**11. The normal spheroid, ellipsoid and geoid**

The earth considered as an ideal spheroid or normal spheroid in case of considering the earth as a completely liquid, means without any lateral density change. The direction of gravity attraction in such case is perpendicular on the earth everywhere and passing through the earth center. But the increase of radius of the earth at equator from that at poles by about 21 km make the ellipsoid shape is better approximation for earth than spheroid shape, (**Figure 4**).

Also, the earth in fact is not uniform and the density change laterally at least in the crust and upper most part of the mantle of the earth. The actual surface of the earth can be represent by the geoid which is equal to sea level and its extension in the land. The geoid surface may be up or down the ellipsoid surface depending on the distribution of density in the earth or the topographic changes, (**Figure 5**). The evidences on the difference between the geoid and ellipsoid obtained from the observation of the deflection of plumb line. This deflection measured during the geodetic and astronomical measurements, where the plump line deflect toward the excess masses in the continent, while it is deflected away from an area of mass deficiency as in oceans area.

The difference between geoid and ellipsoid surfaces small relative to the radius of the earth. For example it is about 40 meters in Rocky Mountains.

**Figure 4.** *The spheroid and ellipsoid relationship [4].*

*Gravity Field Theory DOI: http://dx.doi.org/10.5772/intechopen.99959*

**Figure 5.** *The ellipsoid and geoid relationship [4].*
