Geodetic earth model

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Geodetic earth models are geometrical-physical ideal bodies that serve as reference systems for describing the earth's body and the earth's surface. they provide

Historical and principal aspects

Historically, the first geoscientific model of the earth was the globe , which was the ideal shape of the earth around 400 BC. Became detectable. Aristotle gives 3 proofs of this, and Eratosthenes determined around 240 BC. The circumference of the earth to 250,000 stages. In the Middle Ages, similar earth measurements by Arab astronomers achieved a few percent accuracy.

The model of the ellipsoid of revolution was postulated from the 17th to the 18th century , but it soon became clear to leading scientists that the deviations of the mean figure of the earth (the sea level) from an ellipsoid would have to be greater than the measurement accuracy of the time .

When these deviations - in the form of vertical deviations and later the gravity anomalies  - caused unbearably large discrepancies in the national surveys , a distinction had to be made between the reference surfaces for height measurement (sea level, geoid ) and for position measurement ( reference ellipsoid ). Geodesy is still in this problem area today, which also has to do with its middle position between geophysics ( earth's gravitational field ) and geometry ( earth measurement ).

As potential theory was able to show in the 19th century, the geometrically ideal earth figure of the ellipsoid of revolution is a fiction in the physical sense. Because a terrestrial level surface - as the mean sea ​​level offers itself for a generally available reference surface - could only be of an ellipsoidal shape if the mass distribution in the interior of the earth were completely homogeneous, for example in the density , in the geology and also in the earth's mantle were no differences. Therefore, a geodetic earth model that relies on a mathematically simple earth surface for the calculation of coordinates cannot meet the requirements of geophysics or geodynamics .

Mathematical Simplicity vs. accuracy

The simplest are mathematical calculations on the model of the earth , for which the spherical trigonometry and the methods of leveling provide the formula apparatus. The deviations from reality, however, are of the order of magnitude of the flattening of the earth , i.e. around 0.3 percent.

The earth ellipsoid must be used for higher requirements . The calculations on the surface of an ellipsoid require series expansion , the formulas of which are e.g. B. go over half a page for the two main geodetic tasks , or methods of vector calculation for spatial tasks .

For today's measurement accuracy (smaller than mm at distances of kilometers) further steps are necessary, which can amount to a few cm per km as corrections due to deviations from the perpendicular or irregularities in the gravitational field. It gets a little more complicated for the height measurement , which mostly refers to the physical level surface of the geoid and requires methods of geoid determination accurate to the centimeter . Purely geometric (albeit terrestrially not directly usable) height determinations are possible using GPS and other satellite systems.

Further keywords: earth figure , basket arch , ellipsoid , three-axis ellipsoid , coordinate transformation

Physical plausibility

Since geodetic measurements generally refer to the local plumb line , purely geometric methods are not sufficient for models that are consistent with nature . Because the vertical direction is not only determined by mountains, valleys and types of rock , but also by the physical mass distribution inside the earth's body. This is where astronomical influences (changing Earth's rotation, tides) and geological processes such as continental drift (on average a few cm / year) come into play.

Further keywords: Earth as " solid body " versus geodynamics , tides , ice ages, erosion, mountain formation , slow decrease in earth rotation and flattening , reference system for gravimetry and gravity anomalies , swimming equilibrium ( isostasy ) in the earth's crust, ocean currents ...

Earth models of the 20th century

See also

Literature and web links