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Normal Gravity
In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of Earth's gravity, on or near its surface, by means of a mathematical model. The most common theoretical model is a rotating Earth ellipsoid of revolution (i.e., a spheroid). Other representations of gravity can be used in the study and analysis of other bodies, such as asteroids. Widely used representations of a gravity field in the context of geodesy include spherical harmonics, mascon models, and polyhedral gravity representations. Principles The type of gravity model used for the Earth depends upon the degree of fidelity required for a given problem. For many problems such as aircraft simulation, it may be sufficient to consider gravity to be a constant, defined as: :g=g_= based upon data from ''World Geodetic System 1984'' (WGS-84), where g is understood to be pointing 'down' in the local frame of reference. If it is desirable to model an object's weight on Earth as a function of latit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesy
Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional space, 3D. It is called planetary geodesy when studying other astronomical body, astronomical bodies, such as planets or Natural satellite, circumplanetary systems. Geodynamics, Geodynamical phenomena, including crust (geology), crustal motion, tides, and polar motion, can be studied by designing global and national Geodetic control network, control networks, applying space geodesy and terrestrial geodetic techniques, and relying on Geodetic datum, datums and coordinate systems. Geodetic job titles include geodesist and geodetic surveyor. History Geodesy began in pre-scientific Classical antiquity, antiquity, so the very word geodesy comes from the Ancient Greek word or ''geodaisia'' (literally, "division of Earth"). Early ideas about t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Constant
The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It is also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, denoted by the capital letter . In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse-square law, inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately The modern notation of Newton's law involving was introduced i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-major And Semi-minor Axes
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the cente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geophysical
Geophysics () is a subject of natural science concerned with the physical processes and properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct investigations across a wide range of scientific disciplines. The term ''geophysics'' classically refers to solid earth applications: Earth's shape; its gravitational, magnetic fields, and electromagnetic 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity (mathematics)
In mathematics, the eccentricity of a Conic section#Eccentricity, conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: * The eccentricity of a circle is 0. * The eccentricity of a non-circular ellipse is between 0 and 1. * The eccentricity of a parabola is 1. * The eccentricity of a hyperbola is greater than 1. * The eccentricity of a pair of Line (geometry), lines is \infty. Two conic sections with the same eccentricity are similarity (geometry), similar. Definitions Any conic section can be defined as the Locus (mathematics), locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the ''eccentricity'', commonly denoted as . The eccentricity can also be defined in terms of the intersection of a plane and a Cone (geometry), double-napped cone associated with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carlo Somigliana
Carlo Somigliana (20 September 1860 – 20 June 1955) was an Italian mathematician and a classical mathematical physicist, faithful member of the school of Enrico Betti and Eugenio Beltrami. He made important contributions to linear elasticity: the Somigliana integral equation, analogous to Green's formula in potential theory, and the Somigliana dislocations are named after him. Other fields he contribute to include seismic wave propagation, gravimetry and glaciology. One of his ancestors was Alessandro Volta: he was an ancestor of Carlo's mother, Teresa Volta. Life and career Carlo Somigliana began his university studies in Pavia, where he was a student of Eugenio Beltrami. Later he moved to Pisa and had Betti among his teachers: in Pisa he established a lifelong friendship with Vito Volterra, who was one of his classmates, lasted until the death of the latter. He graduated from Scuola Normale Superiore di Pisa in 1881. In 1887 Somigliana began teaching as an assistant at t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WGS84
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency. History Efforts to supplement the various national surveying systems began in the 19th century with F.R. Helmert's book (''Mathematical and Physical Theories of Physical Geodesy''). Austria and Germany founded the (Central Bureau of International Geodesy), and a series of global ellipsoids of the Earth were derived (e.g., Helmert 1906, Hayford 1910 and 1924). A unified geodetic system for the whole world became essential in the 1950s for several reasons: * International space science and the beginning of astronautics. * The lack of inter-continental ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmert
Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and statistician with important contributions to the theory of errors. Career Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg and Dresden, he entered the Polytechnische Schule, now Technische Universität, in Dresden to study engineering science in 1859. Finding him especially enthusiastic about geodesy, one of his teachers, , hired him while still a student to work on the of the Ore Mountains and the drafting of the trigonometric network for Saxony. In 1863 Helmert became Nagel's assistant on the . After a year's study of mathematics and astronomy Helmert obtained his doctor's degree from the University of Leipzig in 1867 for a thesis based on his work for Nagel. In 1870 Helmert became instructor and in 1872 professor at RWTH Aachen, the new Technical University in Aachen. At Aachen he wrote ''Die mathematischen und physikalischen Theorieen der höheren Geodäsie' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Identity
The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is :\sin^2 \theta + \cos^2 \theta = 1. As usual, \sin^2 \theta means (\sin\theta)^2. Proofs and their relationships to the Pythagorean theorem Proof based on right-angle triangles Any similar triangles have the property that if we select the same angle in all of them, the ratio of the two sides defining the angle is the same regardless of which similar triangle is selected, regardless of its actual size: the ratios depend upon the three angles, not the lengths of the sides. Thus for either of the similar right triangles in the figure, the ratio of its horizontal side to its hypotenuse is the same, namely . The elementary definitions of the sine and cosine functions in terms of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double-angle Formula
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity. Pythagorean identities The basic relationship between the sine and cosine is given by the Pythagorean identity: \sin^2\theta + \cos^2\theta = 1, where \sin^2 \theta means ^2 and \cos^2 \thet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GRS80
The Geodetic Reference System 1980 (GRS80) consists of a global reference ellipsoid and a normal gravity model. The GRS80 gravity model has been followed by the newer more accurate Earth Gravitational Models, but the GRS80 reference ellipsoid is still the most accurate in use for coordinate reference systems, e.g. for the international ITRS, the European ETRS89 and (with a 0,1 mm rounding error) for WGS 84 used for the American Global Navigation Satellite System (GPS). Background Geodesy is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional, time-varying space. The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
