Reference Ellipsoid - Ellipsoid Parameters

Ellipsoid Parameters

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 an oblate ellipsoid of revolution which he termed an oblate spheroid. Current practice (2012) uses the word 'ellipsoid' alone in preference to the full term 'oblate ellipsoid of revolution' or the older term 'oblate spheroid'. In the rare instances (some asteroids and planets) where a more general ellipsoid shape is required as a model the term used is triaxial (or scalene) ellipsoid. A great many ellipsoids have been used with various sizes and centres but modern (post GPS) ellipsoids are centred at the actual center of mass of the Earth or body being modeled.

The shape of an (oblate) ellipsoid (of revolution) is determined by the shape parameters of that ellipse which generates the ellipsoid when it is rotated about its minor axis. The semi-major axis of the ellipse, a, is identified as the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, is identified with the polar distances (from the centre). These two lengths completely specify the shape of the ellipsoid but in practice geodesy publications classify reference ellipsoids by giving the semi-major axis and the inverse flattening, 1/f, The flattening, f, is simply a measure of how much the symmetry axis is compressed relative to the equatorial radius:

For the Earth, is around 1/300 corresponding to a difference of the major and minor semi-axes of approximately 21 km. Some precise values are given in the table below and also in Figure of the Earth. 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 nearly 1/3 to 1/2.

A great many other parameters are used in geodesy but they can all be related to one or two of the set a, b and f. They are listed in ellipse.