Geographic coordinate system

A geographic coordinate system (GCS) is a way to pinpoint any location on Earth using latitude and longitude. It works on a spherical or ellipsoidal model of the planet, not a flat surface. This makes it fundamentally different from a Cartesian coordinate system, even though both use a pair of numbers: in a GCS, those numbers are angles, not distances along a plane. It is the oldest, simplest, and most common type of spatial reference system, and most others are built upon it. A complete GCS, as defined by standards like EPSG and ISO 19111, also specifies a geodetic datum (which includes an Earth ellipsoid), because different datums give different latitude and longitude values for the same physical 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 century later, Hipparchus of Nicaea improved it by using stars to determine latitude (instead of the sun's altitude) and lunar eclipses to determine longitude (instead of dead reckoning). In the 1st or 2nd century, Marinus of Tyre created a detailed gazetteer and a mathematically plotted world map. He measured longitude east from a prime meridian at the westernmost known land—the Fortunate Isles, off West Africa near the Canary or Cape Verde Islands—and latitude north or south of the island of Rhodes. Ptolemy, in his 2nd-century *Geography*, credited Marinus with fully adopting longitude and latitude (rather than measuring latitude by the length of the longest day). Ptolemy used the same prime meridian but measured latitude from the Equator. After their works were translated into Arabic in the 9th century, Al-Khwārizmī's *Book of the Description of the Earth* corrected Marinus and Ptolemy's errors 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 shortly 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 twenty-five nations. Twenty-two agreed to make the Royal Observatory in Greenwich, England, the zero-longitude line. The Dominican Republic voted against, while France and Brazil abstained. France switched to Greenwich Mean Time in 1911, replacing the Paris Observatory's local time.

Latitude (φ) is defined in three ways, each using 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 ellipsoid's normal vector at the surface point hits the equatorial plane; in a geocentric system, it's 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 the GCS, dividing Earth into Northern and Southern Hemispheres. Longitude (λ) is the angle east or west of a reference meridian to the meridian passing through a point. All meridians are halves of great ellipses that converge at the poles. The international prime meridian runs through the Royal Observatory in Greenwich, England, though some organizations (like France's IGN) still use other meridians internally. The antipodal meridian of Greenwich is both 180°W and 180°E, but this should not be confused with the International Date Line, which mostly follows that meridian but deviates in a few places for political and practical reasons (e.g., 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 visual grid of these 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 for precise real-world measurements, a geodetic datum is required. 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 horizontal datums, and a more precise geoid for vertical ones) to the physical planet. Traditionally, this link was established 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.