Spheroid

Abstract

Name for a corpus similar to a sphere or a surface which do not deviate much from a sphere.

Particular

Name for a rotation ellipsoid. In geodesy and cartography this is the standard corpus of the Earth which mathematics deals with; in general a rotation ellipsoid (flattened at the poles) with the semi-axes a and b (a > b).

This rotation ellipsoid has the parameter representation

        fx(u,v)  =  a  *  cos(u) *  cos(v) ,
        fy(u,v)  =  a  *  sin(u)  *  cos(v) ,
        fz(u,v)  =  b  *  sin(v)

with  -  / 2 ≤ ≤  / 2  and  -  ≤ ≤  .

The »official maps« of numerous European countries are based on the Earth ellipsoid by Bessel (1841). This Earth ellipsoid have the semi-axes

        a = 6,377,397.15500 m   and   b = 6,356,078.96325 m .

In 1924 the »Association Géodésique« suggested the International Earth Ellipsoid by Hayford (USA) which has the semi-axes

        a = 6,378,388.00000 m   and   b = 6,356,911.94613 m .