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Earth 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'' () and the ''polar axis'' (); their radial difference is slightly more than 21 km, or 0.335% of (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 Hayfo ...
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Earth Oblateness To Scale
Earth is the third planet from the Sun and the only astronomical object known to harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all of Earth's water is contained in its global ocean, covering 70.8% of Earth's crust. The remaining 29.2% of Earth's crust is land, most of which is located in the form of continental landmasses within Earth's land hemisphere. Most of Earth's land is at least somewhat humid and covered by vegetation, while large sheets of ice at Earth's polar deserts retain more water than Earth's groundwater, lakes, rivers, and atmospheric water combined. Earth's crust consists of slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth has a liquid outer core that generates a magnetosphere capable of deflecting most of the destructive solar winds and cosmic radiation. Earth has a dynamic atmosphere, which sustains Ear ...
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Hayford Ellipsoid
In geodesy, the Hayford ellipsoid is a reference ellipsoid named after the American 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 Helmert's ellipsoid published 1906 ( = , = 1:298.3). It has since been replaced as the "International ellips ...
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Gravity
In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force between objects and the Earth. This force is dominated by the combined gravitational interactions of particles but also includes effect of the Earth's rotation. Gravity gives weight to physical objects and is essential to understanding the mechanisms responsible for surface water waves and lunar tides. Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms. The gravitational attraction between primordial hydrogen and clumps of dark matter in the early universe caused the hydrogen gas to coalesce, eventually condensing and fusing to form stars. At larger scales this results in galaxies and clust ...
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IUGG
The International Union of Geodesy and Geophysics (IUGG; , UGGI) is an international non-governmental organization dedicated to the scientific study of Earth and its space environment using geophysical and geodetic techniques. The IUGG is a member of the International Science Council The International Science Council (ISC) is an international non-governmental organization that unites scientific bodies at various levels across the social and natural sciences. The ISC was formed with its inaugural general assembly on 4 July 20 ... (ISC), which is composed of international scholarly and scientific institutions and national Academies of Science, academies of sciences. History The IUGG was established in Brussels, Belgium in 1919. Objectives IUGG's objectives are the promotion and coordination of studies related to Earth's physical, chemical and mathematical representation. This includes geometrical shape, internal structure, gravity and magnetic fields, seismicity, volc ...
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Astronautics
Astronautics (or cosmonautics) is the practice of sending spacecraft beyond atmosphere of Earth, Earth's atmosphere into outer space. Spaceflight is one of its main applications and space science is its overarching field. The term ''astronautics'' (originally ''astronautique'' in French language, French) was coined in the 1920s by J.-H. Rosny aîné, J.-H. Rosny, president of the Académie Goncourt, Goncourt academy, in analogy with aeronautics. Because there is a degree of technical overlap between the two fields, the term aerospace is often used to describe both at once. In 1930, Robert Esnault-Pelterie published the first book on the new research field. The term ''cosmonautics'' (originally ''cosmonautique'' in French) was introduced in the 1930s by Ary Abramovich Sternfeld, Ary Sternfeld with his book ''Initiation à la Cosmonautique'' (Introduction to cosmonautics) (the book brought him the Robert Esnault-Pelterie#Prix REP-Hirsch, Prix REP-Hirsch, later known as the Prix d'As ...
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Coordinate
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate o ...
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Reduction (mathematics)
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called " reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Minimizing the number of radicals that appear underneath other radicals in an expression is called denesting radicals. Algebra In linear algebra, ''reduction'' refers to applying simple rules to a series of equations or matrices to change them into a simpler form. In the case of matrices, the process involves manipulating either the rows or the columns of the matrix and so is usually referred to as ''row-reduction'' or ''column-reduction'', respectively. Often the aim of reduction is to transform a matrix into its "row-reduced echelon form" or "row-echelon form"; th ...
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Regional
In geography, regions, otherwise referred to as areas, zones, lands or territories, are portions of the Earth's surface that are broadly divided by physical characteristics (physical geography), human impact characteristics (human geography), and the interaction of humanity and the environment (environmental geography). Geographic regions and sub-regions are mostly described by their imprecisely defined, and sometimes transitory boundaries, except in human geography, where Jurisdiction (area), jurisdiction areas such as national borders are defined in law. More confined or well bounded portions are called ''locations'' or ''places''. Apart from the Earth, global continental regions, there are also hydrosphere, hydrospheric and atmosphere, atmospheric regions that cover the oceans, and discrete climates above the land mass, land and water mass, water masses of the planet. The land and water global regions are divided into subregions geographically bounded by large geological feature ...
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Volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape ...
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Mean Sea Level
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. The ''arithmetic mean'', also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the '' sample mean'' (\bar) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x. Outside probability and statistics, a wide rang ...
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Geoid
The geoid ( ) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents (such as might be approximated with very narrow hypothetical canals). According to Carl Friedrich Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century. The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattene ...
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