Reference ellipsoid

In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined. In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined. In the context of standardization and geographic applications, a geodesic reference ellipsoid is the mathematical model used as foundation by Spatial reference system or Geodetic datum definitions. In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of a flattened ('oblate') ellipsoid of revolution, generated by an ellipse rotated around its minor diameter; a shape which he termed an oblate spheroid. In geophysics, geodesy, and related areas, the word 'ellipsoid' is understood to mean 'oblate ellipsoid of revolution', and the older term 'oblate spheroid' is hardly used. For bodies that cannot be well approximated by an ellipsoid of revolution a triaxial (or scalene) ellipsoid is used. The shape of an ellipsoid of revolution is determined by the shape parameters of that ellipse. The semi-major axis of the ellipse, a, becomes the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, becomes the distance from the centre to either pole. These two lengths completely specify the shape of the ellipsoid. In geodesy publications, however, it is common to specify the semi-major axis (equatorial radius) a and the flattening f, defined as That is, f is the amount of flattening at each pole, relative to the radius at the equator. This is often expressed as a fraction 1/m; m = 1/f then being the 'inverse flattening'. A great many other ellipse parameters are used in geodesy but they can all be related to one or two of the set a, b and f. A great many ellipsoids have been used to model the Earth in the past, with different assumed values of a and b as well as different assumed positions of the center and different axis orientations relative to the solid Earth. Starting in the late twentieth century, improved measurements of satellite orbits and star positions have provided extremely accurate determinations of the earth's center of mass and of its axis of revolution; and those parameters have been adopted also for all modern reference ellipsoids. The ellipsoid WGS-84, widely used for mapping and satellite navigation has f close to 1/300 (more precisely, 1/298.257223563, by definition), corresponding to a difference of the major and minor semi-axes of approximately 21 km (13 miles) (more precisely, 21.3846858 km). For comparison, Earth's Moon is even less elliptical, with a flattening of less than 1/825, while Jupiter is visibly oblate at about 1/15 and one of Saturn's triaxial moons, Telesto, is highly flattened, with f between 1/3 to 1/2 (meaning that the polar diameter is between 50% and 67% of the equatorial.