# Triaxial ellipsoid

Triaxial ellipsoid with ${\ displaystyle (a, a ', b) = (4,2,1)}$

In the case of a three-axis ellipsoid - in contrast to an ellipsoid of revolution (flattened or elongated ellipsoid ) - the equator is not sufficiently precisely circular, but rather elliptical . The triaxial ellipsoid is therefore not a solid of revolution and has three defining parameters , usually:

## Application in surveying

Compared to an ellipsoid of revolution, a three-axis ellipsoid means a slightly better adaptation to the geoid , but also a significantly more complicated application. In geodesy , the two semi-axes of the equator are also referred to as the ellipticity of the earth's equator ; However, this is less than 100 meters for the earth figure . For this reason, the Krassowski ellipsoid , which was originally designed as a three-axis ellipsoid, was reduced to two parameters.

In contrast, the shape of the planet Mars is clearly three-axis . The differences are around 20 km, so that an ellipsoid of revolution is not quite sufficient for the most precise location information ( areographic coordinates ).