Clairaut's Theorem (Earth Measurement)
The set of Clairaut describes a relationship between flattening , gravity and rotation of the Earth . It is named after the French mathematician Alexis-Claude Clairaut , who formulated it for the first time in his work Théorie de la Figure de la Terre, tirée des principes de l'hydrostatique (German theory of the shape of the earth according to the laws of hydrostatics ) in 1743 between the geometry and physics of the earth.
statement
Be there
- and the semi-axes of an ellipsoid of revolution (approximating the shape of the earth)
- the acceleration due to gravity at a point on the equator and that at a pole
- the angular velocity of the earth's rotation
- the earth mass and
- the gravitational constant .
Then applies
application
A second formulation of the sentence is
This allows the flattening of the earth to be calculated from measured values for and .
Web links
- Proof of the theorem as well as tables of the most important geometric and physical quantities of earth measurements (PDF file; 558 kB)