latitude

1 the angular distance between an imaginary line around a heavenly body parallel to its equator and the equator itself

2 freedom from normal restraints in conduct; "the new freedom in movies and novels"; "allowed his children considerable latitude in how they spent their money"

3 an imaginary line around the Earth parallel to the equator [syn: line of latitude, parallel of latitude, parallel]

4 scope for freedom of e.g. action or thought; freedom from restriction

English

Etymology

latitude, latitudo, from latus broad, wide, for older stlatus

Pronunciation

rfap UK

• (UK) /ˈlætɪtjuːd/, /"l

Circles 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 a path that bulges toward the nearest pole, first moving farther away from and then back toward the equator (see great circle).

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

Subdivisions

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

Elliptic parameters

Because most planets (including Earth) are ellipsoids of revolution, or spheroids, rather than spheres, both the radius and the length of arc varies with latitude. This variation requires the introduction of elliptic parameters based on an ellipse's angular eccentricity, o\!\varepsilon\,\! (which equals \scriptstyle\,\!, where a\;\! and b\;\! are the equatorial and polar radii; \scriptstyle\;\! is the first eccentricity squared, \;\!; and \scriptstyle\;\! or \scriptstyle\;\! is the flattening, \;\!). Utilized in creating the integrands for curvature is the inverse of the principal elliptic integrand, E'\;\!:

n'(\phi)=\frac =\frac;\,\!

\begin

M(\phi)&=a\cdot\cos^2(o\!\varepsilon)n'(\phi)^3 =\frac;\\ N(\phi)&=an'(\phi) =\frac;\end\,\!

Degree length

The length of an arcdegree of latitude (north-south) is about 60 nautical miles, 111 kilometres or 69 statute miles at any latitude. The length of an arcdegree of longitude (east-west) at the equator is about the same, reducing to zero at the poles.

In the case of a spheroid, a meridian and its anti-meridian form an ellipse, from which an exact expression for the length of an arcdegree of latitude is:

\fracM(\phi)\;\!

This radius of arc (or "arcradius") is in the plane of a meridian, and is known as the meridional radius of curvature, M\;\!.

Types of latitude

With a spheroid that is slightly flattened by its rotation, cartographers refer to a variety of auxiliary latitudes to precisely adapt spherical projections according to their purpose. For planets other than Earth, 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 Earth to account for flattening of the poles and bulging of the equator.

The expressions following assume elliptical polar sections and that all sections parallel to the equatorial plane are circular. Geographic latitude (with longitude) then provides a Gauss map.

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(\phi)^2=\fracb^2\left(\sin(\phi)n'(\phi)^2+\frac\right);\,\!

\begin\xi&=\arcsin\!\left(\frac\right),\\

&=\arcsin\!\left(\frac\right);\end\,\!

Rectifying latitude

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

 \mu=\frac

=\frac\cdot\frac;\,\!

Conformal latitude

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

\chi=2\cdot\arctan\left(\sqrt^\;\right)-\frac;\;\!

Geocentric latitude

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

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.

Palæolatitude

Corrections for latitude

Further reading

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

See also

• American Practical Navigator
• 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
• Orders of magnitude (length)

Footnotes

External links

• 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