Earth radius

The Earth's radius is the radius of the approximated as a spherical shape of the earth, the " globe ". He is an astronomical unit and also a fundamental quantity for many fields of knowledge - especially for the geosciences - and for technology. It is about 6371 kilometers on average. The Earth's diameter is twice the radius of the Earth, on average about 12,742 km.

Depending on the application different detailed earth radii are used that are not based on a spherical shape, but on an ellipsoid of revolution or other approximations.

• 2.1 From antiquity to Columbus
• 2.2 Geodesy in modern times

Commonly used values

As the earth or the sea level ( geoid ) has no exact spherical shape, but at its poles by about 21 km ( 0.335 percent) is flattened, has to be defined in detail for further details of its radius ' of the term " earth ". The most frequent values ​​are used:

• Rounded value R = 6371.0 km to above, or
• The older value 6371.2 kilometers ( Hayford ellipsoid 1924)

• Equal area ball 6,371,007.176 m (GRS 80 ellipsoid )

Radii of some important earth ellipsoids

History

From ancient times up to Columbus

The idea that the earth was spherical, already appeared around 600 BC in the Ionian natural philosophy ( Thales of Miletus, Anaximander ) and v. In the 4th century BC Aristotle was three astronomical evidence for that fact.

The first destination of the earth's circumference is narrated by Eratosthenes (c. 240 BC), the inventor of the degree measurement method. He compared the angular height of the sun is in Egypt between Alexandria and Syene (modern Aswan ), which differ by 1/50 of the full circle. From this 50 resulted as the circumference of the earth 50 times the distance from Alexandria to Aswan, after today's units ie 835 km times equal to 41,750 km. From the periphery of the radius may be derived by calculation. Eratosthenes calculated in stages; for the accuracy of its determination of the radius of the Earth, however, the unit of length used is irrelevant: Eratosthenes came after an earth radius of about 6645 km and thus to a value which is 4.2 percent above today.

In the early Middle Ages, the Arabs found the length of a degree to 56 2/3 Arabic miles. Since this is equivalent to about 2,000 m, the result is the radius of the earth's body R = 6500 km, which differs from the current 2 percent level. The mathematician Al -Biruni determined in the year 1023 with a new measuring technique of his own invention the radius of the globe eventually to 6339.6 km.

In the 15th century, these values ​​were certainly known in Europe, but was partially assigned to the Arab values ​​shorter by 25 percent Italian mile. On this basis, and at the same time overestimating the length of Asia Columbus came to the ultimately erroneous conclusion that one would reach on a westerly course in a few weeks to East Asia.

Ferdinand Magellan began a circumnavigation in August 1519. When the fleet in 1520, the Philippines and thus demonstrably Asian waters reached, the final proof of the sphericity of the Earth was rendered, the long time too short estimated circumference of the earth was now detected correctly.

Geodesy in modern times

The actual size of the Earth was known exactly only at the end of the age of discovery to a few percent. Its deviation from the spherical shape certain French scientists of the 17th century by degree measurements over several hundred kilometers, but was still uncertain and in some cases even led to an extended pole radius. In contrast, Isaac Newton calculated that the Earth's rotation would cause a flattening of the earth because of the resulting centrifugal force.

The answer to this question was carried out by the Geodesy of the French Academy with her two expeditions to Lapland and Peru ( 1736-1741 ). They served simultaneously meter definition ( postulated circumference of the earth over the poles = 40,000 km ), yielding an accuracy of 0.02 percent or 1.5 km ( Meridian Quadrant = 10,002,250 m, mean earth radius R0 = 6369.6 km ).

Since then, the accuracy with which it is known the mathematical figure of the earth, first doubles every 50 years. Around 1965 the satellite geodesy led to an enormous increase in accuracy to 20 meters and now knocks before in the centimeter range. Newly developed gradiometry satellites such as GRACE (2004) and GOCE even aim to change the figure of the earth, who are suspected in the range of a few millimeters per year.

Regional and local details of the earth's

The deviations from the spherical shape of the earth would indeed in an ideal world not yet visible, but the high mountains could be palpated using their " roughness ". The Earth flattening ( flattened at the poles to 21 km or 0.3 per cent), however, must be taken into account in any accurate map, often the typical progression of the curvature of the earth of every continent ( "waves" in the geoid to / - 100 meters). The radius of curvature may vary regionally between about 6330 km and 6400 km, locally even 5000-8000 km.

Overall, the regional variability of the Earth's radius means a change of the scale of maps and computer models to a few kilometers to 1000 km and is to be considered in almost all applications. In the millimeter precision surveying today's technical projects, these effects already have on 100 meters distance.

The elevation or contour of the terrain, however, is not added to the radius of the earth, but - added to the database as an attribute - such as geographical information systems. For tasks with physical background, the variability of gravity is taken into account, which takes on the Earth's surface global values ​​from 9.76 to 9.94 m / s ².

In tasks of astronomy or space of the distance of a point is often required from the center of the Earth, called the geocentric radius. It can be calculated from the Erdellipsoid used and is, for example, in Central Europe, 6365-6368 km, which must be added the altitude of the point comes. However, this is the radius of curvature of the level surfaces and height measurements to distinguish, which can be up to 30 km greater.

Physical influences

The Earth's radius and its variation is not only a fundamental quantity in geometric tasks, but also in physics and various geosciences. Here it occurs about as distance from center of the earth or of the earth's axis to (R * cos ( latitude) ), as a radius of curvature in movement or in measuring beams as Gaussian curvature (1 / R ²) or in the effect of gradients of different forces.

The mean gravity on the Earth's surface depends as much with the radius and the mass of the Earth together as the mean density of the earth. Their value of 5.52 g / cm ³ is the Geophysics - compared with conventional rock densities of 2.5-2.8 g / cm ³ - a clear indication that the density of the Earth must be much higher. For over 100 years it has explored the inner shell structure of the earth, among others, by gravimetry, seismic and mathematical models.

Summary

The exact figure of the earth is already known to a few centimeters, although their height profile varies by 10 to 15 km to both sides:

• Medium ( volume equivalent ) radius of the earth = 6371 km
• Geocentric mean, variation = 6368 km ± 11 km
• Axes of the earth ellipsoid = 6378.1 or 6356.7 km
• Continental radii of curvature ( north-south) = 6330-6400 km
• " Globe " therefore sufficient only to 0.5 % accuracy.

In many cases is unknown, that varies due to the Earth flattening not only the radius of the earth, but also a "wide problem": the geographical and geocentric latitudes differ by up to 0.19 ° or 22 kilometers. For further local variations of the shape of the Earth by a sphere, therefore, the surface was approximated by locally optimal matching reference ellipsoid for the land surveying, of which over a hundred different world are in use. There are no geographical coordinates of a location always refers to a specific reference system ( geodetic datum ).

This means that an extended beneath our feet Lot imaginary up to 20 km misses the center of the earth. Subjects such as geodesy, geophysics and satellite geodesy have to deal daily with the related facts.

Times around the world

Is approximated assumed a spherical shape for the figure of the earth, the earth's circumference can be calculated by calculating the circumference of a circle approximated by the radius of the earth. This results in an earth radius of 6378 km a circumference of the earth of about 40074 km.

Because of the Earth flattening is the circumference at the equator is about 40074 km at its greatest. The distance of the poles from the equator is about 10002 km, this corresponds to a circumference of the earth along a meridian of about 40008 km. This value is remarkably close to the round value of 40,000 km. The reason is that according to an early definition of the unit meter should be set as the 10 millionth part of earth's quadrant.

The length of the parallels is not uniform in contrast to the length of the meridians and takes from the equator towards the poles from. Their length can be neglecting the Earth flattening approximation calculated with, where the latitude means. The length of Mainz passing 50th parallel circuit is thus about.