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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in 'the x-coordinate'. In elementary mathematics the coordinates are taken to be real numbers, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry. In astronomy, a celestial coordinate system is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. Coordinate systems can specify a position in 3-dimensional space, or merely the direction of the object on the celestial sphere, if its distance is not known or not important. The coordinate systems are implemented in either spherical coordinates or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of the Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, are simply the cartesian equivalent of the spherical coordinates, with the same fundamental (x,y) plane and primary (x-axis) direction. Each coordinate system is named for its choice of fundamental plane.