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Geographic coordinate system
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- For the use of coordinates on Wikipedia pages see: Wikipedia:WikiProject Geographical coordinates
A geographic coordinate system enables every location on the earth to be specified, using mainly a spherical coordinate system. There are three coordinates: latitude, longitude and geodesic height.
The earth is not a sphere, but an irregular changing shape approximating to an ellipsoid; the challenge is to define a coordinate system that can accurately state each topographical feature as an unambiguous set of numbers. [1]
Latitude and longitude
- For discussion of latitude on Wikipedia pages see: Latitude
Latitude phi (φ) and Longitude lambda (λ)
Latitude (abbreviation: Lat. or (φ) pronounced phi ) is the angle from a point on the earth's surface and the equatorial plane, measured from the centre of the sphere. Lines joining points of the same latitude are called parallels, and they trace concentric circles on the surface of the earth, parallel to the equator. The north pole 90° N; the south pole 90° S. The 0° parallel of latitude is designated the equator. The equator is the fundamental plane of all geographic coordinate systems. The equator divides the globe into the Northern and Southern Hemispheres.
Longitude (abbreviation: Long. or (λ)pronounced lambda) is the angle east or west of north–south line between the two geographical poles, that passes through an arbitrary point. Lines joining points of the same longitude are called meridians. All meridians are halves of great circles, and are not parallel. They converge at the north and south poles.
The line passing through the (former) Royal Observatory, Greenwich (near London in the UK) has been chosen as the international zero-longitude reference line, the Prime Meridian. Places to east are in the eastern hemisphere, and places to the west in the western hemisphere. The antipodal meridian of Greenwich is both 180°W and 180°E. The choice of Greenwich is arbitrary, and in other cultures and times in history other locations have been used as the prime meridian.[2]
Degrees: a measurement of angle
- For a further discussion of angular measure on Wikipedia pages see: Angle
Before Arabic numbers replaced roman numerals, i.e. before place value was used, decimal fractions were not possible and the number sixty was very important, so we have 60 minutes in an hour to this day. Similarly a degree was divided in sixty parts,minutes and the minute into 60 seconds. This provided sufficient accuracy for navigation systems, but not for today's needs. A minute is designated by ′ or "m" and the second is designated by ″ or "s". Today, if greater accuracy is required, the second can be represented as a decimal number. Alternatively, angle can be expressed as a decimal number. 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.
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]
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.
The Shape of the Earth
The earth is not a sphere, but an irregular changing shape approximating to an 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 very 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 a vertical datum, this is far from reality. The earth can be thought a series of layers of equal potential energy within the earth 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 worlds 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 neighboring Scotland is only rising by 0.2 cm. These changes are insignificant is a local datum is used. Wikipedia uses the global GPS datum so these changes are significant.[1]
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  can be calculated by this formula (to get the width per minute and second, divide by 60 and 3600, respectively):
-
-
-
-
where Earth's average meridional radius  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 by:
-
where Earth's equatorial and polar radii,  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 |
| 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 |
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'.
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.
See also
References
- Portions of this article are from Jason Harris' "Astroinfo" which is distributed with KStars, a desktop planetarium for Linux/KDE. See [1]
External links
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