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Bessel Ellipsoid
The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy. The Bessel ellipsoid was derived in 1841 by Friedrich Wilhelm Bessel, based on several arc measurements and other data of continental geodetic networks of Europe, Russia and the British Survey of India. It is based on 10 meridian arcs and 38 precise measurements of the astronomic latitude and longitude (see also astro geodesy). The dimensions of the Earth ellipsoid axes were defined by logarithms in keeping with former calculation methods. The Bessel and GPS ellipsoids The Bessel ellipsoid fits especially well to the geoid curvature of Europe and Eurasia. Therefore it is optimal for National survey networks in these regions, despite of the fact that its axes are about 700 m shorter than that of the mean Earth ellipsoid d ...
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Reference Ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the ''equatorial axis'' (''a'') and the ''polar axis'' (''b''); their radial difference is slightly more than 21 km, or 0.335% of ''a'' (which is not quite 6,400 km). Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite geodesy or the analysis and interconnection of continental geodetic networks. Amongst the different set of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international H ...
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Flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is :: \mathrm = f =\frac . The ''compression factor'' is \frac\,\! in each case; for the ellipse, this is also its aspect ratio. Definitions There are three variants of flattening; when it is necessary to avoid confusion, the main flattening is called the first flattening.Torge, W. (2001). ''Geodesy'' (3rd edition). de Gruyter. and online web textsOsborne, P. (2008). The Mercator Projections'' Chapter 5.Rapp, Richard H. (1991). ''Geometric Geodesy, Part I''. Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio/ref> In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flatt ...
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Americas
The Americas, which are sometimes collectively called America, are a landmass comprising the totality of North and South America. The Americas make up most of the land in Earth's Western Hemisphere and comprise the New World. Along with their associated islands, the Americas cover 8% of Earth's total surface area and 28.4% of its land area. The topography is dominated by the American Cordillera, a long chain of mountains that runs the length of the west coast. The flatter eastern side of the Americas is dominated by large river basins, such as the Amazon, St. Lawrence River–Great Lakes basin, Mississippi, and La Plata. Since the Americas extend from north to south, the climate and ecology vary widely, from the arctic tundra of Northern Canada, Greenland, and Alaska, to the tropical rain forests in Central America and South America. Humans first settled the Americas from Asia between 42,000 and 17,000 years ago. A second migration of Na-Dene speakers followed later ...
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Continent
A continent is any of several large landmasses. Generally identified by convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continents. Ordered from largest in area to smallest, these seven regions are: Asia, Africa, North America, South America, Antarctica, Europe, and Australia. "Most people recognize seven continents—Asia, Africa, North America, South America, Antarctica, Europe, and Australia, from largest to smallest—although sometimes Asia and Europe are considered a single continent, Eurasia." Variations with fewer continents may merge some of these, for example America, Eurasia, or Afro-Eurasia are sometimes treated as single continents, which can bring the total number as low as four. Zealandia, a largely submerged mass of continental crust, has also been described as a continent. Oceanic islands are frequently grouped with a nearby continent to divide all the world's land into geographical regions. Under t ...
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Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base ''b'' and must be known. ...
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Vertical Deflection
The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes. The vertical deflection are the angular components between the true zenith–nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface). VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10 ″ in flat areas or 20–50″ in mountainous terrain). The deflection of the vertical has a north–south component ''ξ'' ( xi) and an east–west component ''η'' (eta). The value of ''ξ'' is the difference between the ''astronomic latitude'' and the ''geodetic latitude'' (taking ...
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International Ellipsoid
The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford (1868–1925), which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics IUGG in 1924, and was recommended for use all over the world. Many countries retained their previous ellipsoids. The Hayford ellipsoid is defined by its semi-major axis = and its flattening = 1:297.00. Unlike some of its predecessors, such as the Bessel ellipsoid ( = , = 1:299.15), which was a European ellipsoid, the Hayford ellipsoid also included measurements from North America, as well as other continents (to a lesser extent). It also included isostatic measurements to reduce plumbline divergences. Hayfords ellipsoid did not reach the accuracy of Helmerts ellipsoid published 1906 ( = , = 1:298.3). It has since been replaced as the "International ellipsoid" by the ne ...
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International Association Of Geodesy
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Hayford Ellipsoid
The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford (1868–1925), which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics IUGG in 1924, and was recommended for use all over the world. Many countries retained their previous ellipsoids. The Hayford ellipsoid is defined by its semi-major axis = and its flattening = 1:297.00. Unlike some of its predecessors, such as the Bessel ellipsoid ( = , = 1:299.15), which was a European ellipsoid, the Hayford ellipsoid also included measurements from North America, as well as other continents (to a lesser extent). It also included isostatic measurements to reduce plumbline divergences. Hayfords ellipsoid did not reach the accuracy of Helmerts ellipsoid published 1906 ( = , = 1:298.3). It has since been replaced as the "International ellipsoid" by the ne ...
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Geophysical
Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' sometimes refers only to solid earth applications: Earth's shape; its gravitational and magnetic fields; its internal structure and composition; its dynamics and their surface expression in plate tectonics, the generation of magmas, volcanism and rock formation. However, modern geophysics organizations and pure scientists use a broader definition that includes the water cycle including snow and ice; fluid dynamics of the oceans and the atmosphere; electricity and magnetism in the ionosphere and magnetosphere and solar-terrestrial physics; and analogous problems associated with the Moon and other planets. Gutenberg, B., 1929, Lehrbuch der Geophysik. Leipzig. Berlin (Gebruder Borntraeger). Runcorn, S.K, (editor-in-chief), 1967, International ...
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Clarke Ellipsoid
Col Alexander Ross Clarke FRS FRSE (1828–1914) was a British geodesist, primarily remembered for his calculation of the Principal Triangulation of Britain (1858), the calculation of the Figure of the Earth (1858, 1860, 1866, 1880) and one of the most important text books of Geodesy (1880). He was an officer of the Royal Engineers employed on the Ordnance Survey. Biographical details Sources The basic sources of material on Clarke are the two articles by Charles Close, one of the Directors of the Ordnance Survey. The first was an article for the Royal Engineers Journal and the second, a revised and expanded version, appeared in the Empire Survey Review. Although Close was almost thirty years younger than Clarke, and joined the Ordnance Survey only after Clarke's retirement, they knew each other well and they collaborated on the article ''Map'' for the eleventh edition of Encyclopædia Britannica. Much of Close's material is incorporated in the web page ''REubique'' ( de ...
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Asia
Asia (, ) is one of the world's most notable geographical regions, which is either considered a continent in its own right or a subcontinent of Eurasia, which shares the continental landmass of Afro-Eurasia with Africa. Asia covers an area of , about 30% of Earth's total land area and 8.7% of Earth's total surface area. The continent, which has long been home to the majority of the human population, was the site of many of the first civilizations. Its 4.7 billion people constitute roughly 60% of the world's population. In general terms, Asia is bounded on the east by the Pacific Ocean, on the south by the Indian Ocean, and on the north by the Arctic Ocean. The border of Asia with Europe is a historical and cultural construct, as there is no clear physical and geographical separation between them. It is somewhat arbitrary and has moved since its first conception in classical antiquity. The division of Eurasia into two continents reflects East–West cultural, linguistic, ...
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