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 Lines of latitude appear horizontal in this projection, but are actually circular with different radii. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the 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

Longitude IPA: /ˡlɒndʒɪˌtjuːd/, symbolized by the Greek character lambda (λ), is the east-west (Side to Side) geographic coordinate measurement most commonly used in cartography and global navigation. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Lambda (uppercase Λ, lowercase λ; Λάμβδα or el Λάμδα Lamda is the 11th letter of the Greek alphabet. A geographic coordinate system enables every location on the Earth to be specified in three coordinates using mainly a spherical coordinate system. A line of longitude is a meridian and half of a great circle. 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.

## History

Main article: History of longitude

Mariners and explorers for most of history struggled to determine precise longitude. The history of longitude is a record of the effort by navigators and scientists over several centuries to discover a means of determining Longitude. Latitude was calculated by observing with quadrant or astrolabe the inclination of the sun or of charted stars, but longitude presented no such manifest means of study. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the The astrolabe is a historical Astronomical instrument used by classical astronomers, Navigators The Sun (Sol is the Star at the center of the Solar System. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth Amerigo Vespucci was perhaps the first to proffer a solution, after devoting a great deal of time and energy studying the problem during his sojourns in the New World. The Explorer and Cartographer Amerigo Vespucci ( March 9, 1454 - February 22, 1512) was the first person to demonstrate The New World is one of the names used for the non-Eurasian/non-African parts of the Earth specifically the Americas and Australia.

"As to longitude, I declare that I found so much difficulty in determining it that I was put to great pains to ascertain the east-west distance I had covered. The Experimental Advanced Superconducting Tokamak (EAST internal designation HT-7U is an experimental Superconducting Tokamak Magnetic fusion energy This article refers to the cardinal direction for other uses see West (disambiguation. The final result of my labors was that I found nothing better to do than to watch for and take observations at night of the conjunction of one planet with another, and especially of the conjunction of the moon with the other planets, because the moon is swifter in her course than any other planet. Conjunction is a term used in Positional astronomy and Astrology. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is I compared my observations with [an almanac]. After I had made experiments many nights, one night, the twenty-third of August, 1499, there was a conjunction of the moon with Mars, which according to the almanac was to occur at midnight or a half hour before. Midnight is literally "the middle of the night" In most systems it is when one day ends and the next begins when the date changes I found that. . . at midnight Mars's position was three and a half degrees to the east. This article describes the unit of angle For other meanings see Degree. " [1]

By comparing the relative positions of the moon and Mars with their anticipated positions, Vespucci was able to crudely deduce his longitude. But this method had several limitations: First, it required the occurrence of a specific astronomical event (in this case, Mars passing through the same right ascension as the moon), and the observer needed to anticipate this event via an astronomical almanac. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Right ascension (abbrev RA; symbol α) is the Astronomical term for one of the two Coordinates of a point on the Celestial sphere One needed also to know the precise time, which was difficult to ascertain in foreign lands. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Finally, it required a stable viewing platform, rendering the technique useless on the rolling deck of a ship at sea. A ship /ʃɪp/ is a large vessel that floats on water Ships are generally distinguished from Boats based on size An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere.

## Noting and calculating longitude

Longitude is given as an angular measurement ranging from 0° at the prime meridian to +180° eastward and −180° westward. In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called The Greek letter λ (lambda),[2][3] is used to denote the location of a place on Earth east or west of the prime meridian. The Greek alphabet (Ελληνικό αλφάβητο is a set of twenty-four letters that has been used to write the Greek language since the late 9th or early Lambda (uppercase Λ, lowercase λ; Λάμβδα or el Λάμδα Lamda is the 11th 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 Experimental Advanced Superconducting Tokamak (EAST internal designation HT-7U is an experimental Superconducting Tokamak Magnetic fusion energy This article refers to the cardinal direction for other uses see West (disambiguation.

Each degree of longitude is sub-divided into 60 minutes, each of which divided into 60 seconds. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. A longitude is thus specified in sexagesimal notation as 23° 27′ 30" E. Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. For higher precision, the seconds are specified with a decimal fraction. The decimal ( base ten or occasionally denary) Numeral system has ten as its base. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23° 27. 500′ E. Degrees may also be expressed as a decimal fraction: 23. 45833° E. For calculations, the angular measure usually must be converted to radians, so longitude may also be expressed in this manner as a signed fraction of π (pi), or an unsigned fraction of 2π. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems

For calculations, the West/East suffix is replaced by a negative sign in the western hemisphere. The Western Hemisphere, also Western hemisphere or western hemisphere, is a geographical term for the half of the Earth that lies West Confusingly, the convention of negative for East is also sometimes seen. The preferred convention -- that East be positive -- is consistent with a right-handed Cartesian coordinate system with the North Pole up. In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane 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 A specific longitude may then be combined with a specific latitude (usually positive in the northern hemisphere) to give a precise position on the Earth's surface. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the Northern Hemisphere is the half of a Planet that is North of the Equator —the word hemisphere literally means 'half ball'

Longitude at a point may be determined by calculating the time difference between that at its location and Coordinated Universal Time (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360°/24 hours = 15° per hour). So if the time zone a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word near was used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. This article is about the astronomical concept For other uses of the word see Meridian. In order to perform this calculation, however, a person needs to have a chronometer (watch) set to UTC and needs to determine local time by solar observation or astronomical observation. A marine chronometer is a timekeeper precise enough to be used as a portable Time standard; it can therefore be used to determine Longitude by means of Celestial The details are more complex than described here: see the articles on Universal Time and on the Equation of time for more details. The equation of time is the difference over the course of a year between time as read from a Sundial and time as read from a Clock, measured in an ideal situation

## 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, $E'\;\!$:

$n'(\phi)=\frac{1}{E'(\phi)}=\frac{1}{\sqrt{1-\big(\sin(\phi)\sin(o\!\varepsilon)\big)^2}};\,\!$
\begin{align}M(\phi)&=a\cdot\cos(o\!\varepsilon)^2n'(\phi)^3=\frac{(ab)^2}{\Big((a\cos(\phi))^2+(b\sin(\phi))^2\Big)^{3/2}};\\N(\phi)&=a{\cdot}n'(\phi)=\frac{a^2}{\sqrt{(a\cos(\phi))^2+(b\sin(\phi))^2}};\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. [4][5]

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 [4][5]

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. [6] 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. [7] 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 [8]

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

## Ecliptic latitude and longitude

Ecliptic latitude and longitude are defined for the planets, stars, and other celestial bodies in a similar way to that in which the terrestrial counterparts are defined. The pole is the normal to the ecliptic nearest to the celestial north pole. The ecliptic is the apparent path that the Sun traces out in the sky during the year Ecliptic latitude is measured from 0° to 90° north (+) or south (−) of the ecliptic. Ecliptic longitude is measured from 0° to 360° eastward (the direction that the Sun appears to move relative to the stars) along the ecliptic from the vernal equinox. Ecliptic longitude ( solar longitude or celestial longitude) is one of the co-ordinates which can be used to define the location of an Astronomical object An equinox is the event of the Sun passing over the Earth's equator in its annual cycle The equinox at a specific date and time is a fixed equinox, such as that in the J2000 reference frame. In Astronomy, an epoch is a moment in time used as a reference for the Orbital elements of a Celestial body.

However, the equinox moves because it is the intersection of two planes, both of which move. The ecliptic is relatively stationary, wobbling within a 4° diameter circle relative to the fixed stars over millions of years under the gravitational influence of the other planets. The greatest movement is a relatively rapid gyration of Earth's equatorial plane whose pole traces a 47° diameter circle caused by the Moon. This causes the equinox to precess westward along the ecliptic about 50" per year. This moving equinox is called the equinox of date. Ecliptic longitude relative to a moving equinox is used whenever the positions of the Sun, Moon, planets, or stars at dates other than that of a fixed equinox is important, as in calendars, astrology, or celestial mechanics. The word Calendar consist of two words 1 Cal ( in Pashto means Year in Hindi and Persian is Sal- also means Year Astrology (from Greek grc ἄστρον astron, "constellation star" and grc -λογία -logia) is a group of Systems Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically The 'error' of the Julian or Gregorian calendar is always relative to a moving equinox. The Julian calendar, a reform of the Roman calendar, was introduced by Julius Caesar in 46 BC and came into force in 45 BC (709 Ab urbe condita The Gregorian calendar is the most widely used Calendar in the world today The years, months, and days of the Chinese calendar all depend on the ecliptic longitudes of date of the Sun and Moon. The Chinese calendar is lunisolar, incorporating elements of a Lunar calendar with those of a Solar calendar. The 30° zodiacal segments used in astrology are also relative to a moving equinox. Celestial mechanics (here restricted to the motion of solar system bodies) uses both a fixed and moving equinox. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. Sometimes in the study of Milankovitch cycles, the invariable plane of the solar system is substituted for the moving ecliptic. Milankovitch cycles are the collective effect of changes in the Earth 's movements upon its climate named after Serbian civil engineer and Mathematician The invariable plane of a Planetary system is the plane passing through its Barycenter (center of mass which is perpendicular to its Angular momentum Longitude may be denominated from 0 to $\begin{matrix}2\pi\end{matrix}$ radians in either case.

## Longitude on bodies other than Earth

Planetary co-ordinate systems are defined relative to their mean axis of rotation and various definitions of longitude depending on the body. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a crater. In the broadest sense the term impact crater can be applied to any depression natural or manmade resulting from the high velocity impact of a projectile with larger body The north pole is that pole of rotation that lies on the north side of the invariable plane of the solar system (near the ecliptic). 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 invariable plane of a Planetary system is the plane passing through its Barycenter (center of mass which is perpendicular to its Angular momentum The ecliptic is the apparent path that the Sun traces out in the sky during the year The location of the prime meridian as well as the position of body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe If the position angle of the body's prime meridian increases with time, the body has a direct (or prograde) rotation; otherwise the rotation is said to be retrograde. Direct motion is the motion of a Planetary body in a direction similar to that of other bodies within its system and is sometimes called prograde motion. Direct motion is the motion of a Planetary body in a direction similar to that of other bodies within its system and is sometimes called prograde motion.

In the absence of other information, the axis of rotation is assumed to be normal to the mean orbital plane; Mercury and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean orbital period. In the case of the giant planets, since their surface features are constantly changing and moving at various rates, the rotation of their magnetic fields is used as a reference instead. A gas giant (sometimes also known as a Jovian planet after the planet Jupiter, or giant planet) is a large Planet that is not primarily In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In the case of the Sun, even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead. The Sun (Sol is the Star at the center of the Solar System.

For planetographic longitude, west longitudes (i. e. , longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i. e. , longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.

However, planetocentric longitude is always measured positively to the east, regardless of which way the planet rotates. East is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, the following all mean the same thing:

• −90°
• 90°W
• +270°
• 270°E.

The reference surfaces for some planets (such as Earth and Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar radius; in other words, they are oblate spheroids. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. An oblate Spheroid is a rotationally symmetric Ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane Smaller bodies (Io, Mimas, etc. TemplateInfobox Planet.--> Io (ˈaɪoʊ, or as Greek TemplateInfobox Planet. --> Mimas (ˈmaɪməs, or as Greek ) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to map projections. A map projection is any method of representing the Surface of a sphere or other shape on a plane. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.

The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. The meridian of Mars is located at Airy-0 crater. Airy-0 is a crater on Mars whose location defines the position of the Prime meridian of that planet [9]

Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body. A separate article treats the phenomenon of Tidal resonance in Oceanography. [10] However, libration due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an analemma. In Astronomy libration (from the Latin verb librare "to balance to sway" cf Analemma was also a book by Ptolemy. In Astronomy, an analemma ( IPA: /ˌænəˈlɛmə/ Latin for the pedestal of a

## Notes

1. ^ Vespucci, Amerigo. "Letter from Seville to Lorenzo di Pier Francesco de' Medici, 1500. " Pohl, Frederick J. Amerigo Vespucci: Pilot Major. New York: Columbia University Press, 1945. 76-90. Page 80.
2. ^ Coordinate Conversion
3. ^ "λ = Longitude east of Greenwich (for longitude west of Greenwich, use a minus sign). "
John P. Snyder, Map Projections, A Working Manual, USGS Professional Paper 1395, page ix
4. ^ a b The Math Forum
5. ^ a b John P. The United States Geological Survey ( USGS) is a scientific agency of the United States government. Snyder, Map Projections—A Working Manual (1987) 24-25
6. ^ NIMA TR8350.2 page 3-1.
7. ^ IERS Conventions (2003) (Chp. 1, page 12)
8. ^ Length of degree calculator - National Geospatial-Intelligence Agency
9. ^ Where is zero degrees longitude on Mars?
10. ^ First map of extraterrestial planet.