Theoretical gravity

As Schwereabplattung the dependence of the theoretical acceleration due to gravity ( gravity ) is called on the latitude in geophysics. It is calculated from the gravity on the equator of the earth ellipsoid and the gravity at the poles:

It is a consequence of the Earth's rotation and the resulting Earth flattening:

Where and are the semi-axes of the earth ellipsoid are.

The exact values ​​of and depend, inter alia, the used Erdellipsoid from.

In the international Earth model GRS80 applies:

In the global average:

The increase of gravity from the Earth's equator towards the poles is therefore 0.52 percent, for example, to is clearly noticeable in the length of the seconds pendulum.

The (physical ) Schwereabplattung is much stronger than the (geometric ) Earth flattening. Therein, the noticeable difference between the two gravity values ​​at the equator and at the poles is expressed, which are the smallest and largest theoretical gravity at sea level.

The Schwereabplattung is one of the reasons why the level surfaces of the Earth's gravity field are not completely parallel to the sea.

History

While the geometric Earth flattening postulated as early as 1680 by Newton and was only in 1742 confirmed empirically by the Peru - Lapland expeditions of the Paris Academy, it behaved in the Schwereabplattung reversed: Jean Richer presented in 1673 in Cayenne has a significantly shorter second pendulum as in Paris finds to the theory, however, was created in 1743 by Alexis -Claude Clairaut (theory of the earth's shape according to the laws of hydrostatics ). You could of course apply as an additional protection for the definition of the standard meter in Paris (1793).

• Gravimetry
• Geodesy