# Figure of the Earth

As a figure of the earth (or earth's ) a mathematically definable as simple approach is referred to the shape of the earth. Such a reference surface is needed in many areas of geosciences for calculations and for position information. First thoughts on likely already back to South American civilizations, India and Babylonia, but especially to the ionic nature of philosophy.

Instead of the prehistoric notion of a flat earth occurred during the ancient Greek model of the globe - on this historic process, see the article Flat Earth.

## The " globe "

A theoretical ideal globe ( globe) is only of limited use as a calculation area for the sciences, because the earth is flattened by its rotation at the poles by about 0.3 percent. This flattening would indeed be by the naked eye from outer space hardly noticing, but makes de facto 21 km from.

If you take the usual " middle earth radius " of 6371 km, the zonal deviations from this amount to at least still between -14 km and 7 km. With a spherical radius of 6368 km, these deviations would indeed reduce to -11 / 10 km, but, there would be much too small values for surface area and volume of the earth. The same volume with our planet sphere would have a radius of 6371.2 km. The radius of a sphere with the same surface deviates by a few meters.

Therefore, spherical models for the Earth are only useful when no accuracy is better than 10 kilometers required. Even for the maps in a simple school atlas need a about 10 times better model, and even for locations with geographical or Gauss-Krueger - coordinates.

So is often unknown, distinguish that geocentric and geographic latitude by up to 0.19 ° or 22 kilometers. Disciplines such as geodesy, geoinformatics, geophysics and satellite geodesy have to deal daily with this fact.

## Earth's surface, Erdellipsoid and " geoid "

In principle, the shape of the Earth can be defined in several ways:

The first two options are ruled out in practice, because they are too complicated for the majority of applications. Calculations on a sloping, variably inclined surface require much more effort. Also the necessary digital terrain models (DTM, DTM internationally ) are sufficiently accurate and available worldwide only since the 1990s.

The third option separates normally not - despite the relatively uniform sea level - from, because even this space is mathematically complicated. A superposition of spherical harmonics, which represents the sea exactly only two to four kilometers, already requires a formula group with 1024 coefficients. For an accuracy of ± 1 km of effort increases at least tenfold, which is 100 times the computing time.

Nevertheless, the variant No. 3 is used for special purposes ( oceanography, physical geodesy and Geoidforschung ). It corresponds to a mixed physical- mathematical model.

For practical application, the geoid is defined by its deviation from a reference ellipsoid: In a regular grid, the deflection of the vertical are given ( difference between Ellipsoidnormale and plumb line ) and the geoid separation ( difference in height between ellipsoid and geoid ). So can be calculated accurately surveying networks and combined with gravimetry despite the irregularities in the gravitational field.

## Reference ellipsoid and "medium Erdellipsoid "

After all, the model remains No. 4 - being the basis of the vast majority of applications and calculations: A non- physical, but purely geometrically defined, defined by two axes of rotation figure ( equatorial radius a and polar radius b). The concrete values of the axes a, b depend, however, on the particular region because the mean curvature of the earth can vary even within a continent by up to two km.

Details in this regard are in the articles on the ellipsoid of Bessel (1842 ), Krassowski (1940 ), Hayford (1924 ) and Clarke ( 1866/1880 ) and the GPS models GRS 80 and WGS 84 read. For global surveys (about satellite ) or for space, the latter reference systems are intended for the National Survey of individual states is usually the bestangepasste for the country of the aforementioned or used by a hundred or more Referenzellipsoiden. The reference ellipsoid differ from each other by up to 1000 meters. For more accurate location information, the corresponding reference system should therefore be reported whatsoever.

## Summary

So what is the " earth's "? In the geoscience literature since 1900, and in practice it is - depending on the subject and research:

- The reference or Erdellipsoid
- The geoid ( for sub-basin of Geodesy and Geophysics )
- In contrast, the actual surface of the earth is too detailed for general usage, to qualify as a figure of the earth. At most, sees a geologist or geomorphologist differentiated when he analyzes local landforms, mountain building, peak or valley forms.

## Credentials

- Friedrich Robert Helmert. , The mathematical and physical theories of the Higher Geodesy, Volume I. Publisher BG Teubner, Leipzig 1880.
- Veikko Heiskanen, Helmut Moritz: Physical Geodesy (the classic textbook until 2005). Freeman Publishing, San Francisco, 1967, reprint Graz 1979.
- Bernhard Hofmann - Wellenhof (ed.): Physical Geodesy ( modern successor to the obg textbook. ). Springer - Verlag, Wien, 2005, ISBN 3-211-23584-1.
- Wolfgang Thomas, geodesy. 1st edition. Goschen / De Gruyter, Berlin 1975.

- Geodesy
- Geophysics
- Geodesy