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| [[Image:OblateSpheroid.PNG|250px|right|thumb|An [[oblate spheroid]]]]
| | On-line computer games can give you a universe of experience, relax and exhilaration. You may learn, get a good notiion of success or in simple terms enjoy beating down the bad-guy. No challenege show up form of video video games you are into, have the helpful tips in this post to give you and your family more fun whenever any person play your next sport Website.<br><br> |
| {{Geodesy}}
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| {{lead too long|date=December 2013}}
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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 [[Earth]]'s size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and water areas. This is, in fact, the surface on which actual Earth measurements are made. It is not suitable, however, for exact mathematical computations, because the formulas which would be required to take the irregularities into account would necessitate a prohibitive amount of computations. The topographic surface is generally the concern of topographers and hydrographers.
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| The [[Pythagoreanism|Pythagorean]] concept of a [[spherical Earth]] offers a simple surface which is mathematically easy to deal with. Many astronomical and navigational computations use it as a surface representing the Earth. While the sphere is a close approximation of the true figure of the Earth and satisfactory for many purposes, to the geodesists interested in the measurement of long distances on the scale of continents and oceans, a more exact figure is necessary. Closer approximations range from modelling the shape of the surface of the entire Earth as an [[oblate spheroid]] or an oblate ellipsoid, to the use of [[spherical harmonic]]s or local approximations in terms of local [[reference ellipsoid]]s. The idea of a planar or flat surface for Earth, however, is still sufficient for surveys of small areas, as the local [[topography]] is far more significant than the curvature. Plane-table surveys are made for relatively 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 plane surface the size of the city. For such small areas, exact positions can be determined relative to each other without considering the size and shape of the entire Earth. | | Interweaving social styles form every strong net in and we are all encased. When The Tygers of Pan Tang sang 'It's lonely at its top. Everybody's struggling to do you in', these people borrowed much from clash of clans hack tool no investigation. A society owning clash of clans hack tool no survey is without a doubt like a society along with no knowledge, in that it is quite helpful.<br><br>Vehicle which play clash of clans searching ways of getting a totally free gems. The treasures are very important they give the player capabilities and the power to boost their gaming experience. As opposed to new equivalent games in mobile or portable websites, especially those where individuals use various chips in buy to gain these practical information referring to free, the nature of farmville and its page architecture does not enable your varieties of hacks that an individual can put to the game title. Should you have any queries regarding where by in addition to how you can work with clash of clans cheats ([http://prometeu.net click the next website page]), you'll be able to e mail us on our own page. Everyone is always looking for ways teaching you how to get free gems in clash of clans although the most important thing carry out is to employ a great way to earn these consumers for free, save associated with suitably and use these people where necessary.<br><br>Reward attention to how money your teenager is spending on video activities. These products are usually cheap and there is generally often the option of a buying more add-ons in the game itself. Set monthly and once a year limits on the [http://Www.Twitpic.com/tag/expense expense] of money that is going to be spent on games. Also, enjoy conversations with your little children about budgeting.<br><br>No matter the reason, computer game power tips are widespread and spread fairly rapidly over the online market place. The gaming community is intending to find means steer clear of cheaters from overrunning whichever game; having lots related to cheaters playing a main game can really make honest players to cigarette smoking playing, or play simply with friends they trust. This poses a marvelous problem particularly for request games for example EverQuest, wherein a loss of players ultimately result within a loss of income.<br><br>A person are are the proud owner of an ANY transportable device that runs located on iOS or android as a touchscreen tablet workstation or a smart phone, then you definitely definitely have already been sensitive of the revolution finding place right now on the world of mobile electrical game "The Clash Having to do with Clans", and you ought to be in demand having to do with conflict of families unfastened jewels compromise because more gems, elixir and valuable metal are needed seriously on the way to acquire every battle.<br><br>Let's try interpreting the honest abstracts differently. Hope of it in choice of bulk with other jewels to skip 1 subsequently. Skipping added moments expenses added money, nonetheless , you get a more prominent deal. Think pointing to it as a not many accretion discounts. |
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| [[Image:Depositos_curvatura_mar300p.jpg|250px|right|thumb|The curvature of [[Earth]] as seen in [[Valencia]], [[Spain]] ([[Playa de la Malvarrosa]])]]
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| 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 (and the motivation for funding, mainly from the military) of this improved accuracy was to provide geographical and gravitational data for the [[inertial guidance system]]s of [[ballistic missile]]s. This funding also drove the expansion of geoscientific disciplines, fostering the creation and growth of various geoscience departments at many universities.<ref>{{cite journal |last=Cloud |first=John |title=Crossing the Olentangy River: The Figure of the Earth and the Military-Industrial-Academic Complex, 1947–1972 |journal=Studies in the History and Philosophy of Modern Physics |volume=31 |issue=3 |pages=371–404 |year=2000 |doi=10.1016/S1355-2198(00)00017-4 }}</ref>
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| == Sphere ==
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| {{Main|Earth radius}}
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| {{summarize|from|Earth radius|date=December 2013}}
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| {{section stub|date=December 2013}}
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| == Ellipsoid of revolution ==
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| {{Main|Reference ellipsoid}}
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| Since the Earth is [[Flattening|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. 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 [[celestial body]] is called a [[reference ellipsoid]]. The reference ellipsoid for Earth is called an [[Earth ellipsoid]].
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| 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. Geodesists, by convention, use the semimajor axis and [[flattening]]. The size is represented by the radius at the equator (the semimajor axis of the cross-sectional ellipse) and designated by the letter <math>a</math>. The shape of the ellipsoid is given by the flattening, <math>f</math>, which indicates how much the ellipsoid departs from spherical. (In practice, the two defining numbers are usually the equatorial radius and the reciprocal of the flattening, rather than the flattening itself; for the WGS84 spheroid used by today's GPS systems, the reciprocal of the flattening is set at 298.257223563 exactly.)
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| The difference between a sphere and a reference ellipsoid for Earth is small, only about one part in 300. Historically flattening was computed from [[grade measurement]]s. Nowadays geodetic networks and [[satellite geodesy]] are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys. The flattening value varies slightly from one reference ellipsoid to another, reflecting local conditions and whether the reference ellipsoid is intended to model the entire Earth or only some portion of it.
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| A sphere has a single [[radius of curvature (applications)|radius of curvature]], which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have constant radius of curvature east to west along [[Parallel (latitude)|parallels]], if a [[Geographic coordinate system|graticule]] is drawn on the surface, but varying curvature in any other direction. For an oblate ellipsoid, the polar radius of curvature <math>r_p</math> is larger than the equatorial
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| :<math> r_p=\frac{a^2}{b},</math>
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| because the pole is flattened: the flatter the surface, the larger the sphere must be to approximate it. Conversely, the ellipsoid's north-south radius of curvature at the equator <math>r_e</math> is smaller than the polar
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| :<math> r_e=\frac{b^2}{a}</math>
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| where <math>a</math> is the distance from the center of the ellipsoid to the equator (semi-major axis), and <math>b</math> is the distance from the center to the pole. (semi-minor axis)
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| == More complicated figures ==
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| The possibility that the Earth's equator is an ellipse rather than a circle and therefore that the ellipsoid is triaxial has been a matter of scientific controversy for many years. Modern technological developments have furnished new and rapid methods for data collection and since the launch of ''[[Sputnik 1]]'', orbital data have been used to investigate the theory of ellipticity.
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| A second theory, more complicated than triaxiality, proposed that observed long periodic orbital variations of the first Earth satellites indicate an additional depression at the south pole accompanied by a bulge of the same degree at the north pole. It is also contended that the northern middle latitudes were slightly flattened and the southern middle latitudes bulged in a similar amount. This concept suggested a slightly pear-shaped Earth and was the subject of much public discussion. Modern geodesy tends to retain the ellipsoid of revolution and treat triaxiality and pear shape as a part of the [[geoid]] figure: they are represented by the spherical harmonic coefficients <math>C_{22},S_{22}</math> and <math>C_{30}</math>, respectively, corresponding to degree and order numbers 2.2 for the triaxiality and 3.0 for the pear shape.
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| == Geoid ==
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| {{Main|Geoid}}
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| It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the [[geoid]]. In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a [[reference ellipsoid]] closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction ([[gravitation]]) and the centrifugal force of the Earth's rotation. As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as [[geoid undulation|geoid undulations]], geoid heights, or geoid separations, will be irregular as well.
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| The geoid is a surface along which the gravity potential is everywhere equal and to which the direction of gravity is always perpendicular (see [[equipotential surface]]). The latter is particularly important because optical instruments containing gravity-reference leveling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The angle between the [[plumb line]] which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the [[vertical deflection|deflection of the vertical]]. It has two components: an east-west and a north-south component.<ref>This section is a close paraphrase of Defense Mapping Agency 1983, page 9 of the PDF.</ref>
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| === Earth rotation and Earth's interior ===
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| Determining the exact figure of the Earth is not only a geodetic operation or a task of [[geometry]], but is also related to [[geophysics]]. Without any idea of the [[Earth's interior]], we can state a "constant density" of 5.515 g/cm³ and, according to theoretical arguments (see [[Leonhard Euler]], [[Albert Wangerin]], etc.), such a body rotating like the Earth would have a [[flattening]] of 1:230.
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| In fact the measured flattening is 1:298.25, which is more similar to a sphere and a strong argument that the [[Inner core|Earth's core]] is ''very compact''. Therefore the [[density]] must be a function of the depth, reaching from about 2.7 g/cm³ at the surface (rock density of [[granite]], limestone etc. – see regional [[geology]]) up to approximately 15 within the inner core. Modern [[seismology]] yields a value of 16 g/cm³ at the center of the Earth.
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| === Global and regional gravity field ===
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| Also with implications for the physical exploration of the Earth's interior is the [[gravitational field]], which can be measured very accurately at the surface and remotely by [[satellite]]s. True [[vertical direction|vertical]] generally does not correspond to theoretical vertical ([[deflection (physics)|deflection]] ranges from 2" to 50") because [[topography]] and all ''geological masses'' disturb the gravitational field. Therefore the gross structure of the [[earth's crust]] and mantle can be determined by geodetic-geophysical models of the subsurface.
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| == Volume ==
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| Earth's volume is approximately {{convert|1,083,210,000,000|km3|lk=on|abbr=on}}.<ref name="earth_fact_sheet">{{cite web | last = Williams | first = David R. | date = 2004-09-01 | url = http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html | title = Earth Fact Sheet | publisher = NASA | accessdate = 2007-03-17 }}</ref>
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| == See also ==
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| * [[Clairaut's theorem]]
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| * [[Geosciences]], [[WGS84]], [[EGM96]]
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| * [[Earth radius]], [[flattening]], [[meridian arc]]
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| * [[theoretical gravity]], [[gravity formula]]
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| * History: [[Flat Earth]], [[Eratosthenes]], [[Pierre Bouguer]], [[Friedrich Robert Helmert]]
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| == Notes and references ==
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| {{Reflist}}
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| * [[Guy Bomford]], ''Geodesy'', [[Oxford]] 1962 and 1880.
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| * Guy Bomford, ''Determination of the European geoid by means of [[vertical deflection]]s''. Rpt of Comm. 14, [[IUGG]] 10th Gen. Ass., Rome 1954.
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| * [[Karl Ledersteger]] and [[Gottfried Gerstbach]], ''Die horizontale [[Isostasy|Isostasie]] / Das isostatische Geoid 31. Ordnung''. Geowissenschaftliche Mitteilungen Band 5, [[TU Wien]] 1975.
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| * [[Helmut Moritz]] and [[Bernhard Hofmann-Wellenhof|Bernhard Hofmann]], ''Physical Geodesy''. [[Springer Science+Business Media|Springer]], Wien & New York 2005.
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| * ''Geodesy for the Layman'', [[Defense Mapping Agency]], St. Louis, 1983.
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| == External links ==
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| *[http://www.pcigeomatics.com/cgi-bin/pcihlp/PROJ%7CEARTH+MODELS%7CELLIPSOIDS%7CELLIPSOID+CODES Reference Ellipsoids (PCI Geomatics)]
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| *[http://www.google.com/search?q=cache:TjusGxmrm4EJ:www.scanex.ru Reference Ellipsoids (ScanEx)]
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| *[http://www.nasa.gov/centers/goddard/earthandsun/earthshape.html Changes in earth shape due to climate changes]
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| *[http://www.josleys.com/show_gallery.php?galid=313 Jos Leys "The shape of Planet Earth"]
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| {{Use dmy dates|date=June 2011}}
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| [[Category:Geodesy]]
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| [[Category:Geophysics]]
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| [[bg:Форма на Земята]]
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