## Geographic coordinate system

• A geographic coordinate system is a coordinate system used in geography 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. A common choice of coordinates is latitude, longitude and elevation.

To specify a location on a two-dimensional map requires a map projection.

The invention of a geographic coordinate system is generally credited to Eratosthenes of Cyrene, who composed his now-lost Geography at the Library of Alexandria in the 3rd century BC. A century later, Hipparchus of Nicaea improved on this system by determining latitude from stellar measurements rather than solar altitude and determining longitude by using simultaneous timings of lunar eclipses, rather than dead reckoning. In the 1st or 2nd century, Marinus of Tyre compiled an extensive gazetteer and mathematically-plotted world map using coordinates measured east from a prime meridian at the westernmost known land, designated the Fortunate Isles, off the coast of western Africa around the Canary or Cape Verde Islands, and measured north or south of the island of Rhodes off Asia Minor. Ptolemy credited him with the full adoption of longitude and latitude, rather than measuring latitude in terms of the length of the midsummer day. Ptolemy's 2nd-century Geography used the same prime meridian but measured latitude from the equator instead. After their work was translated into Arabic in the 9th century, Al-Khwārizmī's Book of the Description of the Earth corrected Marinus' and Ptolemy's errors regarding the length of the Mediterranean Sea, causing medieval Arabic cartography to use a prime meridian around 10° east of Ptolemy's line. Mathematical cartography resumed in Europe following Maximus Planudes' recovery of Ptolemy's text a little before 1300; the text was translated into Latin at Florence by Jacobus Angelus around 1407.

Longitudinal length equivalents at selected latitudes
Latitude City Degree Minute Second ±0.0001°
60° Saint Petersburg 55.80 km 0.930 km 15.50 m 5.58 m
51° 28′ 38″ N Greenwich 69.47 km 1.158 km 19.30 m 6.95 m
45° Bordeaux 78.85 km 1.31 km 21.90 m 7.89 m
30° New Orleans 96.49 km 1.61 km 26.80 m 9.65 m
Quito 111.3 km 1.855 km 30.92 m 11.13 m

${\displaystyle 111132.92-559.82\,\cos 2\varphi +1.175\,\cos 4\varphi -0.0023\,\cos 6\varphi }$
${\displaystyle 111412.84\,\cos \varphi -93.5\,\cos 3\varphi +0.118\,\cos 5\varphi }$
${\displaystyle {\frac {\pi }{180}}M_{r}\cos \varphi \!}$
${\displaystyle {\frac {\pi }{180}}a\cos \beta \,\!}$
• The origin at the center of mass of the earth, a point close to the Earth's center of figure
• The Z axis on the line between the north and south poles, with positive values increasing northward (but does not exactly coincide with the Earth's rotational axis)
• The X and Y axes in the plane of the equator
• The X axis passing through extending from 180 degrees longitude at the equator (negative) to 0 degrees longitude (prime meridian) at the equator (positive)
• The Y axis passing through extending from 90 degrees west longitude at the equator (negative) to 90 degrees east longitude at the equator (positive)
Wikipedia