Latitude

For other uses, see the geographical term.

Latitude, usually denoted symbolically by the Greek letter phi, $\phi \,\!$, gives the location of a place on Earth north or south of the equator. Lines of Latitude are the horizontal lines shown running east-to-west on maps. Technically, 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.

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).

Sign in northern Vermont.

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).

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:

• Arctic Circle — 66° 33′ 39″ N
• Tropic of Cancer — 23° 26′ 21″ N
• Tropic of Capricorn — 23° 26′ 21″ S
• Antarctic Circle — 66° 33′ 39″ S

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

Subdivisions

As Earth is not a smooth sphere, but slightly oblate, a degree of latitude varies in length from about 111.3195 km at the equator to 110.9462 km at the poles. A degree of arc at a latitude not only varies with latitude, but also with the direction being faced. To simplify calculations where elliptical consideration is not important, the nautical mile was created, equaling exactly 111.12 km per degree of arc or, sub-dividing into minutes, 1852 metres per minute of arc. One minute of latitude can be further divided into 60 seconds. A latitude is thus specified as 13°19'43″ N (for greater precision, a decimal fraction can be added to the seconds). An alternative representation uses only degrees and minutes, where the seconds are expressed as a decimal fraction of minutes, thus the above example is expressed as 13°19.717' N. Degrees can also be expressed singularly, with both the minutes and seconds incorporated as a decimal number and rounded as desired (decimal degree notation): 13.32861° N. Sometimes, the north/south suffix is replaced by a negative sign for south (−90° for the South Pole).

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.

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.

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. Utilized in some of these conversions is a common elliptic integrand:

$n'(\theta )={\frac {1}{E'(\theta )}}={\frac {1}{\sqrt {1-{\big (}\sin(\theta )\sin(o\!\varepsilon ){\big )}^{2}}}};\,\!$

Reduced latitude

• Reduced or parametric latitude, $\beta \,\!$, is the latitude of the same radius on the sphere with the same equator.

$\beta =\arctan {\Big (}\cos(o\!\varepsilon )\tan(\phi ){\Big )};\,\!$

Authalic latitude

• Authalic latitude, $\xi \,\!$, gives an area-preserving transform to the sphere.

${\widehat {S}}(\phi )^{2}={\frac {1}{2}}b^{2}\left(\sin(\phi )n'(\phi )^{2}+{\frac {\ln {\bigg (}n'(\phi ){\Big (}1+\sin(\phi )\sin(o\!\varepsilon ){\Big )}{\bigg )}}{\sin(o\!\varepsilon )}}\right);\,\!$

${\begin{aligned}\xi &=\arcsin \!\left({\frac {{\widehat {S}}(\phi )^{2}}{{\widehat {S}}(90^{\circ })^{2}}}\right),\\&=\arcsin \!\left({\frac {\sin(\phi )\sin(o\!\varepsilon )n'(\phi )^{2}+\ln {\Big (}n'(\phi ){\big (}1+\sin(\phi )\sin(o\!\varepsilon ){\big )}{\Big )}}{\sin(o\!\varepsilon )\sec(o\!\varepsilon )^{2}+\ln {\Big (}\sec(o\!\varepsilon ){\big (}1+\sin(o\!\varepsilon ){\big )}{\Big )}}}\right);\end{aligned}}\,\!$

Rectifying latitude

• Rectifying latitude, $\mu \,\!$, is the surface distance from the equator, scaled so the pole is 90°. Unfortunately, it involves elliptic integration:

$M(\theta )=a\cos(o\!\varepsilon )^{2}n'(\theta )^{3};\,\!$

 $\mu ={\frac {\;\int _{0}^{\phi }\;M(\theta )\,d\theta }{{\frac {2}{\pi }}\int _{0}^{90^{\circ }}M(\phi )\,d\phi }}={\frac {\pi }{2}}\cdot {\frac {\;\int _{0}^{\phi }\;n'(\theta )^{3}\,d\theta }{\int _{0}^{90^{\circ }}n'(\phi )^{3}\,d\phi }};\,\!$

Conformal latitude

• Conformal latitude, $\chi \,\!$, gives an angle-preserving (conformal) transform to the sphere.

$\chi =2\cdot \arctan \left({\sqrt {{\frac {1+\sin(\phi )}{1-\sin(\phi )}}\cdot \left({\frac {1-\sin(\phi )\sin(o\!\varepsilon )}{1+\sin(\phi )\sin(o\!\varepsilon )}}\right)^{\!\!\sin(o\!\varepsilon )}}}^{\color {white}|}\;\right)-{\frac {\pi }{2}};\;\!$

Geocentric latitude

• The geocentric latitude, $\psi \,\!$, is the angle between the equatorial plane and a line from the center of the Earth.

$\psi =\arctan {\Big (}\cos(o\!\varepsilon )^{2}\tan(\phi ){\Big )}.\;\!$

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′

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).

Palæolatitude

Continents move over time, due to continental drift, taking whatever fossils and other features of interest they may have with them. Particularly when discussing fossils, it's often more useful to know where the fossil was when it was laid down, than where it is when it was dug up: this is called the palæolatitude of the fossil. The Palæolatitude can be constrained by palæomagnetic data. If tiny magnetisable grains are present when the rock is being formed, these will align themselves with the Earth's magnetic field like compass needles. A magnetometer can deduce the orientation of these grains by subjecting a sample to a magnetic field, and the declination of the grains can be used to infer the latitude of deposition.

Further reading

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

See also

• Cardinal direction
• Geographic coordinate system
• Geodetic system
• Geodesy
• Geotagging
• Great-circle distance
• Horse latitudes
• List of cities by latitude
• List of cities by longitude
• Longitude
• Navigation
• World Geodetic System

References

• Beals, K. L., Smith, C. L. & Dodd, S. M. (1984). "Brain size, cranial morphology, climate, and time machines". Current Anthropology. 25: 301–330.{{cite journal}}: CS1 maint: multiple names: authors list (link)
• Lynn, R. (1991). "The evolution of racial differences in intelligence". Mankind Quarterly. 32: 99–173.

External links

• Template:PDFlink
• Free GeoCoder
• GEONets Names Server, access to the National Geospatial-Intelligence Agency's (NGA) database of foreign geographic feature names.
• Look-up Latitude and Longitude
• Resources for determining your latitude and longitude
• Convert decimal degrees into degrees, minutes, seconds - Info about decimal to sexagesimal conversion
• Convert decimal degrees into degrees, minutes, seconds
• Latitude and longitude converter – Convert latitude and longitude from degree, decimal form to degree, minutes, seconds form and vice versa. Also included a farthest point and a distance calculator.
• Worldwide Index - Tageo.com – contains 2,700,000 coordinates of places including US towns
  • for each city it gives the satellite map location, country, province, coordinates (dd,dms), variant names and nearby places.
• Distance calculation based on latitude and longitude - JavaScript version
• Template:PDFlink