Geographic coordinate system

A geographic coordinate system (GCS) is a way to pinpoint locations on Earth using latitude and longitude. It works on a spherical or geodetic model of the planet. This is the oldest, simplest, and most common type of spatial reference system, and many others are built on it. While latitude and longitude look like a pair of coordinates in a flat Cartesian system, a GCS is different because its measurements are angles, not distances on a flat surface. A full GCS specification—like those in the EPSG and ISO 19111 standards—also includes a choice of geodetic datum (which involves an Earth ellipsoid), because different datums give different latitude and longitude values for the same spot.

The invention of this system is usually credited to Eratosthenes of Cyrene, who wrote his now-lost *Geography* at the Library of Alexandria in the 3rd century BC. About a hundred years later, Hipparchus of Nicaea improved it by figuring out latitude from star measurements instead of the sun's height, and longitude by timing lunar eclipses rather than dead reckoning. In the 1st or 2nd century, Marinus of Tyre put together a large gazetteer and a mathematically plotted world map. He used coordinates measured east from a prime meridian at the westernmost known land—the Fortunate Isles, off West Africa near the Canary or Cape Verde Islands—and measured north or south from the island of Rhodes. Ptolemy later credited Marinus with fully adopting longitude and latitude, instead of measuring latitude by the length of the longest summer day. Ptolemy's own 2nd-century *Geography* used the same prime meridian but measured latitude from the Equator. 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 mistakes about the Mediterranean Sea's length, leading medieval Arabic cartography to use a prime meridian about 10° east of Ptolemy's. Mathematical cartography returned to Europe after Maximus Planudes rediscovered Ptolemy's text just before 1300; it was translated into Latin in Florence by Jacopo d'Angelo around 1407. In 1884, the United States hosted the International Meridian Conference with representatives from twenty-five nations. Twenty-two agreed to set the prime meridian at the Royal Observatory in Greenwich, England. The Dominican Republic voted against it, while France and Brazil abstained. France switched to Greenwich Mean Time in 1911, replacing local time from the Paris Observatory.

Latitude (φ) for a point on Earth's surface is defined in three ways, depending on the coordinate system. In each case, it's the angle between the equatorial plane and a line from the surface point to a second point on that plane. The difference is how that second point is found: in an astronomical system, it's where the plumb bob vertical from the surface point hits the equatorial plane; in a geodetic system, it's where the normal vector from the ellipsoid's surface at that point hits the equatorial plane; in a geocentric system, it's the Earth's center. All points with the same latitude form a circle on the surface, called a parallel, because they run parallel to the equator and each other. The North Pole is 90° N, the South Pole 90° S. The 0° parallel is the equator, the fundamental plane of a GCS, dividing the globe into Northern and Southern Hemispheres. Longitude (λ) is the angle east or west from a reference meridian to another meridian through the point. All meridians are halves of great ellipses that meet at the poles. The international prime meridian runs through the Royal Observatory in Greenwich, southeast London, though some organizations, like France's Institut national de l'information géographique et forestière, still use other meridians internally. The antipodal meridian of Greenwich is both 180°W and 180°E. This is not the same as the International Date Line, which partly follows the 180° meridian but deviates in several places for political and practical reasons, such as between far eastern Russia and the far western Aleutian Islands. Together, latitude and longitude specify any location on Earth's surface, ignoring altitude or depth. The grid of latitude and longitude lines on a map is called a graticule. The system's origin (0°, 0°) is in the Gulf of Guinea, about 625 km (390 mi) south of Tema, Ghana—a spot sometimes jokingly called Null Island.

To use these theoretical definitions of latitude, longitude, and height for precise measurements on the physical Earth, a geodetic datum is needed. A horizontal datum measures latitude and longitude accurately, while a vertical datum measures elevation or altitude. Both types link a mathematical model of Earth's shape (usually a reference ellipsoid for a horizontal datum, and a more precise geoid for a vertical one) to the actual planet. Traditionally, this link was made through a network of control points—surveyed locations with installed monuments—and these datums were only accurate for a specific region of Earth's surface. Newer datums are more global.