Coordinate Systems

Coordinates Based on Models of the Earth's Shape

The most basic approximation to the shape of the earth is that it is a sphere of approximate radius 6,400 km. Upon the surface of this sphere, coordinates may be defined in terms of the latitude (the angle from the equatorial plane) and longitude (the angle around from a prime meridian, most commonly, but not exclusively, the Greenwich meridian). This establishes a basic two-dimensional coordinate system, which may be expanded to a three-dimensional system by the addition of the height of a point above the sphere. Such systems are generally referred to as geographic coordinates.

A further refinement of the approximation to the true shape of the earth is to model it as an ellipsoid or, more correctly, an ellipsoid of revolution. This may be visualized as a flattened version of the sphere, in which the distance between the poles is less than the distance between points on opposite sides of the equator but rotational symmetry is maintained. The ellipsoid is usually defined in terms of a parameter that expresses its overall size, the semimajor axis, and one that expresses its shape or degree of flattening. The latter may be either the semiminor axis (the distance from the center to one of the poles) or the flattening or the eccentricity. It is important to note that all three of these definitions are interchangeable: That is, a coordinate system may be based on an ellipsoid that is defined in terms of its eccentricity, but a particular software package may require the flattening as input. In such a case, it will be necessary to refer to one of the standard formulae to convert between parameters.

...