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ARTICLE ORIGINS longitude
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{{short description|A geographic coordinate that specifies the east-west position of a point on the Earth's surface}}File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A graticule on the Earth as a sphere or an ellipsoid. The lines from pole to pole are lines of constant longitude, or meridians. The circles parallel to the Equator are circles of constant latitude, or parallels. The graticule shows the latitude and longitude of points on the surface. In this example, meridians are spaced at 6Â° intervals and parallels at 4Â° intervals.]]{{about||Dava Sobel's book about John Harrison|Longitude (book)|the adaptation of Sobel's book| Longitude (TV series)}}{{longlat}}{{Geodesy|notshowfig=1}}Longitude ({{IPAc-en|Ëˆ|l|É’|n|dÊ’|áµ»|tj|uË|d}}, {{small|AU and UK also}} {{IPAc-en|Ëˆ|l|É’|Å‹|É¡|áµ»|-}}),WEB,weblink Definition of LONGITUDE, www.merriam-webster.com, Merriam-Webster, 14 March 2018, Oxford English Dictionary is a geographic coordinate that specifies the eastâ€“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 (Î»). 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 0Â° longitude. The longitude of other places is measured as the angle east or west from the Prime Meridian, ranging from 0Â° at the Prime Meridian to +180Â° eastward and âˆ’180Â° 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 {{mvar|z}}-axis (right hand thumb) pointing from the Earth's center toward the North Pole and the {{mvar|x}}-axis (right hand index finger) extending from the Earth's center through the Equator at the Prime Meridian.)A location's northâ€“south position along a meridian is given by its latitude, which is approximately the angle between the local vertical and the equatorial plane.If the Earth were perfectly spherical and radially homogeneous, then the longitude at a point would be equal to the angle between a vertical northâ€“south plane through that point and the plane of the Greenwich meridian. Everywhere on Earth the vertical northâ€“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 northâ€“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.

Noting and calculating longitude

Longitude is given as an angular measurement ranging from 0Â° at the Prime Meridian to +180Â° eastward and âˆ’180Â° westward. The Greek letter Î» (lambda),WEB,weblink Coordinate Conversion, colorado.edu, 14 March 2018, "Î» = 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 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 23Â° 27â€² 30â€³ 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: 23Â° 27.5â€² E. Degrees may also be expressed as a decimal fraction: 23.45833Â° 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}} (pi), or an unsigned fraction of 2{{pi}}.For calculations, the West/East suffix is replaced by a negative sign in the western hemisphere. The preferred conventionâ€”that East is positiveâ€”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. Confusingly, the convention of negative for East is also sometimes seen, most commonly in the United States; the Earth System Research Laboratory notes that, while it differs from the international standard, it "make(s) coordinate entry less awkward" for applications confined to the Western Hemisphere.NOAA ESRL Sunrise/Sunset Calculator (deprecated). Earth Systems Research Laboratory. Retrieved October 18, 2019.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 (360Â° Ã· 24 hours = 15Â° per hour). So if the time zone a person is in is three hours ahead of UTC then that person is near 45Â° longitude (3 hours Ã— 15Â° per hour = 45Â°). 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 15Â°. 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 Â±180Â° 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 50 to 100mm per year.BOOK, Read HH, Watson Janet, Introduction to Geology, New York, Halsted, 1975, 13â€“15, 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 {{mvar|a}} that radius at latitude {{mvar|Ï†}} is {{math|a cos Ï†}}, and the length of a one-degree (or {{sfrac|{{pi}}|180}} radian) arc along a circle of latitude is
Delta^1_{rm long}= frac{pi}{180^circ}a cos phi {| class="wikitable" style="float: right; margin-left:1em; text-align:right;"
!{{mvar|Ï†}}||{{math|Î”{{su|p=1|b=lat}}}}||{{math|Î”{{su|p=1|b=long}}}}
| 111.320 km
| 107.551 km
| 96.486 km
| 78.847 km
| 55.800 km
| 28.902 km
| 0.000 km
{{WGS84_angle_to_distance_conversion.svg}}When the Earth is modelled by an ellipsoid this arc length becomesBOOK, Osborne, Peter, 2013,weblink 10.5281/zenodo.35392, The Mercator Projections: The Normal and Transverse Mercator Projections on the Sphere and the Ellipsoid with Full Derivations of all Formulae, Chapter 5: The geometry of the ellipsoid, Edinburgh, BOOK, Rapp, Richard H., April 1991, Geometric Geodesy Part I, Chapter 3: Properties of the Ellipsoid, Department of Geodetic Science and Surveying, Ohio State University, Columbus, Ohio.,weblink
Delta^1_{rm long}=frac{pi acosphi}{180^circ sqrt{1 - e^2 sin^2 phi}}
where {{mvar|e}}, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
e^2=frac{a^2-b^2}{a^2}
An alternative formula is
Delta^1_{rm long}= frac{pi}{180^circ}a cos psi quad mbox{where }tan psi = frac{b}{a} tan phi
Cos {{mvar|Ï†}} 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 {{mvar|a}} = {{val|6378137.0|u=m}} and {{mvar|b}} = {{val|6356752.3142|u=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 {{convert|0.6|m|ft|0|abbr=on}}.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 {{convert|1.855|km|mi|disp=or|abbr=in}}, while the length of 1 second of it is 0.016 geographical mile or {{convert|30.916|m|ft|disp=or|abbr=in}}.

Longitude on bodies other than Earth{{anchor|Planets}}

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References

{{reflist}}

{{sisterlinks}} {{Map projection}}{{TimeSig}}{{Time Topics}}{{Time measurement and standards}}

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