Longitude (/ˈlɒndʒɪtjuːd/, AU and UK also /ˈlɒŋɡɪ-/), is a geographic coordinate that specifies the east–west position of a point on the Earth's surface, or the surface of a celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians (lines running from pole to pole) connect points with the same longitude. By convention, one of these, the Prime Meridian, which passes through the Royal Observatory, Greenwich, England, was allocated the position of 0° longitude. The longitude of other places is measured as the angle east or west from the Prime Meridian, ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. Specifically, it is the angle between a plane through the Prime Meridian and a plane through both poles and the location in question. (This forms a right-handed coordinate system with the z-axis (right hand thumb) pointing from the Earth's center toward the North Pole and the x-axis (right hand index finger) extending from the Earth's center through the Equator at the Prime Meridian.)
If the Earth were perfectly spherical and radially homogeneous, then the longitude at a point would be equal to the angle between a vertical north–south plane through that point and the plane of the Greenwich meridian. Everywhere on Earth the vertical north–south plane would contain the Earth's axis. But the Earth is not radially homogeneous and has rugged terrain, which affect gravity and so can shift the vertical plane away from the Earth's axis. The vertical north–south plane still intersects the plane of the Greenwich meridian at some angle; that angle is the astronomical longitude, calculated from star observations. The longitude shown on maps and GPS devices is the angle between the Greenwich plane and a not-quite-vertical plane through the point; the not-quite-vertical plane is perpendicular to the surface of the spheroid chosen to approximate the Earth's sea-level surface, rather than perpendicular to the sea-level surface itself.
The measurement of longitude is important both to cartography and for ocean navigation. Mariners and explorers for most of history struggled to determine longitude. Finding a method of determining longitude took centuries, resulting in the history of longitude recording the effort of some of the greatest scientific minds.
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 final result of my labours 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. 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. I found that...at midnight Mars's position was three and a half degrees to the east.
By comparing the 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. One needed also to know the precise time, which was difficult to ascertain in foreign lands. Finally, it required a stable viewing platform, rendering the technique useless on the rolling deck of a ship at sea. See Lunar distance (navigation).
In 1612 Galileo Galilei demonstrated that with sufficiently accurate knowledge of the orbits of the moons of Jupiter one could use their positions as a universal clock and this would make possible the determination of longitude, but the method he devised was impracticable for navigators on ships because of their instability. In 1714 the British government passed the Longitude Act which offered large financial rewards to the first person to demonstrate a practical method for determining the longitude of a ship at sea. These rewards motivated many to search for a solution.
John Harrison, a self-educated English clockmaker, invented the marine chronometer, the key piece in solving the problem of accurately establishing longitude at sea, thus revolutionising and extending the possibility of safe long distance sea travel. Though the Board of Longitude rewarded John Harrison for his marine chronometer in 1773, chronometers remained very expensive and the lunar distance method continued to be used for decades. Finally, the combination of the availability of marine chronometers and wireless telegraph time signals put an end to the use of lunars in the 20th century.
Unlike latitude, which has the equator as a natural starting position, there is no natural starting position for longitude. Therefore, a reference meridian had to be chosen. It was a popular practice to use a nation's capital as the starting point, but other locations were also used. While British cartographers had long used the Greenwich meridian in London, other references were used elsewhere, including El Hierro, Rome, Copenhagen, Jerusalem, Saint Petersburg, Pisa, Paris (see the article Paris meridian), Philadelphia, and Washington D.C. In 1884 the International Meridian Conference adopted the Greenwich meridian as the universal Prime Meridian or zero point of longitude.
Longitude is given as an angular measurement ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. The Greek letter λ (lambda), is used to denote the location of a place on Earth east or west of the Prime Meridian.
Each degree of longitude is sub-divided into 60 minutes, each of which is divided into 60 seconds. A longitude is thus specified in sexagesimal notation as 23° 27′ 30″ E. For higher precision, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may 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.
For calculations, the West/East suffix is replaced by a negative sign in the western hemisphere. Confusingly, the convention of negative for East is also sometimes seen. The preferred convention—that East is positive—is consistent with a right-handed Cartesian coordinate system, with the North Pole up. 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.
There is no other physical principle determining longitude directly but with time. 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 is 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°. 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 or astronomical observation. The details are more complex than described here: see the articles on Universal Time and on the equation of time for more details.
Note that the longitude is singular at the Poles and calculations that are sufficiently accurate for other positions may be inaccurate at or near the Poles. Also the discontinuity at the ±180° meridian must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, consider replacing latitude and longitude with another horizontal position representation in calculation.
The Earth's tectonic plates move relative to one another in different directions at speeds on the order of 50 to 100mm per year. So points on the Earth's surface on different plates are always in motion relative to one another. For example, the longitudinal difference between a point on the Equator in Uganda, on the African Plate, and a point on the Equator in Ecuador, on the South American Plate, is increasing by about 0.0014 arcseconds per year. These tectonic movements likewise affect latitude.
If a global reference frame (such as WGS84, for example) is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing just with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as "NAD83" for North America or "ETRS89" for Europe.
The length of a degree of longitude (east-west distance) depends only on the radius of a circle of latitude. For a sphere of radius a that radius at latitude φ is a cos φ, and the length of a one-degree (or π/ radian) arc along a circle of latitude is
|0°||110.574 km||111.320 km|
|15°||110.649 km||107.551 km|
|30°||110.852 km||96.486 km|
|45°||111.133 km||78.847 km|
|60°||111.412 km||55.800 km|
|75°||111.618 km||28.902 km|
|90°||111.694 km||0.000 km|
where e, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
An alternative formula is
Cos φ decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude (north-south distance), equator to pole. The table shows both for the WGS84 ellipsoid with a = 6378137.0 m and b = 6356752.3142 m. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is slightly more than the shortest (geodesic) distance between those points (unless on the equator, where these are equal); the difference is less than 0.6 m (2 ft).
A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude), therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km or 1.153 miles, while the length of 1 second of it is 0.016 geographical mile or 30.916 m or 101.43 feet.
Planetary co-ordinate systems are defined relative to their mean axis of rotation and various definitions of longitude depending on the body. 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. 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 location of the prime meridian as well as the position of the 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). 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.
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. 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.
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:
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. Smaller bodies (Io, Mimas, etc.) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to map projections. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere. 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 1610, Galileo thought he might win the Spanish longitude prize with his idea of measuring time by observing the moons of Jupiter ... The trouble with the method was in making accurate measurements of the four moons while on the deck of a moving ship at sea. This problem proved intractable, and the method was therefore not adopted.
The 180th meridian or antimeridian is the meridian 180° both east and west of the Prime Meridian, with which it forms a great circle dividing the earth into the Western and Eastern Hemispheres. It is common to both east longitude and west longitude. It mostly passes through the open waters of the Pacific Ocean, but passes across land in Russia, Fiji and Antarctica. This meridian is used as the basis for the International Date Line, but the latter deviates from it to maintain date consistency within the territories of Russia, the United States, Kiribati, Fiji and New Zealand.
Starting at the North Pole and heading south to the South Pole, the 180th meridian passes through:
The meridian also passes between (but not particularly close to):
the Gilbert Islands and the Phoenix Islands of Kiribati
North Island and the Kermadec Islands of New Zealand
the Bounty Islands and the Chatham Islands, also of New ZealandThe only place where roads cross this meridian, and where there are buildings very close to it, is in Fiji.Argument of periapsis
The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω, is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion.
For specific types of orbits, words such as perihelion (for heliocentric orbits), perigee (for geocentric orbits), periastron (for orbits around stars), and so on may replace the word periapsis. (See apsis for more information.)
An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference.
Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis. However, especially in discussions of binary stars and exoplanets, the terms "longitude of periapsis" or "longitude of periastron" are often used synonymously with "argument of periapsis".Capricorn (astrology)
Capricorn (♑) is the tenth astrological sign in the zodiac, originating from the constellation of Capricornus, the horned goat. It spans the 270–300th degree of the zodiac, corresponding to celestial longitude. Under the tropical zodiac, the sun transits this area from about December 22 to January 19 the following year, and under the sidereal zodiac, the sun transits the constellation of Capricorn from approximately January 16 to February 16. In astrology, Capricorn is considered an earth sign, negative sign, and one of the four cardinal signs. Capricorn is said to be ruled by the planet Saturn. In Vedic Astrology Capricorn was associated with the Crocodile but modern astrologers consider Capricorn as Sea goat.
Its symbol is based on the Sumerians' primordial god of wisdom and waters, Enki, with the head and upper body of a goat and the lower body and tail of a fish. Later known as Ea in Akkadian and Babylonian mythology, Enki was the god of intelligence (gestú, literally "ear"), creation, crafts; magic; water, seawater and lakewater (a, aba, ab).Celestial coordinate system
In astronomy, a celestial coordinate system (or celestial reference system) is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. Coordinate systems can specify an object's position in three-dimensional space or plot merely its direction on a celestial sphere, if the object's distance is unknown or trivial.
The coordinate systems are implemented in either spherical or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, are simply the cartesian equivalent of the spherical coordinates, with the same fundamental (x, y) plane and primary (x-axis) direction. Each coordinate system is named after its choice of fundamental plane.Decimal degrees
Decimal degrees (DD) express latitude and longitude geographic coordinates as decimal fractions and are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap, and GPS devices. Decimal degrees are an alternative to using degrees, minutes, and seconds (DMS). As with latitude and longitude, the values are bounded by ±90° and ±180° respectively.
Positive latitudes are north of the equator, negative latitudes are south of the equator. Positive longitudes are east of Prime meridian, negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence, latitude before longitude.Eastern Hemisphere
The Eastern Hemisphere is a geographical term for the half of Earth which is east of the prime meridian (which crosses Greenwich, London, UK) and west of the antimeridian (which crosses the Pacific Ocean and relatively little land from pole to pole). It is also used to refer to Afro-Eurasia (Africa and Eurasia) and Australia, in contrast with the Western Hemisphere, which includes mainly North and South America. The Eastern Hemisphere may also be called the "Oriental Hemisphere". In addition, it may be used in a cultural or geopolitical sense as a synonym for the "Old World".Geographic coordinate system
A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector.
A common choice of coordinates is latitude, longitude and elevation.
To specify a location on a plane requires a map projection.IERS Reference Meridian
The IERS Reference Meridian (IRM), also called the International Reference Meridian, is the prime meridian (0° longitude) maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east of George Biddell Airy's 1851 transit circle or 102 metres (335 ft) at the latitude of the Royal Observatory, Greenwich. It is also the reference meridian of the Global Positioning System (GPS) operated by the United States Department of Defense, and of WGS84 and its two formal versions, the ideal International Terrestrial Reference System (ITRS) and its realization, the International Terrestrial Reference Frame (ITRF).Indian Standard Time
Indian Standard Time (IST) is the time observed throughout India, with a time offset of UTC+05:30. India does not observe daylight saving time (DST) or other seasonal adjustments. In military and aviation time IST is designated E* ("Echo-Star").Indian Standard Time is calculated on the basis of 82.5' E longitude, in Mirzapur (Amravati Chauraha), Uttar Pradesh, which is nearly on the corresponding longitude reference line.Latitude
In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle (defined below) which ranges from 0° at the Equator to 90° (North or South) at the poles. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the geodetic latitude as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular (or normal) to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six auxiliary latitudes which are used in special applications.Leo (astrology)
Leo (♌) (Greek: Λέων, Leōn), is the fifth astrological sign of the zodiac, originating from the constellation of Leo. It comes after Cancer and before Virgo. The traditional Western zodiac associates Leo with the period between July 23 and August 22, and the sign spans the 120th to 150th degree of celestial longitude.
Leo is a fixed sign along with Taurus, Scorpio, and Aquarius. Under the tropical zodiac, the Sun transits this area on average between July 23 and August 22 each year, and under the sidereal zodiac, the Sun currently transits this area from approximately August 16 to September 15. The symbol of the lion is based on the Nemean lion, a lion with an impenetrable hide. It is a northern sign and its opposite southern sign is Aquarius.Longitude of the ascending node
The longitude of the ascending node (☊ or Ω) is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a reference direction, called the origin of longitude, to the direction of the ascending node, measured in a reference plane. The ascending node is the point where the orbit of the object passes through the plane of reference, as seen in the adjacent image. Commonly used reference planes and origins of longitude include:
For a geocentric orbit, Earth's equatorial plane as the reference plane, and the First Point of Aries as the origin of longitude. In this case, the longitude is also called the right ascension of the ascending node, or RAAN. The angle is measured eastwards (or, as seen from the north, counterclockwise) from the First Point of Aries to the node.
For a heliocentric orbit, the ecliptic as the reference plane, and the First Point of Aries as the origin of longitude. The angle is measured counterclockwise (as seen from north of the ecliptic) from the First Point of Aries to the node.
For an orbit outside the Solar System, the plane tangent to the celestial sphere at the point of interest (called the plane of the sky) as the reference plane, and north, i.e. the perpendicular projection of the direction from the observer to the North Celestial Pole onto the plane of the sky, as the origin of longitude. The angle is measured eastwards (or, as seen by the observer, counterclockwise) from north to the node., pp. 40, 72, 137; , chap. 17.In the case of a binary star known only from visual observations, it is not possible to tell which node is ascending and which is descending. In this case the orbital parameter which is recorded is the longitude of the node, Ω, which is the longitude of whichever node has a longitude between 0 and 180 degrees., chap. 17;, p. 72.Meridian (geography)
A (geographic) meridian (or line of longitude) is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole, connecting points of equal longitude, as measured in angular degrees east or west of the Prime Meridian. The position of a point along the meridian is given by that longitude and its latitude, measured in angular degrees north or south of the Equator. Each meridian is perpendicular to all circles of latitude. Each is also the same length, being half of a great circle on the Earth's surface and therefore measuring 20,003.93 km (12,429.9 miles).Prime meridian
A prime meridian is a meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great circle. This great circle divides a spheroid, e.g., Earth, into two hemispheres. If one uses directions of East and West from a defined prime meridian, then they can be called the Eastern Hemisphere and the Western Hemisphere.
A prime meridian is ultimately arbitrary, unlike an equator, which is determined by the axis of rotation—and various conventions have been used or advocated in different regions and throughout history. The most widely used modern meridian is the IERS Reference Meridian. It is derived but deviates slightly from the Greenwich Meridian, which was selected as an international standard in 1884.Scorpio (astrology)
Scorpio is the eighth astrological sign in the Zodiac, originating from the constellation of Scorpius. It spans 210°–240° ecliptic longitude. Under the tropical zodiac (most commonly used in Western astrology), the Sun transits this area on average from October 23 to November 22. Under the sidereal zodiac (most commonly used in Hindu astrology), the Sun is in Scorpio from approximately November 16 to December 15. Depending on which zodiac system one uses, an individual born under the influence of Scorpio may be called a Scorpio or a Scorpion.Selenographic coordinates
Selenographic coordinates are used to refer to locations on the surface of Earth's moon. Any position on the lunar surface can be referenced by specifying two numerical values, which are comparable to the latitude and longitude of Earth. The longitude gives the position east or west of the Moon's prime meridian, which is the line passing from the lunar north pole through the point on the lunar surface directly facing Earth to the lunar south pole. (See also Earth's prime meridian.) This can be thought of as the midpoint of the visible Moon as seen from the Earth. The latitude gives the position north or south of the lunar equator. Both of these coordinates are given in degrees.
Astronomers defined the fundamental location in the selenographic coordinate system by the small, bowl-shaped satellite crater 'Mösting A'. The coordinates of this crater are defined as:
The coordinate system has become precisely defined due to the Lunar Laser Ranging Experiment.
Anything past 90°E or 90°W would not be seen from Earth, except for libration, which makes 59% of the Moon visible.Western Hemisphere
The Western Hemisphere is a geographical term for the half of Earth which lies west of the prime meridian (which crosses Greenwich, London, United Kingdom) and east of the antimeridian. The other half is called the Eastern Hemisphere.Zodiac
The zodiac is an area of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are also within the belt of the zodiac.In Western astrology, and formerly astronomy, the zodiac is divided into twelve signs, each occupying 30° of celestial longitude and roughly corresponding to the constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces.The twelve astrological signs form a celestial coordinate system, or more specifically an ecliptic coordinate system, which takes the ecliptic as the origin of latitude and the Sun's position at vernal equinox as the origin of longitude.
|Philosophy of time|
and use of time
|Time in physics|
|Archaeology and geology|
|Other units of time|