Geoid

Mathematical definition

On the Ground, any point undergoes a Accélération of gravity

g

. This acceleration derives from a Potentiel of Pesanteur

W

, such as:

g= \ overrightarrow \ operatorname {grad} (W)

Surfaces where the potential of gravity $W$ is constant are equipotential S of gravity. A geoid is an equipotential surface of gravity close to the mean level of the seas.

As the orientation of the field of gravity varies on the surface of the Earth, a geoid is not superimposed rigorously with an ellipsoid. The form a geoid “is indeed deformed”, because of the unequal distribution of the masses on the surface of the Earth and inside. The presence of an assembly line, for example, created a deformation of the surface geoid.

Bond with altitude

A Altitude expresses the distance of a point compared to the geoid, sometimes called " MSL" (for Mean Sea Level: mean level of the seas). The ellipsoid and it and geoid do not agree inevitably. Altitude along a line of field thus differs the height of this same point, measured compared to the ellipsoid. The difference between two surfaces in reference, called height geoid, can go until a hundred meters.

There exist several manners of expressing altitude: dynamic Altitude, orthometric Altitude, normal Altitude.

For what is used a geoid?

Any measurement needs a reference. The geoid, being an equipotential surface of particular gravity, it serves as zero of reference for precise measurements of altitude. The applications are numerous, hydrology (study of the basins slopes), aeronautics, ballistics.

Since one wanted to send bulky objects (fused, intercontinental missiles) according to elliptic trajectories around the Earth, it became important to know with precision the terrestrial field of gravity. A method of prospection geophysical, the Gravimétrie also uses the geoid like reference.

But this irregular surface is difficult to use in calculations, and one then prefers to use a Ellipsoïde, surface regular which when it is quite selected (center, dimensions, orientation…) deviate to the maximum of a few tens of meters of the geoid, whatever the point considered on the surface of the Earth (see geodetic Système).

See too

Figure of the Ellipsoidal Earth
of revolution

External bonds

Fields geophysics, for a description the geoid by decomposition in Harmonic spherical