 0.00′ 0.00′ 0.00′ 0.00′ 0.00′

[edit] Astronomical latitude

A more obscure measure of latitude is the astronomical latitude, which is the angle between the equatorial plane and the normal to the geoid (ie a plumb line). It originated as the angle between horizon and pole star.

Astronomical latitude is not to be confused with declination, the coordinate astronomers use to describe the locations of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to describe the locations of stars north/south of the ecliptic (see ecliptic coordinates).

[edit] Further reading

  • John P. Snyder Map Projections: a working manual excerpts

[edit] See also

[edit] Footnotes

  1. ^ Location, Location, Location. The relationship of climate to, and the effect of disease and agricultural productivity on, the economic success of a city or region.

[edit] References

  • Beals, K. L., Smith, C. L. & Dodd, S. M. (1984). "Brain size, cranial morphology, climate, and time machines". Current Anthropology 25: 301–330. 
  • Lynn, R. (1991). "The evolution of racial differences in intelligence". Mankind Quarterly 32: 99–173. 

[edit] External links

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