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Geographic coordinate system



For a further discussion of angular measure on Wikipedia pages see: Angle

Geographic coordinates were first used by the astronomer and geographer Ptolemy in his Geographia using alphabetic Greek numerals based on sexagesimal (base 60) Babylonian numerals. This was continued by Muslim geographers using alphabetic Abjad numerals and later via Arabic numerals. In these systems a full circle is divided into 360 degrees and each degree is divided into 60 minutes. Although seconds, thirds, fourths, etc. were used by Hellenistic and Arabic astronomers, they were not used by geographers who recognized that their geographic coordinates were imprecise. Today seconds subdivided decimally are used. A minute is designated by ′ or "m" and the second is designated by ″ or "s". Seconds can be expressed as a decimal fraction of a minute, and minutes can be expressed as a decimal fraction of a degree. The letters N,S, E,W can be used to indicate the hemisphere, or we can use "+" and "-" to show this. North and East are "+", and South and West are "-". Latitude and Longitude can be separated by a space or a comma. Thus there are several formats for writing degrees, all of them appearing in the same Lat,Long order.

  • DMS Degree:Minute:Second (49°30'02"N, 123°30'30") or (49d30m02.5s,-123d30m30.17s)
  • DM Degree:Minute (49°30.0'-123°30.0'), (49d30.0m,-123°30.0')
  • DD Decimal Degree (49.5000°,-123.5000°), generally with 4 decimal numbers.

DMS is the most common format, and is standard on all charts and maps, as well as global positioning systems and geographic information systems.

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Geodesic height

To completely specify a location of a topographical feature on, in, or above the earth, one has to also specify the vertical distance from the centre of the sphere, or from the surface of the sphere. Because of the ambiguity of "surface" and "vertical", it is more commonly expressed relative to a more precisely defined vertical datum such as mean sea level at a named point. Each country has defined its own datum. In the United Kingdom the reference point is Newlyn. The distance to the earth's centre can be used both for very deep positions and for positions in space. [1]

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Cartesian coordinates

Every point that is expressed as spherical coordinate can be expressed as a x,y z (Cartesian) coordinate. This is not a useful method for recording the position on maps but is used to calculate distances, and to perform other mathematic operations. The source is usually the centre of the sphere, a point close the centre of the earth.

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Shape of the Earth

The earth is not a sphere, but an irregular changing shape approximating to a biaxial ellipsoid. It is nearly spherical, but has an equatorial bulge making the radius at the equator about 0.3% bigger than the radius measured through the poles. The shorter axis approximately coincides with axis of rotation. Map-makers choose the true ellipsoid that best fits their need for the area they are mapping. They then choose the most appropriate mapping of the spherical coordinate system onto that ellipsoid. In the United Kingdom there are three common latitude, longitude height systems in use. The system used by GPS, WGS84 differs in Greenwich from the one used on published maps OSGB36 by approximately 112m. The military system ED50, used by NATO is different again and gives inaccuracies of about 120m, and 180m.[1]

Though early navigators thought of the sea as a flat surface that could be used as a vertical datum, this is far from reality. The earth can be thought a series of layers of equal potential energy within its gravitational field. Height is a measurement at right angles to this surface, and though gravity pulls mainly toward the centre of the earth, the geocentre, there are local variations. The shape of these layers is irregular but essentially ellipsoidal. The choice of which of these layers to choose is arbitrary. The reference height we have chosen is the one closest to the average height of the world's oceans. This is called the Geoid.[1][4]

The earth is not static, points move relative to each other due to continental plate motion, subsidence and diurnal movement caused by the moon and the tides. The daily movement can be as much as a metre. Continental movement can be up to 10 cm a year, or 10m in a century. A weather system 'high' pressure area can cause a sinking of 5mm. Scandinavia is rising by 1 cm a year as a result of the recession of the last ice age, but neighbouring Scotland is only rising by 0.2 cm. These changes are insignificant if a local datum is used. Wikipedia uses the global GPS datum so these changes are significant.[1]

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Expressing latitude and longitude as linear units

On a spherical surface at sea level, one latitudinal second measures 30.82 metres and one latitudinal minute 1849 metres, and one latitudinal degree is 110.9 kilometres. The circles of longitude, the meridians, meet at the geographical poles, with the west-east width of a second being dependent on the latitude. On the equator at sea level, one longitudinal second measures 30.92 metres ,a longitudinal minute 1855 metres and a longitudinal degree111.3 kilometres.[5]

The width of one longitudinal degree on latitude \scriptstyle{\phi}\,\! can be calculated by this formula (to get the width per minute and second, divide by 60 and 3600, respectively):

\frac{\pi}{180^{\circ}}\cos(\phi)M_r,\,\!

where Earth's average meridional radius \scriptstyle{M_r}\,\! approximately equals 6,367,449 m. Due to the average radius value used, this formula is of course not precise. You can get a better approximation of a longitudinal degree on latitude \scriptstyle{\phi}\,\! by:

\frac{\pi}{180^{\circ}}\cos(\phi)\sqrt{\frac{a^4\cos(\phi)^2+b^4\sin(\phi)^2}{(a\cos(\phi))^2+(b\sin(\phi))^2}},\,\!

where Earth's equatorial and polar radii, \scriptstyle{a,b}\,\! equal 6,378,137 m, 6,356,752.3 m, respectively.

Length equivalent at selected latitudes in km
Latitude Town Degree Minute Second Decimal degree at 4 dp[clarify]
60 Saint Petersburg 55.65km 0.927km 15.42m 5.56m
51° 28' 38" N Greenwich 69.29km 1.155km 19.24m 6.93m
45 Bordeaux 78.7km 1.31km 21.86m 7.87m
30 New Orleans 96.39km 1.61km 26.77m 9.63m
0 Quito 111.3km 1.855km 30.92m 11.13m

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Datums often encountered

Latitude and longitude values can be based on several different geodetic systems or datums, the most common being the WGS 84 used by all GPS equipment, and by Wikipedia. Other datums however are significant because they were chosen by national cartographical organisation as the best method for representing their region, and these are the datum used on printed maps. Using the latitude and longitude found on a map, will not give the same reference as on a GPS receiver. Coordinates from the mapping system can be sometimes be changed into another datum using a simple translation. For example to convert from ETRF89 (GPS) to the Irish Grid by 49m to the east, and subtracting 23.4m from the north. [6] More generally one datum is changed into any other datum using a process called Helmert transformations. This involves, converting the spherical coordinates into Cartesian coordinates and applying a seven parameter transformation (a translation and 3D- rotation), and converting back.[1]

In popular GIS software, data projected in latitude/longitude is often specified via a 'Geographic Coordinate System'. For example, data in latitude/longitude with the datum as the North American Datum of 1983 is denoted by 'GCS_North_American_1983'.

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Geostationary coordinates

Geostationary satellites (e.g., television satellites ) are over the equator. So, their position related to Earth is expressed in longitude degrees. Their latitude does not change, and is always zero over the equator.

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See also

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References

  • Portions of this article are from Jason Harris' "Astroinfo" which is distributed with KStars, a desktop planetarium for Linux/KDE. See [1]
  1. ^ a b c d e f A Guide to coordinate systems in Great Britain v1.7 Oct 2007 D00659 accessed 14.4.2008
  2. ^ The French Institute Géographic Nationale, still displays a latitude and longitude on its maps centred on a meridian that passes through Paris
  3. ^ Haswell, Charles Haynes (1920). Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas. Harper & Brothers. Retrieved on 2007-04-09.
  4. ^ DMA Technical Report Geodesy for the Layman, The Defense Mapping Agency, 1983
  5. ^ Data taken from a previous version of this page.
  6. ^ Making maps compatible with GPS Government of Ireland 1999. Accessed 15.4.2008

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External links




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