# Earth Ellipsoid

## Earth Ellipsoid

the ellipsoid of revolution that best represents the shape of a geoid, that is, the shape of the earth as a whole. For the best representation of a geoid throughout the entire earth, a general earth ellipsoid is usually introduced and defined in such a way that (1) its volume is equal to the volume of a geoid, (2) the plane of the equator and its minor axis coincide with the earth’s equatorial plane and axis of rotation respectively, and (3) the sum of the squares of the deviations of the geoid from the general earth ellipsoid with respect to the entire earth sphere is minimal. For the best representation of the shape of a geoid within some region of the earth’s surface, the most appropriate earth spheroid is used and is defined in such a way that (1) the sum of the squares of the deviations of the geoid within this region is minimal and (2) the equatorial plane and its minor axis are parallel to the earth’s plane and axis of rotation respectively. The general earth ellipsoid differs little from the earth spheroid, which represents the corresponding equilibrium shape of the planet.

Since it has been determined that the earth is oblate not only in the direction of its poles but also about its equator, although only very slightly, an ellipsoid with three unequal axes, the smallest of which coincides with the earth’s axis of rotation, is sometimes used in theoretical calculations. The dimensions of the earth ellipsoid and its location in the body of the earth are determined from degree measurements, measurements of the force of gravity, and observations of artificial satellites of the earth. Knowledge of the dimensions of the earth ellipsoid is necessary for the theoretical practical aims of geodesy and cartography, as well as for other branches of science and technology. The Krasovskii ellipsoid is used in geodetic and cartographic work in the USSR and other socialist countries.

### REFERENCE

Krasovskii, F.*N.Rukovodstvo po vysshei geodezii*, part 2. Moscow, 1942.

A. A. IZOTOV