1.
Geodesy
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Geodesists also study geodynamical phenomena such as crustal motion, tides, and polar motion. For this they design global and national networks, using space and terrestrial techniques while relying on datums. Geodesy — from the Ancient Greek word γεωδαισία geodaisia — is primarily concerned with positioning within the temporally varying gravity field, such geodetic operations are also applied to other astronomical bodies in the solar system. It is also the science of measuring and understanding the earths geometric shape, orientation in space and this applies to the solid surface, the liquid surface and the Earths atmosphere. For this reason, the study of the Earths gravity field is called physical geodesy by some, the geoid is essentially the figure of the Earth abstracted from its topographical features. It is an idealized surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between the geoid and the ellipsoid is called the geoidal undulation. It varies globally between ±110 m, when referred to the GRS80 ellipsoid, a reference ellipsoid, customarily chosen to be the same size as the geoid, is described by its semi-major axis a and flattening f. The quantity f = a − b/a, where b is the axis, is a purely geometrical one. The mechanical ellipticity of the Earth can be determined to high precision by observation of satellite orbit perturbations and its relationship with the geometrical flattening is indirect. The relationship depends on the density distribution, or, in simplest terms. The 1980 Geodetic Reference System posited a 6,378,137 m semi-major axis and this system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics. It is essentially the basis for geodetic positioning by the Global Positioning System and is also in widespread use outside the geodetic community. The locations of points in space are most conveniently described by three cartesian or rectangular coordinates, X, Y and Z. Since the advent of satellite positioning, such systems are typically geocentric. The X-axis lies within the Greenwich observatorys meridian plane, the coordinate transformation between these two systems is described to good approximation by sidereal time, which takes into account variations in the Earths axial rotation. A more accurate description also takes polar motion into account, a closely monitored by geodesists
2.
Geodynamics
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Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It also attempts to probe the internal activity by measuring magnetic fields, gravity, methods of geodynamics are also applied to exploration of other planets. Geodynamics is generally concerned with processes that move throughout the Earth. In the Earth’s interior, movement happens when rocks melt or deform and this deformation may be brittle, elastic, or plastic, depending on the magnitude of the stress and the material’s physical properties, especially the stress relaxation time scale. Rocks are structurally and compositionally heterogeneous and are subjected to variable stresses, when working with geological timescales and lengths, it is convenient to use the continuous medium approximation and equilibrium stress fields to consider the average response to average stress. Experts in geodynamics commonly use data from geodetic GPS, InSAR, rocks and other geological materials experience strain according three distinct modes, elastic, plastic, and brittle depending on the properties of the material and the magnitude of the stress field. Stress is defined as the force per unit area exerted on each part of the rock. Pressure is the part of stress changes the volume of a solid. If there is no shear, the fluid is in hydrostatic equilibrium, since, over long periods, rocks readily deform under pressure, the Earth is in hydrostatic equilibrium to a good approximation. The pressure on rock depends only on the weight of the rock above, and this depends on gravity, in a body like the Moon, the density is almost constant, so a pressure profile is readily calculated. In the Earth, the compression of rocks with depth is significant, elastic deformation is always reversible, which means that if the stress field associated with elastic deformation is removed, the material will return to its previous state. Materials only behave elastically when the arrangement along the axis being considered of material components remains unchanged. This means that the magnitude of the stress cannot exceed the strength of a material. If stress exceeds the strength of a material, bonds begin to break. During ductile deformation, this process of atomic rearrangement redistributes stress, examples include bending of the lithosphere under volcanic islands or sedimentary basins, and bending at oceanic trenches. Ductile deformation happens when transport processes such as diffusion and advection that rely on chemical bonds to be broken, when strain localizes faster than these relaxation processes can redistribute it, brittle deformation occurs. In other words, any fracture, however small, tends to focus strain at its leading edge, in general, the mode of deformation is controlled not only by the amount of stress, but also by the distribution of strain and strain associated features. Structural geologists study the results of deformation, using observations of rock, especially the mode, structural geology is an important complement to geodynamics because it provides the most direct source of data about the movements of the Earth
3.
Geomatics
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Geomatics, also known as surveying engineering or geospatial science, is the discipline of gathering, storing, processing, and delivering geographic information or spatially referenced information. In other words, it consists of products, services and tools involved in the collection, integration, the related field of hydrogeomatics covers the area associated with surveying work carried out on, above or below the surface of the sea or other areas of water. The older term of hydrographics was considered too specific to the preparation of marine charts, a geospatial network is a network of collaborating resources for sharing and coordinating geographical data and data tied to geographical references. One example of such a network is the Open Geospatial Consortiums efforts to provide global access to geographic information. A number of university departments which were once titled surveying, survey engineering or topographic science have re-titled themselves using the terms geomatics or geomatic engineering. The science of deriving information about an object using a sensor without physically contacting it is called remote sensing, Geospatial science is an academic discipline incorporating fields such as surveying, geographic information systems, hydrography and cartography. Spatial science is concerned with the measurement, management, analysis and display of spatial information describing the Earth, its physical features. The term spatial science or spatial sciences is primarily used in Australia, australian universities which offer degrees in spatial science include Curtin University, the University of Tasmania, the University of Adelaide, Melbourne University and RMIT University. Texas A&M University offers a degree in Spatial Sciences and is home to its own Spatial Sciences Laboratory. In place, the university now offers graduate programs strictly related to spatial science, Spatial information practitioners within the Asia-Pacific region are represented by the professional body called the Surveying and Spatial Sciences Institute. Geomatics Engineering, Geomatic Engineering, Geospatial Engineering is a rapidly developing engineering discipline that focuses on spatial information, the location is the primary factor used to integrate a very wide range of data for spatial analysis and visualization. Like how the profession of mechanics is a part of engineering, surveying is a part of geomatic engineering. Therefore, the engineer can be involved in an extremely wide variety of information gathering activities. Geomatics engineers design, develop, and operate systems for collecting and analyzing spatial information about the land, the oceans, natural resources, and manmade features. The tasks more closely related to civil engineering include the design and layout of public infrastructure and urban subdivisions, Geomatics engineers serve society by collecting, monitoring, archiving, and maintaining diverse spatial data infrastructures. These tools enable the geomatics engineer to gather, process, analyze, visualize, Geomatics engineering is the field of activity that integrates the acquisition, processing, analysis, display and management of spatial information. These facts demonstrate the breadth, depth and scope of the highly interdisciplinary nature of geomatics engineering, the job of geospatial engineer is well established in the U. S. military. Geomatic Methods for the Analysis of Data in the Earth Sciences, yvan Bédard, Geomatics in Karen Kemp, Encyclopedia of Geographic Information Science, Sage
4.
Cartography
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Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively, the fundamental problems of traditional cartography are to, Set the maps agenda and select traits of the object to be mapped. This is the concern of map editing, traits may be physical, such as roads or land masses, or may be abstract, such as toponyms or political boundaries. Represent the terrain of the object on flat media. This is the concern of map projections, eliminate characteristics of the mapped object that are not relevant to the maps purpose. This is the concern of generalization, reduce the complexity of the characteristics that will be mapped. This is also the concern of generalization, orchestrate the elements of the map to best convey its message to its audience. This is the concern of map design, modern cartography constitutes many theoretical and practical foundations of geographic information systems. The earliest known map is a matter of debate, both because the term map isnt well-defined and because some artifacts that might be maps might actually be something else. A wall painting that might depict the ancient Anatolian city of Çatalhöyük has been dated to the late 7th millennium BCE, the oldest surviving world maps are from 9th century BCE Babylonia. One shows Babylon on the Euphrates, surrounded by Assyria, Urartu and several cities, all, in turn, another depicts Babylon as being north of the world center. The ancient Greeks and Romans created maps since Anaximander in the 6th century BCE, in the 2nd century AD, Ptolemy wrote his treatise on cartography, Geographia. This contained Ptolemys world map – the world known to Western society. As early as the 8th century, Arab scholars were translating the works of the Greek geographers into Arabic, in ancient China, geographical literature dates to the 5th century BCE. The oldest extant Chinese maps come from the State of Qin, dated back to the 4th century BCE, in the book of the Xin Yi Xiang Fa Yao, published in 1092 by the Chinese scientist Su Song, a star map on the equidistant cylindrical projection. Early forms of cartography of India included depictions of the pole star and these charts may have been used for navigation. Mappa mundi are the Medieval European maps of the world, approximately 1,100 mappae mundi are known to have survived from the Middle Ages. Of these, some 900 are found illustrating manuscripts and the remainder exist as stand-alone documents, the Arab geographer Muhammad al-Idrisi produced his medieval atlas Tabula Rogeriana in 1154
5.
History of geodesy
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Geodesy, also named geodetics, is the scientific discipline that deals with the measurement and representation of the Earth. The history of geodesy began in antiquity and blossomed during the Age of Enlightenment, early ideas about the figure of the Earth held the Earth to be flat, and the heavens a physical dome spanning over it. The early Greeks, in their speculation and theorizing, ranged from the flat disc advocated by Homer to the spherical body postulated by Pythagoras, pythagorass idea was supported later by Aristotle. Pythagoras was a mathematician and to him the most perfect figure was a sphere and he reasoned that the gods would create a perfect figure and therefore the Earth was created to be spherical in shape. Anaximenes, an early Greek philosopher, believed strongly that the Earth was rectangular in shape, since the spherical shape was the most widely supported during the Greek Era, efforts to determine its size followed. Platos figure was a guess and Archimedes a more conservative approximation, in Egypt, a Greek scholar and philosopher, Eratosthenes, is said to have made more explicit measurements. He had heard that on the longest day of the summer solstice, at the same time, he observed the sun was not directly overhead at Alexandria, instead, it cast a shadow with the vertical equal to 1/50th of a circle. Legend has it that he had someone walk from Alexandria to Syene to measure the distance, the circumference of the Earth is 24,902 mi. Over the poles it is more precisely 40,008 km or 24,860 mi, the actual unit of measure used by Eratosthenes was the stadion. No one knows for sure what his stadion equals in modern units, had the experiment been carried out as described, it would not be remarkable if it agreed with actuality. What is remarkable is that the result was only about 0. 4% too high. A parallel later ancient measurement of the size of the Earth was made by another Greek scholar and he is said to have noted that the star Canopus was hidden from view in most parts of Greece but that it just grazed the horizon at Rhodes. Posidonius is supposed to have measured the elevation of Canopus at Alexandria and he assumed the distance from Alexandria to Rhodes to be 5000 stadia, and so he computed the Earths circumference in stadia as 48 times 5000 =240,000. Some scholars see these results as luckily semi-accurate due to cancellation of errors, the abovementioned larger and smaller sizes of the Earth were those used by Claudius Ptolemy at different times,252,000 stadia in his Almagest and 180,000 stadia in his later Geography. The Indian mathematician Aryabhata was a pioneer of mathematical astronomy and he describes the earth as being spherical and that it rotates on its axis, among other things in his work Āryabhaṭīya. Aryabhatiya is divided into four sections, the discovery that the earth rotates on its own axis from west to east is described in Aryabhatiya. Aryabhata gives the radii of the orbits of the planets in terms of the Earth-Sun distance as essentially their periods of rotation around the Sun and he also gave the correct explanation of lunar and solar eclipses and that the Moon shines by reflecting sunlight. The Muslim scholars, who held to the spherical Earth theory, used it to calculate the distance and this determined the Qibla, or Muslim direction of prayer
6.
Geographical distance
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Geographical distance is the distance measured along the surface of the earth. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude and this distance is an element in solving the second geodetic problem. Common abstractions for the surface between two 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. Distance, D, is calculated between two points, P1 and P2, the geographical coordinates of the two points, as pairs, are and, respectively. Which of the two points is designated as P1 is not important for the calculation of distance, latitude and longitude coordinates on maps are usually expressed in degrees. In the given forms of the formulae below, one or more values must be expressed in the units to obtain the correct result. Many electronic calculators allow calculations of trigonometric functions in either degrees or radians, the calculator mode must be compatible with the units used for geometric coordinates. Differences in latitude and longitude are labeled and calculated as follows and it is not important whether the result is positive or negative when used in the formulae below. Mean latitude is labeled and calculated as follows, ϕ m = ϕ1 + ϕ22. Colatitude is labeled and calculated as follows, For latitudes expressed in radians, θ = π2 − ϕ, For latitudes expressed in degrees, θ =90 ∘ − ϕ. Unless specified otherwise, the radius of the earth for the calculations below is, D = Distance between the two points, as measured along the surface of the earth and in the same units as the value used for radius unless specified otherwise. Longitude has singularities at the Poles and a discontinuity at the ±180° meridian, also, planar projections of the circles of constant latitude are highly curved near the Poles. Hence, the equations for delta latitude/longitude and mean latitude may not give the expected answer for positions near the Poles or the ±180° meridian. Consider e. g. the value of Δ λ when λ1 and λ2 are on side of the ±180° meridian. If a calculation based on latitude/longitude should be valid for all Earth positions, it should be verified that the discontinuity, another solution is to use n-vector instead of latitude/longitude, since this representation does not have discontinuities or singularities. A planar approximation for the surface of the earth may be useful over small distances, the accuracy of distance calculations using this approximation become increasingly inaccurate as, The separation between the points becomes greater, A point becomes closer to a geographic pole. The shortest distance between two points in plane is a straight line, the Pythagorean theorem is used to calculate the distance between points in a plane
7.
Geoid
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The geoid is the shape that the surface of the oceans would take under the influence of Earths gravity and rotation alone, in the absence of other influences such as winds and tides. This surface is extended through the continents, all points on a geoid surface have the same gravity potential energy. The geoid can be defined at any value of gravitational potential such as within the earths crust or far out in space and it does not correspond to the actual surface of Earths crust, but to a surface which can only be known through extensive gravitational measurements and calculations. It is often described as the true figure of the Earth. The surface of the geoid is higher than the reference ellipsoid wherever there is a gravity anomaly. The geoid surface is irregular, unlike the ellipsoid which is a mathematical idealized representation of the physical Earth. Although the physical Earth has excursions of +8,848 m and −429 m, If the ocean surface were isopycnic and undisturbed by tides, currents, or weather, it would closely approximate the geoid. The permanent deviation between the geoid and mean sea level is called ocean surface topography, If the continental land masses were criss-crossed by a series of tunnels or canals, the sea level in these canals would also very nearly coincide with the geoid. This means that when traveling by ship, one does not notice the undulations of the geoid, the vertical is always perpendicular to the geoid. Likewise, spirit levels will always be parallel to the geoid, a long voyage, indicate height variations, even though the ship will always be at sea level. This is because GPS satellites, orbiting about the center of gravity of the Earth, to obtain ones geoidal height, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tidal measurement station, as in land surveying. Modern GPS receivers have a grid implemented inside where they obtain the height over the World Geodetic System ellipsoid from the current position. Then they are able to correct the height above WGS ellipsoid to the height above WGS84 geoid, in that case when the height is not zero on a ship it is due to various other factors such as ocean tides, atmospheric pressure and local sea surface topography. The gravitational field of the earth is neither perfect n If that perfect sphere were then covered in water, instead, the water level would be higher or lower depending on the particular strength of gravity in that location. Spherical harmonics are used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96, the geoid is a particular equipotential surface, and is somewhat involved to compute. The gradient of this also provides a model of the gravitational acceleration
8.
Figure of the Earth
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The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earths size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and this is, in fact, the surface on which actual Earth measurements are made. The topographic surface is generally the concern of topographers and hydrographers, the Pythagorean concept of a spherical Earth offers a simple surface that is mathematically easy to deal with. Many astronomical and navigational computations use it as a representing the Earth. The idea of a planar or flat surface for Earth, however, is sufficient for surveys of small areas, as the local topography is far more significant than the curvature. Plane-table surveys are made for small areas, and no account is taken of the curvature of the Earth. A survey of a city would likely be computed as though the Earth were a surface the size of the city. For such small areas, exact positions can be determined relative to each other without considering the size, in the mid- to late 20th century, research across the geosciences contributed to drastic improvements in the accuracy of the figure of the Earth. The primary utility of this improved accuracy was to provide geographical and gravitational data for the guidance systems of ballistic missiles. This funding also drove the expansion of geoscientific disciplines, fostering the creation, the models for the figure of the Earth vary in the way they are used, in their complexity, and in the accuracy with which they represent the size and shape of the Earth. The simplest model for the shape of the entire Earth is a sphere, the Earths radius is the distance from Earths center to its surface, about 6,371 kilometers. The concept of a spherical Earth dates back to around the 6th century BC, the first scientific estimation of the radius of the earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes’s measurement ranging from 2% to 15%. The Earth is only approximately spherical, so no single value serves as its natural radius, distances from points on the surface to the center range from 6,353 km to 6,384 km. Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 kilometers, regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km. The difference 21 kilometers correspond to the polar radius being approximately 0. 3% shorter than the equator radius, since the Earth is flattened at the poles and bulges at the equator, geodesy represents the shape of the earth with an oblate spheroid. The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis and it is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid, an ellipsoid of revolution is uniquely defined by two numbers, two dimensions, or one dimension and a number representing the difference between the two dimensions
9.
Geodetic datum
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A geodetic datum or geodetic system is a coordinate system, and a set of reference points, used to locate places on the Earth. An approximate definition of sea level is the datum WGS84, other datums are defined for other areas or at other times, ED50 was defined in 1950 over Europe and differs from WGS84 by a few hundred meters depending on where in Europe you look. Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there. Datums are used in geodesy, navigation, and surveying by cartographers, each starts with an ellipsoid, and then defines latitude, longitude and altitude coordinates. One or more locations on the Earths surface are chosen as anchor base-points, the difference in co-ordinates between datums is commonly referred to as datum shift. The datum shift between two particular datums can vary from one place to another within one country or region, the North Pole, South Pole and Equator will be in different positions on different datums, so True North will be slightly different. Different datums use different interpolations for the shape and size of the Earth. Because the Earth is an ellipsoid, localised datums can give a more accurate representation of the area of coverage than WGS84. OSGB36, for example, is an approximation to the geoid covering the British Isles than the global WGS84 ellipsoid. However, as the benefits of a global system outweigh the greater accuracy, horizontal datums are used for describing a point on the Earths surface, in latitude and longitude or another coordinate system. Vertical datums measure elevations or depths, in surveying and geodesy, a datum is a reference system or an approximation of the Earths surface against which positional measurements are made for computing locations. Horizontal datums are used for describing a point on the Earths surface, vertical datums are used to measure elevations or underwater depths. The horizontal datum is the used to measure positions on the Earth. A specific point on the Earth can have different coordinates. There are hundreds of local horizontal datums around the world, usually referenced to some convenient local reference point, contemporary datums, based on increasingly accurate measurements of the shape of the Earth, are intended to cover larger areas. The WGS84 datum, which is almost identical to the NAD83 datum used in North America, a vertical datum is used as a reference point for elevations of surfaces and features on the Earth including terrain, bathymetry, water levels, and man-made structures. Vertical datums are either, tidal, based on sea levels, gravimetric, based on a geoid, or geodetic, for the purpose of measuring the height of objects on land, the usual datum used is mean sea level. This is a datum which is described as the arithmetic mean of the hourly water elevation taken over a specific 19 years cycle
10.
Geodesic
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In differential geometry, a geodesic is a generalization of the notion of a straight line to curved spaces. The term has been generalized to include measurements in more general mathematical spaces, for example, in graph theory. In the presence of a connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. If this connection is the Levi-Civita connection induced by a Riemannian metric, geodesics are of particular importance in general relativity. Timelike geodesics in general relativity describe the motion of free falling test particles, the shortest path between two points in a curved space can be found by writing the equation for the length of a curve, and then minimizing this length using the calculus of variations. This has some technical problems, because there is an infinite dimensional space of different ways to parameterize the shortest path. Equivalently, a different quantity may be defined, termed the energy of the curve, intuitively, one can understand this second formulation by noting that an elastic band stretched between two points will contract its length, and in so doing will minimize its energy. The resulting shape of the band is a geodesic, in Riemannian geometry geodesics are not the same as shortest curves between two points, though the two concepts are closely related. The difference is that geodesics are only locally the shortest distance between points, and are parameterized with constant velocity, going the long way round on a great circle between two points on a sphere is a geodesic but not the shortest path between the points. The map t → t2 from the interval to itself gives the shortest path between 0 and 1, but is not a geodesic because the velocity of the corresponding motion of a point is not constant. Geodesics are commonly seen in the study of Riemannian geometry and more generally metric geometry, in general relativity, geodesics describe the motion of point particles under the influence of gravity alone. In particular, the path taken by a rock, an orbiting satellite. More generally, the topic of sub-Riemannian geometry deals with the paths that objects may take when they are not free and this article presents the mathematical formalism involved in defining, finding, and proving the existence of geodesics, in the case of Riemannian and pseudo-Riemannian manifolds. The article geodesic discusses the case of general relativity in greater detail. The most familiar examples are the lines in Euclidean geometry. On a sphere, the images of geodesics are the great circles, the shortest path from point A to point B on a sphere is given by the shorter arc of the great circle passing through A and B. If A and B are antipodal points, then there are infinitely many shortest paths between them, geodesics on an ellipsoid behave in a more complicated way than on a sphere, in particular, they are not closed in general. In metric geometry, a geodesic is a curve which is locally a distance minimizer
11.
Geographic coordinate system
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A geographic coordinate system is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are chosen such that one of the numbers represents a vertical position. A common choice of coordinates is latitude, longitude and elevation, to specify a location on a two-dimensional map requires a map projection. The invention of a coordinate system is generally credited to Eratosthenes of Cyrene. Ptolemy credited him with the adoption of longitude and latitude. Ptolemys 2nd-century Geography used the prime meridian but measured latitude from the equator instead. Mathematical cartography resumed in Europe following Maximus Planudes recovery of Ptolemys text a little before 1300, in 1884, the United States hosted the International Meridian Conference, attended by representatives from twenty-five nations. Twenty-two of them agreed to adopt the longitude of the Royal Observatory in Greenwich, the Dominican Republic voted against the motion, while France and Brazil abstained. France adopted Greenwich Mean Time in place of local determinations by the Paris Observatory in 1911, the latitude of a point on Earths surface is the angle between the equatorial plane and the straight line that passes through that point and through the center of the Earth. Lines joining points of the same latitude trace circles on the surface of Earth called parallels, as they are parallel to the equator, the north pole is 90° N, the south pole is 90° S. The 0° parallel of latitude is designated the equator, the plane of all geographic coordinate systems. The equator divides the globe into Northern and Southern Hemispheres, the longitude of a point on Earths surface is the angle east or west of a reference meridian to another meridian that passes through that point. All meridians are halves of great ellipses, which converge at the north and south poles, the prime meridian determines the proper Eastern and Western Hemispheres, although maps often divide these hemispheres further west in order to keep the Old World on a single side. The antipodal meridian of Greenwich is both 180°W and 180°E, the combination of these two components specifies the position of any location on the surface of Earth, without consideration of altitude or depth. The grid formed by lines of latitude and longitude is known as a graticule, the origin/zero point of this system is located in the Gulf of Guinea about 625 km south of Tema, Ghana. To completely specify a location of a feature on, in, or above Earth. Earth is not a sphere, but a shape approximating a biaxial ellipsoid. It is nearly spherical, but has an equatorial bulge making the radius at the equator about 0. 3% larger than the radius measured through the poles, the shorter axis approximately coincides with the axis of rotation
12.
Horizontal position representation
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A position representation is the parameters used to express a position relative to a reference. Representing position in three dimensions is often done by a Euclidean vector, there are also several applications where only the horizontal position is of interest, this might e. g. be the case for ships and ground vehicles/cars. There are several options for horizontal position representations, each with different properties which makes them appropriate for different applications, latitude/longitude and UTM are common horizontal position representations. The horizontal position has two degrees of freedom, and thus two parameters are sufficient to describe such a position. The most common horizontal position representation is latitude and longitude, the parameters are intuitive and well known, and are thus suited for communicating a position to humans, e. g. using a position plot. However, latitude and longitude should be used with care in mathematical expressions, the main reason is the singularities at the Poles, which makes longitude undefined at these points. Also near the poles the latitude/longitude grid is highly non-linear, another problematic area is the meridian at ±180° longitude, where the longitude has a discontinuity, and hence specific program code must often be written to handle this. An example of the consequences of omitting such code is the crash of the systems of twelve F-22 Raptors while crossing this meridian. N-vector is a three parameter non-singular horizontal position representation that can replace latitude and longitude, geometrically, it is a unit vector which is normal to the reference ellipsoid. The vector is decomposed in an Earth centered earth fixed coordinate system and it behaves the same at all Earth positions, and it holds the mathematical one-to-one property. Using three parameters, n-vector is inconvenient for communicating a position directly to humans and before showing a position plot, when carrying out several calculations within a limited area, a Cartesian coordinate system might be defined with the origin at a specified Earth-fixed position. The origin is selected at the surface of the reference ellipsoid. Hence position vectors relative to this frame will have two horizontal and one vertical parameter. The axes are typically selected as North-East-Down or East-North-Up, and thus this system can be viewed as a linearization of the meridians and parallels. For small areas a local system can be convenient for relative positioning. The alignment along the north and east directions is not possible at the Poles, instead of one local Cartesian grid, that needs to be repositioned as the position of interest moves, a fixed set of map projections covering the Earth can be defined. UTM is one system, dividing the Earth into 60 longitude zones. UTM is widely used, and the coordinates approximately corresponds to meters north, however, as a set of map-projections it has inherent distortions, and thus most calculations based on UTM will not be exact
13.
Latitude
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In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earths surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles, lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the location of features on the surface of the Earth. Without qualification the term latitude should be taken to be the latitude as defined in the following sections. Also defined are six auxiliary latitudes which are used in special applications, there is a separate article on the History of latitude measurements. Two levels of abstraction are employed in the definition of latitude and longitude, in the first step the physical surface is modelled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface, the simplest choice for the reference surface is a sphere, but the geoid is more accurately modelled by an ellipsoid. The definitions of latitude and longitude on such surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface, latitude and longitude together with some specification of height constitute a geographic coordinate system as defined in the specification of the ISO19111 standard. This is of importance in accurate applications, such as a Global Positioning System, but in common usage, where high accuracy is not required. In English texts the latitude angle, defined below, is denoted by the Greek lower-case letter phi. It is measured in degrees, minutes and seconds or decimal degrees, the precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its field is the science of geodesy. These topics are not discussed in this article and this article relates to coordinate systems for the Earth, it may be extended to cover the Moon, planets and other celestial objects by a simple change of nomenclature. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface, the plane through the centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator. Planes parallel to the plane intersect the surface in circles of constant latitude. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North, the latitude of an arbitrary point is the angle between the equatorial plane and the radius to that point. The latitude, as defined in this way for the sphere, is termed the spherical latitude
14.
Map projection
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A map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. Map projections are necessary for creating maps, all map projections distort the surface in some fashion. There is no limit to the number of map projections. More generally, the surfaces of bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid. Even more generally, projections are the subject of several mathematical fields, including differential geometry. However, map projection refers specifically to a cartographic projection and these useful traits of maps motivate the development of map projections. However, Carl Friedrich Gausss Theorema Egregium proved that a spheres surface cannot be represented on a plane without distortion, the same applies to other reference surfaces used as models for the Earth. Since any map projection is a representation of one of surfaces on a plane. Every distinct map projection distorts in a distinct way, the study of map projections is the characterization of these distortions. Projection is not limited to perspective projections, such as those resulting from casting a shadow on a screen, rather, any mathematical function transforming coordinates from the curved surface to the plane is a projection. Few projections in actual use are perspective, for simplicity, most of this article assumes that the surface to be mapped is that of a sphere. In reality, the Earth and other celestial bodies are generally better modeled as oblate spheroids. These other surfaces can be mapped as well, therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane. Many properties can be measured on the Earths surface independent of its geography, some of these properties are, Area Shape Direction Bearing Distance Scale Map projections can be constructed to preserve at least one of these properties, though only in a limited way for most. Each projection preserves or compromises or approximates basic metric properties in different ways, the purpose of the map determines which projection should form the base for the map. Because many purposes exist for maps, a diversity of projections have been created to suit those purposes, another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Data sets are geographic information, their collection depends on the datum of the Earth. Different datums assign slightly different coordinates to the location, so in large scale maps, such as those from national mapping systems
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Reference ellipsoid
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In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. Current practice uses the word alone in preference to the full term oblate ellipsoid of revolution or the older term oblate spheroid. In the rare instances where a more general shape is required as a model the term used is triaxial ellipsoid. A great many ellipsoids have been used with various sizes and centres, the shape of an ellipsoid is determined by the shape parameters of that ellipse which generates the ellipsoid when it is rotated about its minor axis. The semi-major axis of the ellipse, a, is identified as the radius of the ellipsoid. For the Earth, f is around 1/300 corresponding to a difference of the major and minor semi-axes of approximately 21 km, some precise values are given in the table below and also in Figure of the Earth. A great many other parameters are used in geodesy but they can all be related to one or two of the set a, b and f, a primary use of reference ellipsoids is to serve as a basis for a coordinate system of latitude, longitude, and elevation. For this purpose it is necessary to identify a zero meridian, for other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater Airy-0. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid, the longitude measures the rotational angle between the zero meridian and the measured point. By convention for the Earth, Moon, and Sun it is expressed in degrees ranging from −180° to +180° For other bodies a range of 0° to 360° is used. The latitude measures how close to the poles or equator a point is along a meridian, and is represented as an angle from −90° to +90°, the common or geodetic latitude is the angle between the equatorial plane and a line that is normal to the reference ellipsoid. Depending on the flattening, it may be different from the geocentric latitude. For non-Earth bodies the terms planetographic and planetocentric are used instead, see geodetic system for more detail. If these coordinates, i. e. N is the radius of curvature in the prime vertical, in contrast, extracting φ, λ and h from the rectangular coordinates usually requires iteration. A straightforward method is given in an OSGB publication and also in web notes, more sophisticated methods are outlined in geodetic system. Currently the most common reference used, and that used in the context of the Global Positioning System, is the one defined by WGS84. Traditional reference ellipsoids or geodetic datums are defined regionally and therefore non-geocentric, modern geodetic datums are established with the aid of GPS and will therefore be geocentric, e. g. WGS84. Reference ellipsoids are also useful for mapping of other planetary bodies including planets, their satellites, asteroids
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Satellite geodesy
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It belongs to the broader field of space geodesy. Traditional astronomical geodesy is not commonly considered a part of satellite geodesy, satellite geodesy relies heavily on orbital mechanics. Satellite geodesy began shortly after the launch of Sputnik in 1957, observations of Explorer 1 and Sputnik 2 in 1958 allowed for an accurate determination of Earths flattening. The 1960s saw the launch of the Doppler satellite Transit-1B and the balloon satellites Echo 1, Echo 2, the first dedicated geodetic satellite was ANNA-1B, a collaborative effort between NASA, the DoD, and other civilian agencies. ANNA-1B carried the first of the US Armys SECOR instruments and these missions led to the accurate determination of the leading spherical harmonic coefficients of the geopotential, the general shape of the geoid, and linked the worlds geodetic datums. Soviet military satellites undertook geodesic missions to assist in ICBM targeting in the late 1960s, the Transit satellite system was used extensively for Doppler surveying, navigation, and positioning. Observations of satellites in the 1970s by worldwide triangulation networks allowed for the establishment of the World Geodetic System, the development of GPS by the United States in the 1980s allowed for precise navigation and positioning and soon became a standard tool in surveying. In the 1980s and 1990s satellite geodesy began to be used for monitoring of geodynamic phenomena, such as motion, Earth rotation. The 1990s were focused on the development of permanent geodetic networks, dedicated satellites were launched to measure Earths gravity field in the 2000s, such as CHAMP, GRACE, and GOCE. Global navigation satellite systems are dedicated radio positioning services, which can locate a receiver to within a few meters, the most prominent system, GPS, consists of a constellation of 31 satellites in high, 12-hour circular orbits, distributed in six planes with 55° inclinations. The principle of location is based on trilateration, each satellite transmits a precise ephemeris with information on its own position and a message containing the exact time of transmission. The receiver compares this time of transmission with its own clock at the time of reception, four pseudoranges are needed to obtain the precise time and the receivers position within a few meters. More sophisticated methods, such as real-time kinematic can yield positions to within a few millimeters, in geodesy, GNSS is used as an economical tool for surveying and time transfer. It is also used for monitoring Earths rotation, polar motion, the presence of the GPS signal in space also makes it suitable for orbit determination and satellite-to-satellite tracking. Satellite laser ranging is a proven geodetic technique with significant potential for important contributions to studies of the Earth/Atmosphere/Oceans system. Example, LAGEOS Doppler positioning involves recording the Doppler shift of a signal of stable frequency emitted from a satellite as the satellite approaches and recedes from the observer. The observed frequency depends on the velocity of the satellite relative to the observer. If the observer knows the orbit of the satellite, then the recording the Doppler profile determines the observers position, conversely, if the observers position is precisely known, then the orbit of the satellite can be determined and used to study the Earths gravity
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Satellite navigation
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A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows small electronic receivers to determine their location to high precision using time signals transmitted along a line of sight by radio from satellites, the system can be used for providing position, navigation or for tracking the position of something fitted with a receiver. The signals also allow the receiver to calculate the current local time to high precision. Satnav systems operate independently of any telephonic or internet reception, though these technologies can enhance the usefulness of the information generated. A satellite navigation system with global coverage may be termed a global satellite system. As of December 2016 only the United States NAVSTAR Global Positioning System, the Russian GLONASS, the European Unions Galileo GNSS is scheduled to be fully operational by 2020. China is in the process of expanding its regional BeiDou Navigation Satellite System into the global BeiDou-2 GNSS by 2020, India currently has satellite-based augmentation system, GPS Aided GEO Augmented Navigation, which enhances the accuracy of NAVSTAR GPS and GLONASS positions. India has already launched the IRNSS, with an operational name NAVIC and it is expected to be fully operational by June 2016. France and Japan are in the process of developing regional navigation systems as well, Global coverage for each system is generally achieved by a satellite constellation of 18–30 medium Earth orbit satellites spread between several orbital planes. The actual systems vary, but use orbital inclinations of >50°, Ground based augmentation is provided by systems like the Local Area Augmentation System. GNSS-2 is the generation of systems that independently provides a full civilian satellite navigation system. These systems will provide the accuracy and integrity monitoring necessary for civil navigation and this system consists of L1 and L2 frequencies for civil use and L5 for system integrity. Development is also in progress to provide GPS with civil use L2 and L5 frequencies, making it a GNSS-2 system. ¹ Core Satellite navigation systems, currently GPS, GLONASS, Galileo, Global Satellite Based Augmentation Systems such as Omnistar and StarFire. Regional SBAS including WAAS, EGNOS, MSAS and GAGAN, Regional Satellite Navigation Systems such as Chinas Beidou, Indias NAVIC, and Japans proposed QZSS. Continental scale Ground Based Augmentation Systems for example the Australian GRAS, Regional scale GBAS such as CORS networks. Local GBAS typified by a single GPS reference station operating Real Time Kinematic corrections, early predecessors were the ground based DECCA, LORAN, GEE and Omega radio navigation systems, which used terrestrial longwave radio transmitters instead of satellites. These positioning systems broadcast a radio pulse from a known master location, the delay between the reception of the master signal and the slave signals allowed the receiver to deduce the distance to each of the slaves, providing a fix. The first satellite system was Transit, a system deployed by the US military in the 1960s
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Global Positioning System
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The Global Positioning System is a space-based radionavigation system owned by the United States government and operated by the United States Air Force. The GPS system operates independently of any telephonic or internet reception, the GPS system provides critical positioning capabilities to military, civil, and commercial users around the world. The United States government created the system, maintains it, however, the US government can selectively deny access to the system, as happened to the Indian military in 1999 during the Kargil War. The U. S. Department of Defense developed the system and it became fully operational in 1995. Roger L. Easton of the Naval Research Laboratory, Ivan A, getting of The Aerospace Corporation, and Bradford Parkinson of the Applied Physics Laboratory are credited with inventing it. Announcements from Vice President Al Gore and the White House in 1998 initiated these changes, in 2000, the U. S. Congress authorized the modernization effort, GPS III. In addition to GPS, other systems are in use or under development, mainly because of a denial of access. The Russian Global Navigation Satellite System was developed contemporaneously with GPS, GLONASS can be added to GPS devices, making more satellites available and enabling positions to be fixed more quickly and accurately, to within two meters. There are also the European Union Galileo positioning system and Chinas BeiDou Navigation Satellite System, special and general relativity predict that the clocks on the GPS satellites would be seen by the Earths observers to run 38 microseconds faster per day than the clocks on the Earth. The GPS calculated positions would quickly drift into error, accumulating to 10 kilometers per day, the relativistic time effect of the GPS clocks running faster than the clocks on earth was corrected for in the design of GPS. The Soviet Union launched the first man-made satellite, Sputnik 1, two American physicists, William Guier and George Weiffenbach, at Johns Hopkinss Applied Physics Laboratory, decided to monitor Sputniks radio transmissions. Within hours they realized that, because of the Doppler effect, the Director of the APL gave them access to their UNIVAC to do the heavy calculations required. The next spring, Frank McClure, the deputy director of the APL, asked Guier and Weiffenbach to investigate the inverse problem — pinpointing the users location and this led them and APL to develop the TRANSIT system. In 1959, ARPA also played a role in TRANSIT, the first satellite navigation system, TRANSIT, used by the United States Navy, was first successfully tested in 1960. It used a constellation of five satellites and could provide a navigational fix approximately once per hour, in 1967, the U. S. Navy developed the Timation satellite, which proved the feasibility of placing accurate clocks in space, a technology required by GPS. In the 1970s, the ground-based OMEGA navigation system, based on comparison of signal transmission from pairs of stations. Limitations of these systems drove the need for a more universal navigation solution with greater accuracy, during the Cold War arms race, the nuclear threat to the existence of the United States was the one need that did justify this cost in the view of the United States Congress. This deterrent effect is why GPS was funded and it is also the reason for the ultra secrecy at that time
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GLONASS
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GLONASS, or Global Navigation Satellite System, is a space-based satellite navigation system operating in the radionavigation-satellite service and used by the Russian Aerospace Defence Forces. It provides an alternative to GPS and is the second alternative navigational system in operation with global coverage, smartphones generally tend to use the same chipsets and the versions used since 2015 receive GLONASS signals and positioning information along with GPS. Since 2012, GLONASS was the second most used positioning system in mobile phones after GPS, the system has the advantage that smartphone users receive a more accurate reception identifying location to within 2 meters. Development of GLONASS began in the Soviet Union in 1976, beginning on 12 October 1982, numerous rocket launches added satellites to the system until the constellation was completed in 1995. After a decline in capacity during the late 1990s, in 2001, under Vladimir Putins presidency, GLONASS is the most expensive program of the Russian Federal Space Agency, consuming a third of its budget in 2010. By 2010, GLONASS had achieved 100% coverage of Russias territory and in October 2011, the GLONASS satellites designs have undergone several upgrades, with the latest version being GLONASS-K. GLONASS is a satellite navigation system, providing real time position and velocity determination for military. The satellites are located in middle circular orbit at 19,100 kilometres altitude with a 64.8 degree inclination, GLONASS orbit makes it especially suited for usage in high latitudes, where getting a GPS signal can be problematic. The constellation operates in three planes, with eight evenly spaced satellites on each. A fully operational constellation with global coverage consists of 24 satellites, to get a position fix the receiver must be in the range of at least four satellites. GLONASS satellites transmit two types of signal, open standard-precision signal L1OF/L2OF, and obfuscated high-precision signal L1SF/L2SF, the signals use similar DSSS encoding and binary phase-shift keying modulation as in GPS signals.0 MHz, known as the L1 band. The center frequency is 1602 MHz + n ×0.5625 MHz, signals are transmitted in a 38° cone, using right-hand circular polarization, at an EIRP between 25 and 27 dBW. The L2 band signals use the same FDMA as the L1 band signals, but transmit straddling 1246 MHz with the center frequency 1246 MHz + n×0.4375 MHz, the pseudo-random code is generated with a 9-stage shift register operating with a period of 1 ms. The navigational message is modulated at 50 bits per second, the superframe of the open signal is 7500 bits long and consists of 5 frames of 30 seconds, taking 150 seconds to transmit the continuous message. Each frame is 1500 bits long and consists of 15 strings of 100 bits, with 85 bits for data and check-sum bits, and 15 bits for time mark. Strings 1-4 provide immediate data for the satellite, and are repeated every frame, the data include ephemeris, clock and frequency offsets. Strings 5-15 provide non-immediate data for each satellite in the constellation, with frames I-IV each describing five satellites, the almanac uses modified Keplerian parameters and is updated daily. The details of the signal have not been disclosed
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BeiDou Navigation Satellite System
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The BeiDou Navigation Satellite System is a Chinese satellite navigation system. It consists of two separate satellite constellations – a limited test system that has been operating since 2000, the first BeiDou system, officially called the BeiDou Satellite Navigation Experimental System and also known as BeiDou-1, consists of three satellites and offers limited coverage and applications. It has been offering services, mainly for customers in China and neighboring regions. It became operational in China in December 2011, with 10 satellites in use and it is planned to begin serving global customers upon its completion in 2020. In-mid 2015, China started the build-up of the third generation BeiDou system in the global coverage constellation, the first BDS-3 satellite was launched 30 September 2015. As of March 2016,4 BDS-3 in-orbit validation satellites have been launched, the official English name of the system is BeiDou Navigation Satellite System. It is named after the Big Dipper constellation, which is known in Chinese as Běidǒu, the name literally means Northern Dipper, the name given by ancient Chinese astronomers to the seven brightest stars of the Ursa Major constellation. Historically, this set of stars was used in navigation to locate the North Star Polaris, as such, the name BeiDou also serves as a metaphor for the purpose of the satellite navigation system. The original idea of a Chinese satellite navigation system was conceived by Chen Fangyun, the third satellite, BeiDou-1C, was put into orbit on 25 May 2003. The successful launch of BeiDou-1C also meant the establishment of the BeiDou-1 navigation system. On 2 November 2006, China announced that from 2008 BeiDou would offer a service with an accuracy of 10 meters, timing of 0.2 microseconds. In February 2007, the fourth and last satellite of the BeiDou-1 system and it was reported that the satellite had suffered from a control system malfunction but was then fully restored. In April 2007, the first satellite of BeiDou-2, namely Compass-M1 was successfully put into its working orbit, the second BeiDou-2 constellation satellite Compass-G2 was launched on 15 April 2009. On 2 June 2010, the satellite was launched successfully into orbit. The fifth orbiter was launched into space from Xichang Satellite Launch Center by an LM-3I carrier rocket on 1 August 2010, three months later, on 1 November 2010, the sixth satellite was sent into orbit by LM-3C. Another satellite, the Beidou-2/Compass IGSO-5 satellite, was launched from the Xichang Satellite Launch Center by a Long March-3A on 1 December 2011. In September 2003, China intended to join the European Galileo positioning system project and was to invest €230 million in Galileo over the few years. At the time, it was believed that Chinas BeiDou navigation system would only be used by its armed forces
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Galileo (satellite navigation)
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The €5 billion project is named after the Italian astronomer Galileo Galilei. The use of basic Galileo services will be free and open to everyone, the higher-precision capabilities will be available for paying commercial users. Galileo is intended to provide horizontal and vertical measurements within 1-metre precision. Galileo is to provide a new search and rescue function as part of the MEOSAR system. Satellites will be equipped with a transponder which will relay distress signals from emergency beacons to the Rescue coordination centre, which will then initiate a rescue operation. At the same time, the system is projected to provide a signal and this latter feature is new and is considered a major upgrade compared to the existing Cospas-Sarsat system, which does not provide feedback to the user. The first Galileo test satellite, the GIOVE-A, was launched 28 December 2005, as of December 2016 the system has 18 of 30 satellites in orbit. Galileo started offering Early Operational Capability on 15 December 2016 and is expected to reach Full Operational Capability in 2019, the complete 30-satellite Galileo system is expected by 2020. In 1999, the different concepts of the three main contributors of ESA for Galileo were compared and reduced to one by a joint team of engineers from all three countries. The first stage of the Galileo programme was agreed upon officially on 26 May 2003 by the European Union, the system is intended primarily for civilian use, unlike the more military-orientated systems of the United States, Russia, and China. The European system will only be subject to shutdown for military purposes in extreme circumstances and it will be available at its full precision to both civil and military users. On 17 January 2002, a spokesman for the stated that, as a result of US pressure and economic difficulties. A few months later, however, the situation changed dramatically, European Union member states decided it was important to have a satellite-based positioning and timing infrastructure that the US could not easily turn off in times of political conflict. The European Union and the European Space Agency agreed in March 2002 to fund the project, the starting cost for the period ending in 2005 is estimated at €1.1 billion. The required satellites were to be launched between 2011 and 2014, with the system up and running and under control from 2019. The final cost is estimated at €3 billion, including the infrastructure on Earth, the plan was for private companies and investors to invest at least two-thirds of the cost of implementation, with the EU and ESA dividing the remaining cost. The base Open Service is to be available without charge to anyone with a Galileo-compatible receiver, by early 2011 costs for the project had run 50% over initial estimates. Galileo is intended to be an EU civilian GNSS that allows all users access to it, initially GPS reserved the highest quality signal for military use, and the signal available for civilian use was intentionally degraded
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Indian Regional Navigation Satellite System
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The Indian government approved the project in May 2006. The constellation of seven NAVIC satellites is already in orbit and the system is expected to be operational from September 2016, NAVIC will provide two levels of service, the standard positioning service will be open for civilian use, and a restricted service for authorized users. As part of the project, the Indian Space Research Organisation opened a new satellite navigation center within the campus of ISRO Deep Space Network at Byalalu, in Karnataka on 28 May 2013. A network of 21 ranging stations located across the country will provide data for the determination of the satellites. A goal of complete Indian control has been stated, with the segment, ground segment. Its location in low latitudes facilitates a coverage with low-inclination satellites, three satellites will be in geostationary orbit over the Indian Ocean. Missile targeting could be an important military application for the constellation, the total cost of the project is expected to be ₹1,420 crore, with the cost of the ground segment being ₹300 crore. Each satellites costing ₹150 crore and the PSLV-XL version rocket costs around ₹130 crore, the seven rockets would involve an outlay of around ₹910 crore. The NAVIC signal was released for evaluation in September 2014, in April 2010, it was reported that India plans to start launching satellites by the end of 2011, at a rate of one satellite every six months. This would have made NAVIC functional by 2015, but the program was delayed, and India also launched 3 new satellites to supplement this. Seven satellites with the prefix IRNSS-1 will constitute the space segment of the IRNSS, IRNSS-1A, the first of the seven satellites, was launched on 1 July 2013. IRNSS-1B was launched on 4 April 2014 on board the PSLV-C24 rocket, the satellite has been placed in geosynchronous orbit. IRNSS-1C was launched on 16 October 2014, IRNSS-1D on 28 March 2015, IRNSS-1E on 20 January 2016, IRNSS-1F on 10 March 2016, the system consists of a constellation of seven satellites and a support ground segment. Three of the satellites in the constellation are located in orbit at 32. 5° East, 83° East. The other four are inclined geosynchronous orbit, two of the GSOs cross the equator at 55° East and two at 111. 75° East. The four GSO satellites will appear to be moving in the form of an 8, in addition, various ground-based systems will control, track orbits, check integration and send radio signals to the satellites. The land-based Master Control Center will run navigational software, NAVIC signals will consist of a Standard Positioning Service and a Precision Service. Both will be carried on L5 and S band, the SPS signal will be modulated by a 1 MHz BPSK signal
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Quasi-Zenith Satellite System
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The first satellite Michibiki was launched on 11 September 2010. Full operational status was expected by 2013, in March 2013, Japans Cabinet Office announced the expansion of the Quasi-Zenith Satellite System from three satellites to four. The $526 million contract with Mitsubishi Electric for the construction of three satellites is slated for launch before the end of 2017, the basic four-satellite system is planned to be operational in 2018. The work was taken over by the Satellite Positioning Research and Application Center, QZSS is targeted at mobile applications, to provide communications-based services and positioning information. With regards to its service, QZSS can only provide limited accuracy on its own and is not currently required in its specifications to work in a stand-alone mode. As such, it is viewed as a GNSS Augmentation service. S, federal Aviation Administrations Wide Area Augmentation System. QZSS uses three satellites, each 120° apart, in highly inclined, slightly elliptical, geosynchronous orbits, because of this inclination, they are not geostationary, they do not remain in the same place in the sky. Instead, their ground traces are asymmetrical figure-8 patterns, designed to ensure one is almost directly overhead over Japan at all times. The nominal orbital elements are, The primary purpose of QZSS is to increase the availability of GPS in Japans numerous urban canyons, a secondary function is performance enhancement, increasing the accuracy and reliability of GPS derived navigation solutions. The Quasi-Zenith Satellites transmit signals compatible with the GPS L1C/A signal, as well as the modernized GPS L1C, L2C signal and this minimizes changes to existing GPS receivers. It also improves reliability by means of monitoring and system health data notifications. QZSS also provides other support data to users to improve GPS satellite acquisition, according to its original plan, QZSS was to carry two types of space-borne atomic clocks, a hydrogen maser and a rubidium atomic clock. The development of a hydrogen maser for QZSS was abandoned in 2006. The positioning signal will be generated by a Rb clock and a similar to the GPS timekeeping system will be employed. Although the first generation QZSS timekeeping system will be based on the Rb clock, during the first half of the two year in-orbit test phase, preliminary tests will investigate the feasibility of the atomic clock-less technology which might be employed in the second generation QZSS. This allows the system to operate optimally when satellites are in contact with the ground station. Low satellite mass and low satellite manufacturing and launch cost are significant advantages of this system
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Sea Level Datum of 1929
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The Sea Level Datum of 1929 was the vertical control datum established for vertical control surveying in the United States of America by the General Adjustment of 1929. The datum was used to measure elevation above, and depression below, Mean sea level was measured at 26 tide gauges,21 in the United States and 5 in Canada. The datum was defined by the heights of mean sea level at the 26 tide gauges. The adjustment required a total of 66,315 miles of leveling with 246 closed circuits and 25 circuits at sea level. Since the Sea Level Datum of 1929 was a model, it was not a pure model of mean sea level. Therefore, it was renamed the National Geodetic Vertical Datum of 1929 in 1973, altitude Datum Geodesy Mean sea level North American Vertical Datum of 1988 Storm Surge Topographic elevation Topography Reference ellipsoid Geoid United States Geological Survey home page. U. S. National Geodetic Survey home page
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Ordnance Survey National Grid
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The Ordnance Survey National Grid reference system is a system of geographic grid references used in Great Britain, different from using Latitude and Longitude. It is often called British National Grid, the Ordnance Survey devised the national grid reference system, and it is heavily used in their survey data, and in maps based on those surveys. Grid references are commonly quoted in other publications and data sources. The Universal Transverse Mercator coordinate system is used to provide references for worldwide locations. European-wide agencies also use UTM when mapping locations, or may use the Military Grid Reference System system, the grid is based on the OSGB36 datum, and was introduced after the retriangulation of 1936–1962. It replaced the previously used Cassini Grid which, up to the end of World War Two, had issued only to the military. The Airy ellipsoid is a regional best fit for Britain, more modern mapping tends to use the GRS80 ellipsoid used by the GPS, the British maps adopt a Transverse Mercator projection with an origin at 49° N, 2° W. Over the Airy ellipsoid a straight grid, the National Grid, is placed with a new false origin. This false origin is located south-west of the Isles of Scilly, the distortion created between the OS grid and the projection is countered by a scale factor in the longitude to create two lines of longitude with zero distortion rather than one. Grid north and true north are aligned on the 400 km easting of the grid which is 2° W. 2° 0′ 5″ W. OSGB36 was also used by Admiralty nautical charts until 2000 after which WGS84 has been used, a geodetic transformation between OSGB36 and other terrestrial reference systems can become quite tedious if attempted manually. The most common transformation is called the Helmert datum transformation, which results in a typical 7 m error from true, the definitive transformation from ETRS89 that is published by the OSGB is called the National Grid Transformation OSTN02. This models the detailed distortions in the 1936–1962 retriangulation, and achieves backwards compatibility in grid coordinates to sub-metre accuracy, the difference between the coordinates on different datums varies from place to place. The longitude and latitude positions on OSGB36 are the same as for WGS84 at a point in the Atlantic Ocean well to the west of Great Britain. In Cornwall, the WGS84 longitude lines are about 70 metres east of their OSGB36 equivalents, the smallest datum shift is on the west coast of Scotland and the greatest in Kent. But Great Britain has not shrunk by 100+ metres, a point near Lands End now computes to be 27.6 metres closer to a point near Duncansby Head than it did under OSGB36. For the first letter, the grid is divided into squares of size 500 km by 500 km, there are four of these which contain significant land area within Great Britain, S, T, N and H. The O square contains an area of North Yorkshire, almost all of which lies below mean high tide
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ED50
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ED50 is a geodetic datum which was defined after World War II for the international connection of geodetic networks. This led to the setting up of ED50 as a consistent mapping datum for much of Western Europe and it was, and still is, used in much of Western Europe apart from Great Britain, Ireland, Sweden and Switzerland, which have their own datums. It used the International Ellipsoid of 1924 and that spheroid was an early attempt to model the whole Earth and was widely used around the world until the 1980s when GRS80 and WGS84 were established. Many national coordinate systems of Gauss–Krüger are defined by ED50 and oriented by means of geodetic astronomy, up to now it has been used in databases of gravity fields, cadastre, small surveying networks in Europe and America, and by some developing countries with no modern baselines. ED50 was also part of the fundamentals of the NATO coordinates up to the 1980s, the adjustments for later versions of the datum used the Munich Frauenkirche as starting point. The longitude and latitude lines on the two datums are the same in the Archangel region of north-west Russia, as one moves westwards across Europe, the longitude lines on ED50 gradually become further west than their WGS84 equivalents, and are around 100 metres west in Spain and Portugal. Moving southwards, the lines on ED50 gradually become further south than the WGS84 lines. This means that if the lines are further west, the value of any given point becomes more easterly. Similarly, if the lines are south, the values become northerly, the datum shift for the Universal Transverse Mercator grid is different. It should be noted that UTM northings are measured from the Equator, the French datum RGF93 The Great Britain datum OSGB36. For Ireland, the Irish Transverse Mercator
27.
GRS 80
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GRS80, or Geodetic Reference System 1980, is a geodetic reference system consisting of a global reference ellipsoid and a gravity field model. The geoid is essentially the figure of the Earth abstracted from its topographic features and 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 masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the surface on which to solve geometrical problems like point positioning. The geometrical separation between it and the ellipsoid is called the geoidal undulation. It varies globally between ±110 m, a reference ellipsoid, customarily chosen to be the same size as the geoid, is described by its semi-major axis a and flattening f. The quantity f = /a, where b is the axis, is a purely geometrical one. The mechanical ellipticity of the earth is determined to high precision by observation of satellite orbit perturbations and its relationship with the geometric flattening is indirect. The relationship depends on the density distribution. The 1980 Geodetic Reference System posited a 6378 137m semi-major axis and this system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics in Canberra, Australia,1979. The GRS80 reference system was used by the World Geodetic System 1984. The reference ellipsoid of WGS84 now differs slightly due to later refinements, the equation is solved iteratively to give e 2 =0.006694380022903415749574948586289306212443890 … which gives f =1 /298.2572221008827112431628366 …. Additional derived physical constants and geodetic formulas are found in the reference, Geodetic Reference System 1980, Bulletin Géodésique. Republished in Moritz, H.2000, Geodetic Reference System 1980, J. Geod
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North American Datum
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The North American Datum is the datum now used to define the geodetic network in North America. A datum is a description of the shape of the Earth along with an anchor point for the coordinate system. In surveying, cartography, and land-use planning, two North American Datums are in use, the North American Datum of 1927 and the North American Datum of 1983, both are geodetic reference systems based on slightly different assumptions and measurements. In 1901 the United States Coast and Geodetic Survey adopted a national horizontal datum called the United States Standard Datum and it was fitted to data previously collected for regional datums, which by that time had begun to overlap. In 1913, Canada and Mexico adopted that datum, so it was renamed the North American Datum. As more data were gathered, discrepancies appeared, so the datum was recomputed in 1927, using the same spheroid, the datum declares the Meades Ranch Triangulation Station to be 39°13′26. 686″ north latitude, 98°32′30. 506″ west longitude. NAD27 is oriented by declaring the azimuth from Meades Ranch to Waldo to be 255°28′14. 52″ from north. These are the dimensions for NAD27, but Clarke actually defined his 1866 spheroid as a =20,926,062 British feet. The conversion to meters uses Clarkes 1865 inch-meter ratio of 39.370432, because Earth deviates significantly from a perfect ellipsoid, the ellipsoid that best approximates its shape varies region by region across the world. Clarke 1866, and North American Datum of 1927 with it, were surveyed to best suit North America as a whole, likewise, historically, most regions of the world used ellipsoids measured locally to best suit the vagaries of Earths shape in their respective locales. While ensuring the most accuracy locally, this practice makes integrating and disseminating information across regions troublesome and this is because satellites naturally deal with Earth as a monolithic body. Therefore, the GRS80 ellipsoid was developed for best approximating the Earth as a whole, the North American Datum of 1983 is based on a newer defined spheroid, it is an Earth-centered datum having no initial point or initial direction. NOAA provides a converter between the two systems, the initial definition of NAD83 was intended to match GRS80 and WGS84, and many older publications indicate no difference. Subsequent more accurate measurements found a difference typically on the order of a meter over much of the United States, each datum has undergone refinements with more accurate and later measurements. Thus there is a change over time as to the difference between the systems, for much of the United States the relative rate is on the order of 1 to 2 cm per year. 1994 SBE National Convention and World Media Expo
29.
North American Vertical Datum of 1988
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NAVD88 was established in 1991 by the minimum-constraint adjustment of geodetic leveling observations in Canada, the United States, and Mexico. It held fixed the height of the tidal bench mark, referenced to the International Great Lakes Datum of 1985 local mean sea level height value, at Rimouski, Quebec. The definition of NAVD88 uses the Helmert orthometric height, which calculates the location of the geoid from modeled local gravity, the NAVD88 model is based on then-available measurements, and remains fixed despite later improved geoid models. NAVD88 replaced the National Geodetic Vertical Datum of 1929, previously known as the Sea Level Datum of 1929, the elevation difference between points in a local area will show negligible change from one datum to the other, even though the elevation of both does change. NGVD29 used a model of gravity based on latitude to calculate the geoid and did not take into account other variations. Thus, the difference for points across the country does change between datums. Altitude Geodesy Sea Level Datum of 1929 Topographic elevation Topography Reference ellipsoid Geoid United States Geological Survey home page, U. S. National Geodetic Survey home page
30.
European Terrestrial Reference System 1989
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The European Terrestrial Reference System 1989 is an ECEF geodetic Cartesian reference frame, in which the Eurasian Plate as a whole is static. The coordinates and maps in Europe based on ETRS89 are not subject to change due to the continental drift.0, according to the resolution, this system was named European Terrestrial Reference System 89. Since then ETRS89 and ITRS diverge due to the drift at a speed about 2.5 cm per year. By the year 2000 the two coordinate systems differed by about 25 cm, the 89 in its name does not refer to the year of solution, but rather the year of initial definition, when ETRS89 was fully equivalent to ITRS. The solutions of ETRS89 correspond to the ITRS solutions, for each ITRS solution, a matching ETRS89 solution is being made. ETRF2000, for example, is an ETRS89 solution, which corresponds to ITRF2000, ETRS89 is realized by EUREF through the maintenance of the EUREF Permanent Network and continuous processing of the EPN data in a few processing centres. Users have access to ETRS89 via EPN data products and real-time streams of differential corrections from a set of public providers based on the EPN stations, the transformation from ETRS89 to ITRS is time-dependent and was formulated by C. Boucher and Z. Altamimi ETRS89 is the EU-recommended frame of reference for geodata for Europe and it is the only geodetic datum to be used for mapping and surveying purposes in Europe. It plays the role for Europe as NAD-83 for North America. ETRS89 and NAD-83 are based on the GRS80 ellipsoid, wGS84 originally used the GRS80 reference ellipsoid, but has undergone some minor refinements in later editions since its initial publication. WGS84 ED50 AFREF ETRS89 site ETRS89 site ETRS89 site ETRS89 site Information from the Ordnance Survey of Ireland
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Restrictions on geographic data in China
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According to articles 7,26,40 and 42 of the Surveying and Mapping Law of the Peoples Republic of China, private surveying and mapping activities have been illegal in mainland China since 2002. The law prohibits Fines range from 10,000 to 500,000 CNY, foreign individuals or organizations that wish to conduct surveying must form a Chinese-foreign joint venture. Between 2006 and 2011, the authorities pursued nearly 40 illegal cases of mapping and surveying,20096 January - Chinese authorities fine UK students for “illegal map-making activities”. 2010 - Chinese authorities to crack down on the unregistered or illegal among 42,000 online map providers, targeting incorrect information, new standards require all Internet map providers to keep servers storing map data inside China. 201414 March - Coca-Cola is accused of illegal mapping, as a consequence, major digital camera manufacturers including Panasonic, Leica, FujiFilm, Nikon and Samsung restrict location information within China. OpenStreetMap, the project to assemble a map of the world. Chinese regulations mandate that approved map service providers in China use a coordinate system. Baidu Maps uses yet another coordinate system - BD-09, which seems to be based on GCJ-02, GCJ-02 is a geodetic datum formulated by the Chinese State Bureau of Surveying and Mapping, and based on WGS-84. It uses an algorithm which adds apparently random offsets to both the latitude and longitude, with the alleged goal of improving national security. A marker with GCJ-02 coordinates will be displayed at the location on a GCJ-02 map. However, the offsets can result in a 100 -700 meter error from the location if a WGS-84 marker is placed on a GCJ-02 map. The Google. com street map is offset by 50–500 meters from reality, Maps also displays the street map without major errors when compared to the satellite imagery. MapQuest overlays OpenStreetMap data perfectly as well and they appear to be based on leaked code for the WGS to GCJ part. Other solutions to the conversion involve interpolating coordinates based on regression from a set of Google China. An attempt by Wu Yongzheng using FFT analysis gave a result much like the leaked code, from the leaked code, GCJ-02 appears to use the SK-42 reference system for applying offsets to the WGS-84 input. Similar to GCJ-02, there are no APIs to convert in the other direction, GCJ-02 appears to use multiple high-frequency noises of the form 20 n sin , effectively generating a transcendental equation and thus eliminating analytical solutions. Since the two properties ensure some basic functionality of the system, its unlikely that the methods will change with new coordinate systems. The BD-to-GCJ code works in a manner much like the rough method, the establishment of working conversion methods both ways largely obsoletes datasets for deviations mentioned below
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SRID
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A spatial reference system or coordinate reference system is a coordinate-based local, regional or global system used to locate geographical entities. A spatial reference system defines a map projection, as well as transformations between different spatial reference systems. Spatial reference systems are defined by the OGCs Simple feature access using well-known text, Spatial reference systems can be referred to using a SRID integer, including EPSG codes defined by the International Association of Oil and Gas Producers. It is specified in ISO19111,2007 Geographic information—Spatial referencing by coordinates, also published as OGC Abstract Specification, Topic 2 and these coordinate systems form the heart of all GIS applications. Virtually all major spatial vendors have created their own SRID implementation or refer to those of an authority, sRIDs are the primary key for the Open Geospatial Consortium spatial_ref_sys metadata table for the Simple Features for SQL Specification, Versions 1.1 and 1. SRIDs are typically associated with a well known text string definition of the coordinate system, from the Well Known Text Wikipedia page, “A WKT string for a spatial reference system describes the datum, geoid, coordinate system, and map projection of the spatial objects”. Engineering datum Geodesy Georeferencing Geographic coordinate systems Geographic information system, list of National Coordinate Reference Systems spatialreference. org – A website that defines spatial reference systems, in a variety of formats
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Earth
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Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
34.
Spheroid
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A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes, in other words, an ellipsoid with two equal semi-diameters. If the ellipse is rotated about its axis, the result is a prolate spheroid. If the ellipse is rotated about its axis, the result is an oblate spheroid. If the generating ellipse is a circle, the result is a sphere, because of the combined effects of gravity and rotation, the Earths shape is not quite a sphere but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere, the current World Geodetic System model uses a spheroid whose radius is 6,378.137 km at the equator and 6,356.752 km at the poles. The semi-major axis a is the radius of the spheroid. There are two cases, c < a, oblate spheroid c > a, prolate spheroid The case of a = c reduces to a sphere. An oblate spheroid with c < a has surface area S o b l a t e =2 π a 2 where e 2 =1 − c 2 a 2. The oblate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. A prolate spheroid with c > a has surface area S p r o l a t e =2 π a 2 where e 2 =1 − a 2 c 2. The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a and these formulas are identical in the sense that the formula for Soblate can be used to calculate the surface area of a prolate spheroid and vice versa. However, e then becomes imaginary and can no longer directly be identified with the eccentricity, both of these results may be cast into many other forms using standard mathematical identities and relations between parameters of the ellipse. The volume inside a spheroid is 4π/3a2c ≈4. 19a2c, if A = 2a is the equatorial diameter, and C = 2c is the polar diameter, the volume is π/6A2C ≈0. 523A2C. Both of these curvatures are always positive, so every point on a spheroid is elliptic. These are just two of different parameters used to define an ellipse and its solid body counterparts. The most common shapes for the density distribution of protons and neutrons in an atomic nucleus are spherical, prolate and oblate spheroidal, deformed nuclear shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects. An extreme example of a planet in science fiction is Mesklin, in Hal Clements novel Mission of Gravity. The prolate spheroid is the shape of the ball in several sports, several moons of the Solar system approximate prolate spheroids in shape, though they are actually triaxial ellipsoids
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Altitude
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Altitude or height is defined based on the context in which it is used. As a general definition, altitude is a measurement, usually in the vertical or up direction. The reference datum also often varies according to the context, although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage. Vertical distance measurements in the direction are commonly referred to as depth. In aviation, the altitude can have several meanings, and is always qualified by explicitly adding a modifier. Parties exchanging altitude information must be clear which definition is being used, aviation altitude is measured using either mean sea level or local ground level as the reference datum. When flying at a level, the altimeter is always set to standard pressure. On the flight deck, the instrument for measuring altitude is the pressure altimeter. There are several types of altitude, Indicated altitude is the reading on the altimeter when it is set to the local barometric pressure at mean sea level. In UK aviation radiotelephony usage, the distance of a level, a point or an object considered as a point, measured from mean sea level. Absolute altitude is the height of the aircraft above the terrain over which it is flying and it can be measured using a radar altimeter. Also referred to as radar height or feet/metres above ground level, true altitude is the actual elevation above mean sea level. It is indicated altitude corrected for temperature and pressure. Height is the elevation above a reference point, commonly the terrain elevation. Pressure altitude is used to indicate flight level which is the standard for reporting in the U. S. in Class A airspace. Pressure altitude and indicated altitude are the same when the setting is 29.92 Hg or 1013.25 millibars. Density altitude is the altitude corrected for non-ISA International Standard Atmosphere atmospheric conditions, aircraft performance depends on density altitude, which is affected by barometric pressure, humidity and temperature. On a very hot day, density altitude at an airport may be so high as to preclude takeoff and these types of altitude can be explained more simply as various ways of measuring the altitude, Indicated altitude – the altitude shown on the altimeter
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Gravity
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Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since energy and mass are equivalent, all forms of energy, including light, on Earth, gravity gives weight to physical objects and causes the ocean tides. Gravity has a range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a hole, from which nothing can escape once past its event horizon. More gravity results in time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature, the gravitational attraction is approximately 1038 times weaker than the strong force,1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, gravity has an influence on the behavior of subatomic particles. On the other hand, gravity is the dominant interaction at the macroscopic scale, for this reason, in part, pursuit of a theory of everything, the merging of the general theory of relativity and quantum mechanics into quantum gravity, has become an area of research. While the modern European thinkers are credited with development of gravitational theory, some of the earliest descriptions came from early mathematician-astronomers, such as Aryabhata, who had identified the force of gravity to explain why objects do not fall out when the Earth rotates. Later, the works of Brahmagupta referred to the presence of force, described it as an attractive force. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and this was a major departure from Aristotles belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere, galileos work set the stage for the formulation of Newtons theory of gravity. In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. Newtons theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the position of the planet. A discrepancy in Mercurys orbit pointed out flaws in Newtons theory, the issue was resolved in 1915 by Albert Einsteins new theory of general relativity, which accounted for the small discrepancy in Mercurys orbit. The simplest way to test the equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the rate when other forces are negligible
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Equipotential
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Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential. This usually refers to a potential, although it can also be applied to vector potentials. An equipotential of a potential function in n-dimensional space is typically an dimensional space. The del operator illustrates the relationship between a field and its associated scalar potential field. Note that an equipotential region might be referred as being of equipotential or simply be called an equipotential, an equipotential region of a scalar potential in three-dimensional space is often an equipotential surface, but it can also be a three-dimensional region in space. The gradient of the potential is everywhere perpendicular to the equipotential surface. Electrical conductors offer an intuitive example, thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential, in gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity. In electrostatics a conductor is an equipotential region. In the case of a conductor, the equipotential region includes the space inside. A ball will not be accelerated by the force of gravity if it is resting on a flat, horizontal surface, equipotential surface Potential gradient Isopotential map Scalar potential Electric Field Applet
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Center of mass
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The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are simplified when formulated with respect to the center of mass. It is a point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the equivalent of a given object for application of Newtons laws of motion. In the case of a rigid body, the center of mass is fixed in relation to the body. The center of mass may be located outside the body, as is sometimes the case for hollow or open-shaped objects. In the case of a distribution of separate bodies, such as the planets of the Solar System, in orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is a frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of center of mass in the form of the center of gravity was first introduced by the ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, in work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes, Newtons second law is reformulated with respect to the center of mass in Eulers first law. The center of mass is the point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the location of a distribution of mass in space. Solving this equation for R yields the formula R =1 M ∑ i =1 n m i r i, solve this equation for the coordinates R to obtain R =1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has density, which means ρ is constant. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves, in analogy with statistics, the median is not the same as the mean. The coordinates R of the center of mass of a system, P1 and P2, with masses m1. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point
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IERS Reference Meridian
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The IERS Reference Meridian, also called the International Reference Meridian, is the prime meridian maintained by the International Earth Rotation and Reference Systems Service. It passes about 5.3 arcseconds east of George Biddell Airys 1851 transit circle or 102.478 metres at the latitude of the Royal Observatory, the International Hydrographic Organization adopted an early version of the IRM in 1983 for all nautical charts. The IRM was adopted for air navigation by the International Civil Aviation Organization on 3 March 1989, examples include the North American Datum 1983, the European Terrestrial Reference Frame 1989, and the Geocentric Datum of Australia 1994. Versions fixed to a tectonic plate differ from the version by at most a few centimetres. However, the IRM is not fixed to any point on Earth, instead, all points on the European portion of the Eurasian plate, including the Royal Observatory, are slowly moving northeast about 2.5 cm per year relative to it. Thus this IRM is the average of the reference meridians of the hundreds of ground stations contributing to the IERS network. The network includes GPS stations, Satellite Laser Ranging stations, Lunar Laser Ranging stations, all stations coordinates are adjusted annually to remove net rotation relative to the major tectonic plates. The 180th meridian is opposite the IERS Reference Meridian and forms a circle with it dividing the earth into Western Hemisphere. Universal Time is notionally based on the WGS84 meridian, because of changes in the rate of Earths rotation, standard international time UTC can differ from the mean observed solar time at noon on the prime meridian by up to 0.9 second. Leap seconds are inserted periodically to keep UTC close to Earths angular position relative to the Sun, see mean solar time
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Minute and second of arc
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A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
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Prime meridian (Greenwich)
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A prime meridian, based at the Royal Observatory, Greenwich, in London, was established by Sir George Airy in 1851. By 1884, over two-thirds of all ships and tonnage used it as the meridian on their charts. In October of that year, at the behest of U. S. President Chester A. Arthur,41 delegates from 25 nations met in Washington, United States, for the International Meridian Conference. This conference selected the meridian passing through Greenwich as the prime meridian due to its popularity. However, France abstained from the vote, and French maps continued to use the Paris meridian for several decades, the prime meridian passes through the Airy transit circle of the Greenwich observatory. The actual reason for the discrepancy is that the strip is indeed at astronomical longitude zero degrees, zero minutes. Before the establishment of a meridian, most maritime countries established their own prime meridian. In 1721, Great Britain established its own meridian passing through a transit circle at the newly established Royal Observatory at Greenwich. The meridian was moved around 10 metres or so east on three occasions as transit circles with newer and better instruments were built, on each occasion next door to the existing one and this was to allow uninterrupted observation during each new construction. The final meridian was established as a line from the north pole to the south pole passing through the Airy transit circle. This became Great Britains meridian in 1851, for all practical purposes of the period, the changes as the meridian was moved went unnoticed. Transit instruments are installed to be perpendicular to the local level, in 1884, the International Meridian Conference took place to establish an internationally recognised single meridian. The meridian chosen was that which passed through the Airy transit circle at Greenwich, at around the time of this conference, scientists were making measurements to determine the deflection of the vertical on a large scale. The downward extended plumb lines dont even all intersect the axis of the Earth. To make computations feasible, scientists defined ellipsoids of revolution, a given ellipsoid would be a compromise for measurements in a given area. When the Airy transit circle was built, a basin was used to align the telescope to the perpendicular. While the local vertical defined at the Airy transit circle still points to the celestial meridian. As a result of this, the ITRF zero meridian, defined by a passing through the Earths rotation axis, is 102 metres to the east of the prime meridian
42.
Royal Observatory, Greenwich
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The Royal Observatory, Greenwich is an observatory situated on a hill in Greenwich Park, overlooking the River Thames. It played a role in the history of astronomy and navigation. The observatory was commissioned in 1675 by King Charles II, with the stone being laid on 10 August. The site was chosen by Sir Christopher Wren and he appointed John Flamsteed as the first Astronomer Royal. The building was completed in the summer of 1676, the building was often called Flamsteed House, in reference to its first occupant. The scientific work of the observatory was relocated elsewhere in stages in the first half of the 20th century,1675 –22 June, Royal Observatory founded. 1675 –10 August, construction began,1714 Longitude Act established the Board of Longitude and Longitude rewards. The Astronomer Royal was, until the Board was dissolved in 1828,1767 Astronomer Royal Nevil Maskelyne began publication of the Nautical Almanac, based on observations made at the Observatory. 1833 Daily time signals began, marked by dropping a Time ball,1899 The New Physical Observatory was completed. 1924 Hourly time signals from the Royal Observatory were first broadcast on 5 February,1948 Office of the Astronomer Royal was moved to Herstmonceux. 1957 Royal Observatory completed its move to Herstmonceux, becoming the Royal Greenwich Observatory, the Greenwich site is renamed the Old Royal Observatory. Greenwich site is returned to its name, the Royal Observatory. The Ordnance Office was given responsibility for building the Observatory, with Moore providing the key instruments, Moore donated two clocks, built by Thomas Tompion, which were installed in the 20 foot high Octagon Room, the principal room of the building. They were of unusual design, each with a pendulum 13 feet in length mounted above the face, giving a period of four seconds. British astronomers have used the Royal Observatory as a basis for measurement. Four separate meridians have passed through the buildings, defined by successive instruments, subsequently, nations across the world used it as their standard for mapping and timekeeping. When the Airy circle became the reference for the meridian, the difference resulting from the change was considered enough to be neglected. When a new triangulation was done between 1936 and 1962, scientists determined that in the Ordnance Survey system the longitude of the international Greenwich meridian was not 0° and this old astronomical prime meridian has been replaced by a more precise prime meridian
43.
Equator
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The Equator usually refers to an imaginary line on the Earths surface equidistant from the North Pole and South Pole, dividing the Earth into the Northern Hemisphere and Southern Hemisphere. The Equator is about 40,075 kilometres long, some 78. 7% lies across water and 21. 3% over land, other planets and astronomical bodies have equators similarly defined. Generally, an equator is the intersection of the surface of a sphere with the plane that is perpendicular to the spheres axis of rotation. The latitude of the Earths equator is by definition 0° of arc, the equator is the only line of latitude which is also a great circle — that is, one whose plane passes through the center of the globe. The plane of Earths equator when projected outwards to the celestial sphere defines the celestial equator, in the cycle of Earths seasons, the plane of the equator passes through the Sun twice per year, at the March and September equinoxes. To an observer on the Earth, the Sun appears to travel North or South over the equator at these times, light rays from the center of the Sun are perpendicular to the surface of the Earth at the point of solar noon on the Equator. Locations on the Equator experience the quickest sunrises and sunsets because the sun moves nearly perpendicular to the horizon for most of the year. The Earth bulges slightly at the Equator, the diameter of the Earth is 12,750 kilometres. Because the Earth spins to the east, spacecraft must also launch to the east to take advantage of this Earth-boost of speed, seasons result from the yearly revolution of the Earth around the Sun and the tilt of the Earths axis relative to the plane of revolution. During the year the northern and southern hemispheres are inclined toward or away from the sun according to Earths position in its orbit, the hemisphere inclined toward the sun receives more sunlight and is in summer, while the other hemisphere receives less sun and is in winter. At the equinoxes, the Earths axis is not tilted toward the sun, instead it is perpendicular to the sun meaning that the day is about 12 hours long, as is the night, across the whole of the Earth. Near the Equator there is distinction between summer, winter, autumn, or spring. The temperatures are usually high year-round—with the exception of high mountains in South America, the temperature at the Equator can plummet during rainstorms. In many tropical regions people identify two seasons, the wet season and the dry season, but many places close to the Equator are on the oceans or rainy throughout the year, the seasons can vary depending on elevation and proximity to an ocean. The Equator lies mostly on the three largest oceans, the Pacific Ocean, the Atlantic Ocean, and the Indian Ocean. The highest point on the Equator is at the elevation of 4,690 metres, at 0°0′0″N 77°59′31″W and this is slightly above the snow line, and is the only place on the Equator where snow lies on the ground. At the Equator the snow line is around 1,000 metres lower than on Mount Everest, the Equator traverses the land of 11 countries, it also passes through two island nations, though without making a landfall in either. Starting at the Prime Meridian and heading eastwards, the Equator passes through, Despite its name, however, its island of Annobón is 155 km south of the Equator, and the rest of the country lies to the north
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This article incorporates public domain material from websites or documents of the National Geodetic Survey.