Geoid und Ellipsoid

The Earth is best described as an ellipsoid, or an oblate spheroid, formed by rotating an ellipse around its minor axis. 

This shape is slightly flattened at the poles, with the polar axis approximately 21 kilometers shorter than the equatorial axis.

In contrast, the geoid represents Earth's shape based on gravitational forces, closely aligning with mean sea level or MSL over oceans when external influences like tides are excluded. 

It is an equipotential surface, with gravity acting perpendicular at all points. Unlike the smooth ellipsoid, the geoid is irregular due to mass distribution variations, causing global MSL undulations of up to 100 meters.

Historically, surveyors referenced MSL or the geoid using spirit levels, focusing on local measurements. 

However, modern GPS provides a global perspective, measuring elevation relative to the ellipsoid. Based on the World Geodetic System 1984 ellipsoid, this data must be converted using a geoid model to approximate MSL for practical use. 

GPS observations calculate Cartesian coordinates in an Earth-Centered, Earth-Fixed system, which are transformed into geographic coordinates such as latitude, longitude, and height for precise mapping and