Longitude (λ) Map of Earth Lines of longitude appear curved in this projection, but are actually halves of great circles. A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, Regions, and Themes EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement Lines of latitude appear horizontal in this projection, but are actually circular with different radii. In Astronomy, Geography, Geometry and related sciences and contexts a plane is said to be horizontal at a given point if it is locally All locations with a given latitude are collectively referred to as a circle of latitude. A circle of latitude, on the Earth, is an imaginary East - West circle connecting all locations (not taking into account elevation that share a given The equator divides the planet into a Northern Hemisphere and a Southern Hemisphere, and has a latitude of 0°. The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the Northern Hemisphere is the half of a Planet that is North of the Equator —the word hemisphere literally means 'half ball' Southern Hemisphere is the half of a Planet that is South of the Equator —the word hemisphere literally means 'half ball' This box: view • talk • edit

Latitude, usually denoted symbolically by the Greek letter phi, $\phi\,\!$, gives the location of a place on Earth (or other planetary body) north or south of the equator. Phi (uppercase Φ, lowercase φ or ϕ) pronounced in modern Greek and as in English is the 21st letter of the Greek alphabet EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the 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). In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called This article describes the unit of angle For other meanings see Degree. The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is subject to the caveats explained below defined as the point in the northern The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is the southernmost point on the surface of the Earth. The complementary angle of a latitude is called the colatitude. A pair of Angles is complementary if the sum of their measures add up to 90 degrees. In Spherical coordinates, colatitude is the Complementary angle of the Latitude, i

## 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. A circle of latitude, on the Earth, is an imaginary East - West circle connecting all locations (not taking into account elevation that share a given A circle of latitude, on the Earth, is an imaginary East - West circle connecting all locations (not taking into account elevation that share a given In Geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the 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). A small circle of a Sphere is the circle constructed by a plane crossing the sphere not in its center In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces A great circle is a Circle on the surface of a Sphere that has the same circumference as the sphere dividing the sphere into two equal Hemispheres.

Sign in northern Vermont. Vermont ( is a state in the New England region of the northeastern United States of America.

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). Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement Global Navigation Satellite System (GNSS is the standard generic term for satellite navigation systems that provide autonomous geo-spatial positioning with global coverage

### 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. The Arctic Circle is one of the five major circles of latitude that mark maps of the Earth. For the novel by Henry Miller, see Tropic of Cancer (novel. The Tropic of Cancer, or Northern tropic, is one of five For the novel by Henry Miller, see Tropic of Capricorn (novel. The Antarctic Circle is one of the five major circles (or parallels of latitude that mark maps of the Earth. The Sun (Sol is the Star at the center of the Solar System. In broad terms the zenith is the direction pointing directly above a particular location ( Perpendicular, Orthogonal) Only north of the Arctic Circle or south of the Antarctic Circle is the midnight sun possible. The Arctic Circle is one of the five major circles of latitude that mark maps of the Earth. The Antarctic Circle is one of the five major circles (or parallels of latitude that mark maps of the Earth. The midnight sun is a phenomenon occurring in Latitudes north and nearby to the south of the Arctic Circle and south and nearby to the north of the

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″. In Astronomy, axial tilt is the Inclination angle of a planet's rotational axis in relation to its orbital plane. This article describes the unit of angle For other meanings see Degree.

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

To simplify calculations where elliptical consideration is not important, the nautical mile was created, equaling exactly 111. A nautical mile or sea mile is a unit of Length. It corresponds approximately to one minute of Latitude along any meridian. 12 km per degree of arc or, sub-dividing into minutes, 1852 metres per minute of arc. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International 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). The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is the southernmost point on the surface of the Earth.

## Effect of latitude

Average temperatures vary strongly with latitude.

A region's latitude has a great effect on its climate and weather (see Effect of sun angle on climate). Climate encompasses the temperatures humidity rainfall atmospheric particle count and numerous other meteorogical factors in a given region over long periods of The weather is a set of all the phenomena occurring in a given Atmosphere at a given Time. The amount of heat energy received at any location on the globe is a direct effect of sun angle of climate, as the angle at which Sunlight strikes the earth Latitude more loosely determines tendencies in polar auroras, prevailing winds, and other physical characteristics of geographic locations. The prevailing winds are the trends in speed and direction of Wind over a particular point on the Earth 's surface

Researchers at Harvard's Center for International Development (CID) found in 2001 that only three tropical economies — Hong Kong, Singapore, and 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. The Tropics are centered on the Equator and limited in Latitude by the Tropic of Cancer in the northern hemisphere at approximately 23°26' (23 Hong Kong ( officially the Hong Kong Special Administrative Region, is a territory located on China 's south coast on the Pearl River Delta, and borders Singapore Taiwan ( Taiwanese: Tâi-oân/Tāi-oân (historically 大灣/台員/大員/台圓/大圓/台窩灣 is an Island in East Asia. The World Bank is an internationally supported Bank that provides financial and technical assistance to developing countries for development programs (e [1]

## 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. An oblate Spheroid is a rotationally symmetric Ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe This variation requires the introduction of elliptic parameters based on an ellipse's angular eccentricity, $o\!\varepsilon\,\!$ (which equals $\scriptstyle{\arccos(\frac{b}{a})}\,\!$, where $a\;\!$ and $b\;\!$ are the equatorial and polar radii; $\scriptstyle{\sin(o\!\varepsilon)^2}\;\!$ is the first eccentricity squared, ${e^2}\;\!$; and $\scriptstyle{2\sin(\frac{o\!\varepsilon}{2})^2}\;\!$ or $\scriptstyle{1-\cos(o\!\varepsilon)}\;\!$ is the flattening, ${f}\;\!$). In the study of ellipses and related geometry various parameters in the distortion of a circle into an ellipse are identified and employed Aspect ratio Flattening and eccentricity In Mathematics, the eccentricity, denoted e or \varepsilon is a parameter associated with every conic section. Ellipticity redirects here For the mathematical topic of ellipticity see Elliptic operator. Utilized in creating the integrands for curvature is the inverse of the principal elliptic integrand, $E'\;\!$:

$n'(\phi)=\frac{1}{E'(\phi)} =\frac{1}{\sqrt{1-\sin^2(\phi)\sin^2(o\!\varepsilon)}};\,\!$
\begin{align} M(\phi)&=a\cdot\cos^2(o\!\varepsilon)n'(\phi)^3 =\frac{(ab)^2}{\Big(a^2\cos^2(\phi)+b^2\sin^2(\phi)\Big)^{3/2}};\\ N(\phi)&=a{\cdot}n'(\phi) =\frac{a^2}{\sqrt{a^2\cos^2(\phi)+b^2\sin^2(\phi)}};\end{align}\,\!

## 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 European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry In Integral calculus, elliptic integrals originally arose in connection with the problem of giving the Arc length of an Ellipse. This article describes the unit of angle For other meanings see Degree. A nautical mile or sea mile is a unit of Length. It corresponds approximately to one minute of Latitude along any meridian. The kilometre ( American spelling: kilometer) symbol km is a unit of Length in the Metric system, equal to one thousand A mile is a unit of Length, usually used to measure Distance, in a number of different systems including Imperial units United States 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:

$\frac{\pi}{180^\circ}M(\phi)\;\!$

This radius of arc (or "arcradius") is in the plane of a meridian, and is known as the meridional radius of curvature, $M\;\!$. This article is about the geographical concept For other uses of the word see Meridian. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a The distance from the center of a Sphere or Ellipsoid to its surface is its Radius. [2][3]

Similarly, an exact expression for the length of an arcdegree of longitude is:

$\frac{\pi}{180^\circ}\cos(\phi)N(\phi)\;\!$

The arcradius contained here is in the plane of the prime vertical, the east-west plane perpendicular (or "normal") to both the plane of the meridian and the plane tangent to the surface of the ellipsoid, and is known as the normal radius of curvature, $N\;\!$. In Astronomy and Astrology, the prime vertical is the Vertical circle passing east and west through the Zenith, and intersecting the Horizon In Mathematics, two Vectors are orthogonal if they are Perpendicular, i [2][3]

Along the equator (east-west), $N\;\!$ equals the equatorial radius. The radius of curvature at a right angle to the equator (north-south), $M\;\!$, is 43 km shorter, hence the length of an arcdegree of latitude at the equator is about 1 km less than the length of an arcdegree of longitude at the equator. In Geometry and Trigonometry, a right angle is an angle of 90 degrees corresponding to a quarter turn (that is a quarter of a full circle The radii of curvature are equal at the poles where they are about 64 km greater than the north-south equatorial radius of curvature because the polar radius is 21 km less than the equatorial radius. The shorter polar radii indicate that the northern and southern hemispheres are flatter, making their radii of curvature longer. This flattening also 'pinches' the north-south equatorial radius of curvature, making it 43 km less than the equatorial radius. Both radii of curvature are perpendicular to the plane tangent to the surface of the ellipsoid at all latitudes, directed toward a point on the polar axis in the opposite hemisphere (except at the equator where both point toward Earth's center). The east-west radius of curvature reaches the axis, whereas the north-south radius of curvature is shorter at all latitudes except the poles.

The WGS84 ellipsoid, used by all GPS devices, uses an equatorial radius of 6378137. The World Geodetic System defines a reference frame for the earth for use in Geodesy and Navigation. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth 0 m and an inverse flattening, (1/f), of 298. 257223563, hence its polar radius is 6356752. 3142 m and its first eccentricity squared is 0. 00669437999014. [4] The more recent but little used IERS 2003 ellipsoid provides equatorial and polar radii of 6378136. "IERS" redirects here for other uses see IERS (disambiguation The International Earth Rotation and Reference Systems Service is 6 and 6356751. 9 m, respectively, and an inverse flattening of 298. 25642. [5] Lengths of degrees on the WGS84 and IERS 2003 ellipsoids are the same when rounded to six significant digits. The significant figures (also called significant digits and abbreviated sig figs) of a number are those digits that carry meaning contributing to its accuracy An appropriate calculator for any latitude is provided by the U. S. government's National Geospatial-Intelligence Agency (NGA). The National Geospatial-Intelligence Agency ( NGA) is an agency of the United States Government with the primary mission of collection analysis and [6]

of curvature,
$M\;\!$
Degree of
latitude
of curvature,
$N\;\!$
Degree of
longitude
6335. 44 km110. 574 km6378. 14 km111. 320 km
15°6339. 70 km110. 649 km6379. 57 km107. 551 km
30°6351. 38 km110. 852 km6383. 48 km96. 486 km
45°6367. 38 km111. 132 km6388. 84 km78. 847 km
60°6383. 45 km111. 412 km6394. 21 km55. 800 km
75°6395. 26 km111. 618 km6398. 15 km28. 902 km
90°6399. 59 km111. 694 km6399. 59 km0. 000 km

## 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. Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the Equation A spheroid centered at the origin and rotated about the z axis is defined by the implicit equation \left(\frac{x}{a}\right^2+\left(\frac{y}{a}\right^2+\left(\frac{z}{b}\right^2

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. In Differential geometry, the Gauss map (named after Carl F Gauss) maps a Surface in Euclidean space R 3 to the unit

### 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{align}\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{align}\,\!

### Rectifying latitude

• Rectifying latitude, $\mu\,\!$, is the surface distance from the equator, scaled so the pole is 90°, but involves elliptic integration:
$\mu=\frac{\;\int_{0}^\phi\;M(\theta)\,d\theta}{\frac{2}{\pi}\int_{0}^{90^\circ}M(\phi)\,d\phi}=\frac{\pi}{2}\cdot\frac{\;\int_{0}^\phi\;n'(\theta)^3\,d\theta}{\int_{0}^{90^\circ}n'(\phi)^3\,d\phi};\,\!$

### 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 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. 00′0. 00′0. 00′0. 00′0. 00′
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). The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through 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). In Astronomy, declination (abbrev dec or δ) is one of the two coordinates of the Equatorial coordinate system, the other being either Historically Astronomy was more concerned with the classification and description of phenomena in the sky while Astrophysics attempted to explain these phenomena The celestial equator is a Great circle on the imaginary Celestial sphere, in the same plane as the Earth 's Equator. The equatorial coordinate system is probably the most widely used Celestial coordinate system, whose equatorial coordinates are Declination (\delta Ecliptic latitude, or Celestial latitude is one of the co-ordinates which can be used to define the location of an Astronomical object on the Celestial sphere in The ecliptic is the apparent path that the Sun traces out in the sky during the year The ecliptic coordinate system is a Celestial coordinate system that uses the Ecliptic for its Fundamental plane.

### Palæolatitude

Continents move over time, due to continental drift, taking whatever fossils and other features of interest they may have with them. Continental drift is the movement of the Earth 's Continents relative to each other 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. Paleomagnetism is the study of the record of the Earth's magnetic field preserved in various Magnetic Minerals through time If tiny magnetisable grains are present when the rock is being formed, these will align themselves with 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 magnetic declination of the grains can be used to infer the latitude of deposition. A magnetometer is a scientific instrument used to measure the strength and/or direction of the Magnetic field in the vicinity of the instrument The magnetic declination (also known as grid magnetic angle in military circles at any point on the Earth is the angle between the local magnetic field -- the direction

### Corrections for altitude

Line IH is normal to the spheroid at point H. The angle it forms with the equator corresponds to geodetic latitude.

When converting from geodetic ("common") latitude, corrections must be made for altitude for systems which do not measure the angle from the normal of the spheroid. In the figure at right, point H (located on the surface of the spheroid) and point H' (located at some greater elevation) have different geocentric latitudes (angles β and γ respectively), even though they share the same geodetic latitude (angle α). (Note that the flatness of the spheroid and elevation of point H' is significantly greater than what is found on the Earth, exaggerating the errors commonly found in such calculations. )