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Longitude (, ), is a geographic coordinate that specifies the eastwest 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. The prime meridian, which passes near the Royal Observatory, Greenwich, England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west. Because of the earth's rotation, there is a close connection between longitude and time. Local time (for example from the position of the sun) varies with longitude, a difference of 15° longitude corresponding to a one-hour difference in local time. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or wireless. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds. A location's northsouth position along a meridian is given by its latitude, which is approximately the angle between the local vertical and the equatorial plane. Longitude is generally given using the geometrical or astronomical vertical. This can differ slightly from the gravitational vertical because of small variations in Earth's gravitational field.

History

Noting and calculating 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 (pi), or an unsigned fraction of 2. For calculations, the West/East suffix is replaced by a negative sign in the western hemisphere. The international standard convention (ISO 6709)—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 (positive in the northern hemisphere) to give a precise position on the Earth's surface. Confusingly, the convention of negative for East is also sometimes seen, most commonly in the United States; the Earth System Research Laboratory used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the Western Hemisphere. They have since shifted to the standard approach. 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.

Singularity and discontinuity of longitude

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.

Plate movement and longitude

The Earth's tectonic plates move relative to one another in different directions at speeds on the order of 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.

Length of a degree of longitude

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 that radius at latitude is , and the length of a one-degree (or radian) arc along a circle of latitude is :$\Delta^1_= \fraca \cos \phi$ When the Earth is modelled by an ellipsoid this arc length becomes :$\Delta^1_=\frac$ where , the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by :$e^2=\frac$ An alternative formula is :$\Delta^1_= \fraca \cos \beta \quad \mbox\tan \beta = \frac \tan \phi$; here $\beta$ is the so-called parametric or reduced latitude. Cos 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 = and = . 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 . 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 , while the length of 1 second of it is 0.016 geographical mile or .

Longitude on bodies other than Earth

– Center of Astrophysics. 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.

* American Practical Navigator * Cardinal direction * Ecliptic longitude * Geodesy * Geodetic system * Geographic coordinate system * Geographical distance * Geotagging * Great-circle distance * History of longitude * ''The Island of the Day Before'' * Latitude * Meridian arc * Natural Area Code * Navigation * Orders of magnitude * Right ascension on celestial sphere * World Geodetic System

References

Resources for determining your latitude and longitude

* ttp://entertainment.timesonline.co.uk/tol/arts_and_entertainment/the_tls/article5136819.ece "Longitude forged" an essay exposing a hoax solution to the problem of calculating longitude, undetected in Dava Sobel's Longitude, fro
TLS
November 12, 2008.
Board of Longitude Collection, Cambridge Digital Library
– complete digital version of the Board's archive
Longitude And Latitude Of Points of Interest

A land beyond the stars - Museo Galileo