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and λ is the longitude, λ 0 is the central meridian, φ is the latitude, and R is the radius of the globe to be projected. The map has area 4 π R 2, conforming to the surface area of the generating globe. The x-coordinate has a range of [−2R √ 2, 2R √ 2], and the y-coordinate has a range of [−R √ 2, R √ 2].
The figure below shows a point P at latitude φ and longitude λ on the globe and a nearby point Q at latitude φ + δφ and longitude λ + δλ. The vertical lines PK and MQ are arcs of meridians of length Rδφ. [d] The horizontal lines PM and KQ are arcs of parallels of length R(cos φ)δλ.
A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of Earth as coordinates.It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space.
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. [1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane.
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. [1] It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others.
The latitude and longitude on a map made against a local datum may not be the same as one obtained from a GPS receiver. Converting coordinates from one datum to another requires a datum transformation such as a Helmert transformation, although in certain situations a simple translation may be sufficient. [29]
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
With this value for R the meridian length of 1 degree of latitude on the sphere is 111.2 km (69.1 statute miles) (60.0 nautical miles). The length of one minute of latitude is 1.853 km (1.151 statute miles) (1.00 nautical miles), while the length of 1 second of latitude is 30.8 m or 101 feet (see nautical mile ).