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Earth Section Paths
Earth section paths are plane curves defined by the intersection of an earth ellipsoid and a Plane (geometry), plane (ellipsoid plane sections). Common examples include the ''great ellipse'' (containing the center of the ellipsoid) and normal sections (containing an ellipsoid normal direction). Earth section paths are useful as approximate solutions for geodetic problems, the direct and inverse calculation of geographic distances. The rigorous solution of geodetic problems involves skew curves known as ''geodesics on an ellipsoid, geodesics''. Inverse problem The inverse problem for earth sections is: given two points, P_1 and P_2 on the surface of the reference ellipsoid, find the length, s_, of the short arc of a spheroid section from P_1 to P_2 and also find the departure and arrival azimuths (angle from true north) of that curve, \alpha_1 and \alpha_2. The figure to the right illustrates the notation used here. Let P_k have geodetic latitude \phi_k and longitude \lambda_k ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Position Vector
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point ''P'' in space. Its length represents the distance in relation to an arbitrary reference origin ''O'', and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from ''O'' to ''P''. In other words, it is the displacement or translation that maps the origin to ''P'': :\mathbf=\overrightarrow. The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus. Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.Keller, F. J., Gettys, W. E. et al. (1993), p. 28–29. Relative position The relative position of a point ''Q'' with respect to point ''P'' is the Euclidean vector res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographical Distance
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the Geodesy#Geodetic problems, second (inverse) geodetic problem. Introduction Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an ''exact'' distance, which is unattainable if one attempted to account for every irregularity in the surface of the Earth. Common abstractions for the surface between two geographic points are: *Flat surface; *Spherical surface; *Ellipsoidal surface. All abstractions above ignore changes in elevation. Calculation of distances which account for changes in elevation relative to the idealized surface are not discussed in this article. Classification of Formulae based on Appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Section
In geometry, a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane (geometry), plane section of the quadric, as this circle is the intersection with the quadric of the plane containing the circle. Any plane section of a sphere is a circular section, if it contains at least 2 points. Any surface of revolution, quadric of revolution contains circles as sections with planes that are orthogonal to its axis; it does not contain any other circles, if it is not a sphere. More hidden are circles on other quadrics, such as tri-axial ellipsoids, elliptic cylinders, etc. Nevertheless, it is true that: *Any quadric surface which contains ellipses contains circles, too. Equivalently, all quadric surfaces contain circles except parabolic and hyperbolic cylinders and hyperbolic paraboloids. If a quadric contains a circle, then every intersection of the quadric with a plane parallel to this circle is also a circle, provided it contains at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Projection
The vector projection (also known as the vector component or vector resolution) of a vector on (or onto) a nonzero vector is the orthogonal projection of onto a straight line parallel to . The projection of onto is often written as \operatorname_\mathbf \mathbf or . The vector component or vector resolute of perpendicular to , sometimes also called the vector rejection of ''from'' (denoted \operatorname_ \mathbf or ), is the orthogonal projection of onto the plane (or, in general, hyperplane) that is orthogonal to . Since both \operatorname_ \mathbf and \operatorname_ \mathbf are vectors, and their sum is equal to , the rejection of from is given by: \operatorname_ \mathbf = \mathbf - \operatorname_ \mathbf. To simplify notation, this article defines \mathbf_1 := \operatorname_ \mathbf and \mathbf_2 := \operatorname_ \mathbf. Thus, the vector \mathbf_1 is parallel to \mathbf, the vector \mathbf_2 is orthogonal to \mathbf, and \mathbf = \mathbf_1 + \mathbf_2. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NS 5000nm Eq
NS as an abbreviation can mean: Arts and entertainment Gaming * ''Natural Selection'' (video game), a mod for the game ''Half-Life'' * '' NetStorm: Islands At War'', a real-time strategy game published in 1997 by Activision * Nintendo Switch, a hybrid video game console and handheld. * '' NationStates'', a web-based simulation game Literature * '' New Spring'' (known to fans as "NS"), a 1999 anthology edited by Robert Silverberg and derivative 2004 novella by Robert Jordan * NS-series robots from the book '' I, Robot'' Companies * National Semiconductor (also known as "Natsemi"), an American integrated circuit design and manufacturing company * Nederlandse Spoorwegen, the main public transport railway company in the Netherlands * Norfolk Southern Railway, a major Class I railroad in the United States, owned by the Norfolk Southern Corporation * Norfolk Southern Railway (1942–1982), the final name of a railroad running in Virginia and North Carolina before its acquisition by 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] |
Spherical Trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Jean Baptiste Joseph Delambre, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook ''Spherical trigonometry for the use of colleges and Schools''. Since then, significant developments have been the application of vector methods, quaternion m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shows The Geodesic Deviation For Various Sections Connecting New York And Paris
Show or The Show may refer to: Competition, event, or artistic production * Agricultural show, associated with agriculture and animal husbandry * Animal show, a judged event in the hobby of animal fancy ** Cat show ** Dog show ** Horse show ** Specialty show, a dog show which reviews a single breed *Fashion show, showcase of clothing and/or accessories *Show, an artistic production, such as: ** Concert ** Game show ** Radio show ** Talk show ** Television show ** Theatre production * Trade show Arts, entertainment, and media Films * ''Show'' (film), a 2002 film * ''The Show'' (1922 film), starring Oliver Hardy * ''The Show'' (1927 film), directed by Tod Browning * ''The Show'' (1995 film), a hip hop documentary * ''The Show'' (2017 film), an American satirical drama * ''The Show'' (2020 film), a British mystery film Albums * ''Show'' (The Cure album), 1993 * ''Show'' (The Jesus Lizard album), 1994 * ''The Show'' (eMC album), 2008 * ''The Show'' (Niall Horan a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meridian Arc
In geodesy and navigation, a meridian arc is the curve (geometry), curve between two points near the Earth's surface having the same longitude. The term may refer either to a arc (geometry), segment of the meridian (geography), meridian, or to its Arc length, length. Both the practical determination of meridian arcs (employing measuring instruments in field campaigns) as well as its theoretical calculation (based on geometry and abstract mathematics) have been pursued for many years. Measurement The purpose of measuring meridian arcs is to determine a figure of the Earth. One or more measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements. Measurements of meridian arcs at several latitudes along many meridians around the world can be combined in order to approximate a ''geocentric ellipsoid'' intended to fit the entire world. The earliest determinations of the size of a spherical E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
