1.
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
2.
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
3.
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
4.
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
5.
Surveying
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Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional position of points and the distances and angles between them. A land surveying professional is called a land surveyor, Surveyors work with elements of geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages and the law. Surveying has been an element in the development of the environment since the beginning of recorded history. The planning and execution of most forms of construction require it and it is also used in transport, communications, mapping, and the definition of legal boundaries for land ownership. It is an important tool for research in other scientific disciplines. Basic surveyance has occurred since humans built the first large structures, the prehistoric monument at Stonehenge was set out by prehistoric surveyors using peg and rope geometry. In ancient Egypt, a rope stretcher would use simple geometry to re-establish boundaries after the floods of the Nile River. The almost perfect squareness and north-south orientation of the Great Pyramid of Giza, built c.2700 BC, the Groma instrument originated in Mesopotamia. The mathematician Liu Hui described ways of measuring distant objects in his work Haidao Suanjing or The Sea Island Mathematical Manual, the Romans recognized land surveyors as a profession. They established the basic measurements under which the Roman Empire was divided, Roman surveyors were known as Gromatici. In medieval Europe, beating the bounds maintained the boundaries of a village or parish and this was the practice of gathering a group of residents and walking around the parish or village to establish a communal memory of the boundaries. Young boys were included to ensure the memory lasted as long as possible, in England, William the Conqueror commissioned the Domesday Book in 1086. It recorded the names of all the owners, the area of land they owned, the quality of the land. It did not include maps showing exact locations, abel Foullon described a plane table in 1551, but it is thought that the instrument was in use earlier as his description is of a developed instrument. Gunters chain was introduced in 1620 by English mathematician Edmund Gunter and it enabled plots of land to be accurately surveyed and plotted for legal and commercial purposes. Leonard Digges described a Theodolite that measured horizontal angles in his book A geometric practice named Pantometria, joshua Habermel created a theodolite with a compass and tripod in 1576. Johnathon Sission was the first to incorporate a telescope on a theodolite in 1725, in the 18th century, modern techniques and instruments for surveying began to be used. Jesse Ramsden introduced the first precision theodolite in 1787 and it was an instrument for measuring angles in the horizontal and vertical planes
6.
U.S. National Geodetic Survey
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United States Coast Survey and United States Coast and Geodetic Survey redirect here. Since its foundation in its present form in 1970, it has been part of the National Oceanic and Atmospheric Administration, the National Geodetic Surveys history and heritage are intertwined with those of other NOAA offices. As the U. S. Coast Survey and U. S, upon the creation of the Environmental Science Services Administration in 1965, the commissioned corps was separated from the Survey to become the Environmental Science Services Administration Corps. Thus, the National Geodetic Surveys ancestor organizations are also the ancestors of todays NOAA Corps, in addition, todays National Institute of Standards and Technology, although long since separated from the Survey, got its start as the Surveys Office of Weights and Measures. The National Geodetic Survey is an office of NOAAs National Ocean Service, NGS is responsible for defining the NSRS and its relationship with the International Terrestrial Reference Frame. The NSRS enables precise and accessible knowledge of things are in the United States. The NSRS may be divided into its geometric and physical components, the official geodetic datum of the United States, NAD83 defines the geometric relationship between points within the United States in three-dimensional space. The datum may be accessed via NGSs network of marks or through the Continuously Operating Reference Station network of GPS reference antennas. NGS is responsible for computing the relationship between NAD83 and the ITRF, the physical components of the NSRS are reflected in its height system, defined by the vertical datum NAVD88. This datum is a network of orthometric heights obtained through spirit leveling, NGS will release new datums in 2022. The North American Terrestrial Reference Frame of 2022 will supersede NAD83 in defining the relationship between the North American plate and the ITRF. United States territories on the Pacific, Caribbean, and Mariana plates will have their own respective geodetic datums, the North American-Pacific Geopotential Datum of 2022 will separately define the height system of the United States and its territories, replacing NAVD88. It will use a geoid model accurate to 1 centimeter to relate orthometric height to ellipsoidal height measured by GPS, NGS provides a number of other public services. The Online Positioning and User Service processes user-input GPS data and outputs position solutions within the NSRS, the agency offers other tools for conversion between datums. A Swiss immigrant with expertise in surveying and the standardization of weights and measures, Ferdinand R. Hassler, was selected to lead the Survey. Hassler departed on August 29,1811, but eight months later, while he was in England, Hassler did not return to the United States until August 16,1815. The Survey finally began surveying operations in 1816, when Hassler started work in the vicinity of New York City, the first baseline was measured and verified in 1817. S. S. Army and U. S. Navy responsibility for coastal surveys, Hassler was reappointed as the Surveys superintendent that year
7.
Alexander Ross Clarke
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He was an officer of the Royal Engineers employed on the Ordnance Survey. The basic sources of material on Clarke are the two articles by Charles Close, one of the Directors of the Ordnance Survey, the first was an article for the Royal Engineers Journal and the second, a revised and expanded version, appeared in the Empire Survey Review. Much of Closes material is incorporated in the web page REubique along with details of his career and further information communicated by one of Clarkes living descendants. Other sources of information are to be found in the Times of London, two recent histories of the Ordnance Survey include information on Clarke, Owen and Pilbeam, and Seymour. Clarke was born in Reading, Berkshire, England on 16 December 1828, the parents, David and Eliza, were back in England by 1834 but they soon moved up to Davids family home at Eriboll in the far north of Scotland. The school teaching there was primitive but effective, anyway he learned Latin and mathematics. Close adds that The mathematics that was kicked into him determined his career in after life. David Clarke and his moved to London, before 1846, and eventually settled at 35 Devonshire Place. His wife, Eliza Ann, died in 1887 and it was from this London address that Alexander Clarke, at the age of seventeen in 1846, applied to the Royal Military Academy, Woolwich as a Gentleman Cadet. Clarke was very unprepared for the examination, having left a space of only three weeks for revision, and he was placed bottom of the list of candidates. At Woolwich he would undergo basic training and formal teaching in subjects such as mathematics. Clarke excelled at his studies and he passed out first, with the reputation of being a capable young man. He was commissioned as a lieutenant in the Royal Engineers on 1 October 1847. After his commissioning, Clarke attended the Young Officers Course at the Royal School of Military Engineering at Chatham and he was promoted to the rank of Lieutenant on 11 July 1849 at the end of that course. Before Clarke could make progress on the calculation of the triangulation, the nature of the posting is not recorded but it had one happy outcome. Clarke met, and married, Frances Maria, youngest daughter of Colonel Matthew C, Superintendent Hall retired in 1854 and Yolland, the most competent member of the Survey, was passed over in favour of Colonel Henry James. Yolland resigned immediately and Clarke was the only qualified candidate for the analysis of the triangulation, the magnitude of this task is discussed below. The report was accomplished by 1858, a short period of time
8.
Triangulation station
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The station is usually set up by a government with known coordinate and elevation published. Many stations are located on hilltops for the purposes of visibility, a graven metal plate on the top of a pillar may provide a mounting point for a theodolite or reflector. Trigonometrical stations are grouped together to form a network of triangulation, positions of all land boundaries, roads, railways, bridges and other infrastructure can be accurately located by the network, a task that is essential to the construction of modern infrastructure. Apart from the known stations set up by government, some temporary trigonometrical stations are set up near construction sites for monitoring the precision, some trigonometrical stations use the Global Positioning System for convenience, however, the accuracy depends on factors such as ionospheric and tropospheric propagation delay errors. Although stations are no longer required for many surveying purposes, they remain useful to hikers as navigational aids and these trig stations are clearly visible for many kilometres and useful for hikers. In Japan, there are five classes of triangulation stations, Class 1 They are installed approximately every 40 kilometres, There are about 1000 throughout Japan. The pillars are 18 centimetres on a side, and each pillar is anchored with two large perpendicular rocks buried underground. Class 2 They are installed approximately every 8 kilometres, There are about 5000 throughout Japan, and the pillars are 15 centimetres on a side. Each pillar is anchored with a large perpendicular rock buried underground. Class 3 There are about 32,000 installed throughout Japan, the pillars are 15 centimetres on a side, and each pillar is anchored with a large perpendicular rock buried underground. Class 4 They are installed approximately every 2 kilometres, and there are about 69,000 throughout Japan, the pillars are 12 centimetres on a side, and each pillar is anchored with a large perpendicular rock buried underground. Class 5 These markers were installed in 1899 and are the predecessors to the modern triangulation stations used in Japan today and they are generally not used anymore since the installation of the Class 1-4 stations. Some of them still exist at various locations throughout Japan, in Spain there are 11,000 triangulation stations, concrete buildings which typically consist of a cylinder 120 cm high and 30 cm diameter over a concrete cubic base. They were erected by the Instituto Geográfico Nacional, usually painted in white, in the United Kingdom, trig points are typically concrete pillars, and were erected by the Ordnance Survey. The process of placing trig points on top of prominent hills, the Ordnance Surveys first trig point was erected on 18 April 1936 near Cold Ashby, Northamptonshire. In low-lying or flat areas some trig points are only a few metres above sea level, in most of the UK, trig points are truncated square concrete pyramids or obelisks tapering towards the top. On the top a brass plate with three arms and a depression is fixed, it is used to mount and centre a theodolite used to take angular measurements to neighbouring trig points. A benchmark is set on the side, marked with the letters O S B M
9.
Geographic center of the contiguous United States
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The geographic center of the contiguous United States is the center of 48 U. S. states. It has been regarded as such by the U. S. National Geodetic Survey since the 1912 additions of New Mexico and Arizona to the United States. Its position as located in a 1918 survey is located at 39°50′N 98°35′W, in Kansas about 2.6 miles northwest of the center of Lebanon, approximately 12 miles south of the Kansas-Nebraska border. It is accessible by a turn-off from U. S. Route 281.8333333, -98.585522 to 38.0000, -97.0000. In order to protect the privacy of the land owner where the point identified by the 1918 survey falls. Its inscription reads, The GEOGRAPHIC CENTER of the UNITED STATES LAT, -98°35 NE 1/4 - SE 1/4 - S32 - T2S - R11W Located by L. T. Hagadorn of Paulette & Wilson - Engineers and L. A. Beardslee - County Engineer, from data furnished by U. S. Coast and Geodetic Survey. April 25,1940 An American flag usually flies atop a pole placed on the monument, a covered picnic area and small four-pew chapel are nearby. Geographic center Geographic center of the United States Geographic centers of the United States Mean center of U. S
10.
Meades Ranch Triangulation Station
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The Meades Ranch Triangulation Station is a survey marker in Osborne County in the state of Kansas in the Midwestern United States. In surveying, a datum is a point or set of points used to establish a coordinate system. By designating the location of one point, and the direction from that point to a second point, the first nationwide datum in the United States was established in 1879. At that time, a region of contiguous triangulation existed from Maine to Georgia, the New England Datum was chosen with a benchmark in Maryland, near the middle of this region, as the horizontal datum, and a second Maryland mark used to define the azimuth direction. To account for the Earths curvature, the datum used a model called the Clarke spheroid, the U. S. Coast and Geodetic Survey established a triangulation station, officially known as the Meades Ranch Triangulation Station, in 1891. In 1901, the Meades Ranch station was chosen as the United States standard horizontal datum, in light of this, its name was changed to the North American Datum. As more new surveys and previously isolated survey networks were incorporated into the system, by the mid-1920s, it was realized that the coordinate system needed to be adjusted. From 1927 to 1932, the approximately 25,000 existing control locations were recalculated, the new system continued to use the 1901 coordinates of Meades Ranch as its horizontal datum, and the Clarke spheroid as its model for the Earths surface. However, it now defined horizontal directions in terms of 175 Laplace azimuths, under NAD27, the azimuth to the Waldo station changed by about 5. In 1973, the Meades Ranch site was added to the National Register of Historic Places, as the survey network was extended further north into Canada, similar discrepancies appeared. To address these, a new datum was developed, designated NAD83 and it replaced the Clarke spheroid with a new ellipsoid, the Geographic Reference System 1980, centered at the Earths center of mass as determined by the Bureau International de lHeure. The new datum was based on adjustment of 250,000 points, NAD83 was officially adopted by the U. S. government in 1989, and by the Canadian government in 1990. Under the new system, Meades Ranch lost its special standing, as of 2012, the location of the Meades Ranch station was 39°13′26. 71220″N 98°32′31. 74540″W. It lies about 12 miles north of Lucas and about 10 miles southwest of Tipton, the station is on a low grassy ridge in a pasture. It is marked by a disc, inscribed Meades Ranch 1891, embedded in the top of a dome-shaped concrete marker 21 inches in diameter. Two reference marks and a mark are located nearby. The Meades Ranch station is on land, with no public access. Geodesy 1940 re-installation At the geodetic center of North America two journal essays
11.
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
12.
Earth radius
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Earth radius is the distance from the Earths center to its surface, about 6,371 km. This length is used as a unit of distance, especially in astronomy and geology. This article deals primarily with spherical and ellipsoidal models of the Earth, see Figure of the Earth for a more complete discussion of the models. 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 km. It can also mean some kind of average of such distances, Aristotle, writing in On the Heavens around 350 BC, reports that the mathematicians guess the circumference of the Earth to be 400,000 stadia. Due to uncertainty about which stadion variant Aristotle meant, scholars have interpreted Aristotles figure to be anywhere from highly accurate to almost double the true value, the first known scientific measurement and calculation of the radius of the Earth was performed by Eratosthenes about 240 BC. Estimates of the accuracy of Eratosthenes’s measurement range from within 0. 5% to within 17%, as with Aristotles report, uncertainty in the accuracy of his measurement is due to modern uncertainty over which stadion definition he used. Earths rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere, local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of the Earths surface must be simpler than reality in order to be tractable, hence, we create models to approximate characteristics of the Earths surface, generally relying on the simplest model that suits the need. Each of the models in use involve some notion of the geometric radius. Strictly speaking, spheres are the solids to have radii. In the case of the geoid and ellipsoids, the distance from any point on the model to the specified center is called a radius of the Earth or the radius of the Earth at that point. It is also common to refer to any mean radius of a model as the radius of the earth. When considering the Earths real surface, on the hand, it is uncommon to refer to a radius. Rather, elevation above or below sea level is useful, 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. Hence, the Earth deviates from a sphere by only a third of a percent. While specific values differ, the concepts in this article generalize to any major planet
