World Geodetic System

The World Geodetic System (WGS) is a standard for use in cartography, geodesy, and satellite navigation including GPS. This standard includes the definition of the coordinate system's fundamental and derived constants, the ellipsoidal (normal) Earth Gravitational Model (EGM), a description of the associated World Magnetic Model (WMM), and a current list of local datum transformations.[1]

The latest revision is WGS 84 (also known as WGS 1984, EPSG:4326), established in 1984 and last revised in 2004.[2] Earlier schemes included WGS 72, WGS 66, and WGS 60. WGS 84 is the reference coordinate system used by the Global Positioning System.

Defining Parameters

The coordinate origin of WGS 84 is meant to be located at the Earth's center of mass; the uncertainty is believed to be less than 2 cm.[3]

The WGS 84 meridian of zero longitude is the IERS Reference Meridian,[4] 5.3 arc seconds or 102 metres (335 ft) east of the Greenwich meridian at the latitude of the Royal Observatory.[5][6]

The WGS 84 datum surface is an oblate spheroid with equatorial radius a = 6378137 m at the equator and flattening f = 1/298.257223563. The refined value of the WGS 84 gravitational constant (mass of Earth’s atmosphere included) is GM = 3986004.418×108 m³/s². The angular velocity of the Earth is defined to be ω = 72.92115×10−6 rad/s.[7]

This leads to several computed parameters such as the polar semi-minor axis b which equals a × (1 − f) = 6356752.3142 m, and the first eccentricity squared,  = 6.69437999014×10−3.[7]

Currently, WGS 84 uses the Earth Gravitational Model 2008.[8] This geoid defines the nominal sea level surface by means of a spherical harmonics series of degree 360 (which provides about 100 km latitudinal resolution near the Equator).[9] The deviations of the EGM96 geoid from the WGS 84 reference ellipsoid range from about −105 m to about +85 m.[10] EGM96 differs from the original WGS 84 geoid, referred to as EGM84.

WGS 84 currently uses the World Magnetic Model 2015v2.[11] The new version of WMM 2015 became necessary due to extraordinarily large and erratic movements of the north magnetic pole. The next regular update (WMM2020) will occur in late 2019.

History

Efforts to supplement the various national surveying systems began in the 19th century with F.R. Helmert's famous book Mathematische und Physikalische Theorien der Physikalischen Geodäsie (Mathematical and Physical Theories of Physical Geodesy). Austria and Germany founded the Zentralbüro für die Internationale Erdmessung (Central Bureau of International Geodesy), and a series of global ellipsoids of the Earth were derived (e.g., Helmert 1906, Hayford 1910/ 1924).

A unified geodetic system for the whole world became essential in the 1950s for several reasons:

In the late 1950s, the United States Department of Defense, together with scientists of other institutions and countries, began to develop the needed world system to which geodetic data could be referred and compatibility established between the coordinates of widely separated sites of interest. Efforts of the U.S. Army, Navy and Air Force were combined leading to the DoD World Geodetic System 1960 (WGS 60). The term datum as used here refers to a smooth surface somewhat arbitrarily defined as zero elevation, consistent with a set of surveyor's measures of distances between various stations, and differences in elevation, all reduced to a grid of latitudes, longitudes, and elevations. Heritage surveying methods found elevation differences from a local horizontal determined by the spirit level, plumb line, or an equivalent device that depends on the local gravity field (see physical geodesy). As a result, the elevations in the data are referenced to the geoid, a surface that is not readily found using satellite geodesy. The latter observational method is more suitable for global mapping. Therefore, a motivation, and a substantial problem in the WGS and similar work is to patch together data that were not only made separately, for different regions, but to re-reference the elevations to an ellipsoid model rather than to the geoid.

In accomplishing WGS 60, a combination of available surface gravity data, astro-geodetic data and results from HIRAN [12] and Canadian SHORAN surveys were used to define a best-fitting ellipsoid and an earth-centered orientation for each of initially selected datum. (Every datum is relatively oriented with respect to different portions of the geoid by the astro-geodetic methods already described.) The sole contribution of satellite data to the development of WGS 60 was a value for the ellipsoid flattening which was obtained from the nodal motion of a satellite.

GRAVIMETRIC DATUM ORIENTATION
Gravimetric datum orientation

Prior to WGS 60, the U.S. Army and U.S. Air Force had each developed a world system by using different approaches to the gravimetric datum orientation method. To determine their gravimetric orientation parameters, the Air Force used the mean of the differences between the gravimetric and astro-geodetic deflections and geoid heights (undulations) at specifically selected stations in the areas of the major datums. The Army performed an adjustment to minimize the difference between astro-geodetic and gravimetric geoids. By matching the relative astro-geodetic geoids of the selected datums with an earth-centered gravimetric geoid, the selected datums were reduced to an earth-centered orientation. Since the Army and Air Force systems agreed remarkably well for the NAD, ED and TD areas, they were consolidated and became WGS 60.

The United States Department of Defense World Geodetic System 1966

Improvements to the global system included the Astrogeoid of Irene Fischer and the astronautic Mercury datum. In January 1966, a World Geodetic System Committee composed of representatives from the United States Army, Navy and Air Force was charged with developing an improved WGS, needed to satisfy mapping, charting and geodetic requirements. Additional surface gravity observations, results from the extension of triangulation and trilateration networks, and large amounts of Doppler and optical satellite data had become available since the development of WGS 60. Using the additional data and improved techniques, WGS 66 was produced which served DoD needs for about five years after its implementation in 1967. The defining parameters of the WGS 66 Ellipsoid were the flattening (1/298.25 determined from satellite data) and the semimajor axis (6,378,145 meters determined from a combination of Doppler satellite and astro-geodetic data). A worldwide 5° × 5° mean free air gravity anomaly field provided the basic data for producing the WGS 66 gravimetric geoid. Also, a geoid referenced to the WGS 66 Ellipsoid was derived from available astrogeodetic data to provide a detailed representation of limited land areas.

The United States Department of Defense World Geodetic System 1972

After an extensive effort over a period of approximately three years, the Department of Defense World Geodetic System 1972 was completed. Selected satellite, surface gravity and astrogeodetic data available through 1972 from both DoD and non-DoD sources were used in a Unified WGS Solution (a large scale least squares adjustment). The results of the adjustment consisted of corrections to initial station coordinates and coefficients of the gravitational field.

The largest collection of data ever used for WGS purposes was assembled, processed and applied in the development of WGS 72. Both optical and electronic satellite data were used. The electronic satellite data consisted, in part, of Doppler data provided by the U.S. Navy and cooperating non-DoD satellite tracking stations established in support of the Navy's Navigational Satellite System (NNSS). Doppler data was also available from the numerous sites established by GEOCEIVERS during 1971 and 1972. Doppler data was the primary data source for WGS 72 (see image). Additional electronic satellite data was provided by the SECOR (Sequential Collation of Range) Equatorial Network completed by the U.S. Army in 1970. Optical satellite data from the Worldwide Geometric Satellite Triangulation Program was provided by the BC-4 camera system (see image). Data from the Smithsonian Astrophysical Observatory was also used which included camera (Baker–Nunn) and some laser ranging.

DOPPLER SATELLITE GROUND STATIONS PROVIDING DATA FOR WGS 72 DEVELOPMENT
Doppler satellite ground stations providing data for WGS 72 development
WORLDWIDE GEOMETRIC SATELLITE TRIANGULATION NETWORK, BC-4 CAMERAS
Worldwide geometric satellite triangulation network, BC-4 cameras

The surface gravity field used in the Unified WGS Solution consisted of a set of 410 10° × 10° equal area mean free air gravity anomalies determined solely from terrestrial data. This gravity field includes mean anomaly values compiled directly from observed gravity data wherever the latter was available in sufficient quantity. The value for areas of sparse or no observational data were developed from geophysically compatible gravity approximations using gravity-geophysical correlation techniques. Approximately 45 percent of the 410 mean free air gravity anomaly values were determined directly from observed gravity data.

The astrogeodetic data in its basic form consists of deflection of the vertical components referred to the various national geodetic datums. These deflection values were integrated into astrogeodetic geoid charts referred to these national datums. The geoid heights contributed to the Unified WGS Solution by providing additional and more detailed data for land areas. Conventional ground survey data was included in the solution to enforce a consistent adjustment of the coordinates of neighboring observation sites of the BC-4, SECOR, Doppler and Baker–Nunn systems. Also, eight geodimeter long line precise traverses were included for the purpose of controlling the scale of the solution.

The Unified WGS Solution, as stated above, was a solution for geodetic positions and associated parameters of the gravitational field based on an optimum combination of available data. The WGS 72 ellipsoid parameters, datum shifts and other associated constants were derived separately. For the unified solution, a normal equation matrix was formed based on each of the mentioned data sets. Then, the individual normal equation matrices were combined and the resultant matrix solved to obtain the positions and the parameters.

The value for the semimajor axis (a) of the WGS 72 Ellipsoid is 6 378 135 meters. The adoption of an a-value 10 meters smaller than that for the WGS 66 Ellipsoid was based on several calculations and indicators including a combination of satellite and surface gravity data for position and gravitational field determinations. Sets of satellite derived station coordinates and gravimetric deflection of the vertical and geoid height data were used to determine local-to-geocentric datum shifts, datum rotation parameters, a datum scale parameter and a value for the semimajor axis of the WGS Ellipsoid. Eight solutions were made with the various sets of input data, both from an investigative point of view and also because of the limited number of unknowns which could be solved for in any individual solution due to computer limitations. Selected Doppler satellite tracking and astro-geodetic datum orientation stations were included in the various solutions. Based on these results and other related studies accomplished by the Committee, an a-value of 6 378 135 meters and a flattening of 1/298.26 were adopted.

In the development of local-to WGS 72 datum shifts, results from different geodetic disciplines were investigated, analyzed and compared. Those shifts adopted were based primarily on a large number of Doppler TRANET and GEOCEIVER station coordinates which were available worldwide. These coordinates had been determined using the Doppler point positioning method.

A new World Geodetic System: WGS 84

WGS 84 reference frame (vector graphic)
WGS 84 reference frame. The oblateness of the ellipsoid is exaggerated in this image.
Garmin GPS at Greenwich Observatory
Handheld GPS receiver indicating the Greenwich meridian is 0.089 arcminutes (or 5.34 arcseconds) west to the WGS 84 datum

In the early 1980s the need for a new world geodetic system was generally recognized by the geodetic community and also within the US Department of Defense. WGS 72 no longer provided sufficient data, information, geographic coverage, or product accuracy for all then-current and anticipated applications. The means for producing a new WGS were available in the form of improved data, increased data coverage, new data types and improved techniques. GRS 80 parameters together with available Doppler, satellite laser ranging and Very Long Baseline Interferometry (VLBI) observations constituted significant new information. An outstanding new source of data had become available from satellite radar altimetry. Also available was an advanced least squares method called collocation which allowed for a consistent combination solution from different types of measurements all relative to the Earth's gravity field, i.e. geoid, gravity anomalies, deflections, dynamic Doppler, etc.

The new World Geodetic System was called WGS 84. It is the reference system used by the Global Positioning System. It is geocentric and globally consistent within ±1 m. Current geodetic realizations of the geocentric reference system family International Terrestrial Reference System (ITRS) maintained by the IERS are geocentric, and internally consistent, at the few-cm level, while still being metre-level consistent with WGS 84.

The WGS 84 originally used the GRS 80 reference ellipsoid, but has undergone some minor refinements in later editions since its initial publication. Most of these refinements are important for high-precision orbital calculations for satellites but have little practical effect on typical topographical uses. The following table lists the primary ellipsoid parameters.

Ellipsoid reference Semi-major axis a Semi-minor axis b Inverse flattening (1/f)
GRS 80 6 378 137.0 m ≈ 6 356 752.314 140 m 298.257 222 100 882 711...
WGS 84 6 378 137.0 m ≈ 6 356 752.314 245 m 298.257 223 563
WGS84 mean Earth radius
Equatorial (a), polar (b) and mean Earth radii as defined in the 1984 World Geodetic System revision (not to scale)

The very small difference in the flattening thus results in a tiny difference of 0.105 mm in the semi polar axis.

Longitudes on WGS 84

WGS 84 uses the IERS Reference Meridian as defined by the Bureau International de l'Heure,[4] which was defined by compilation of star observations in different countries.

The longitude positions on WGS 84 agree with those on the older North American Datum 1927 at roughly 85° longitude west, in the east-central United States.

Updates and new standards

The latest major revision of WGS 84 is also referred to as "Earth Gravitational Model 1996" (EGM96), first published in 1996, with revisions as recent as 2004. This model has the same reference ellipsoid as WGS 84, but has a higher-fidelity geoid (roughly 100 km resolution versus 200 km for the original WGS 84).

Many of the original authors of WGS 84 contributed to a new higher-fidelity model, called EGM2008.[13] This new model will have a geoid with accuracy approaching 10 cm, requiring over 4.6 million terms in the spherical expansion (versus 130,317 in EGM96 and 32,757 in WGS 84).

See also

References

  1. ^ "NGA Geomatics - WGS 84". earth-info.nga.mil. Retrieved 2019-03-19.
  2. ^ "World Geodetic System website of the NGA (archived April 2012)". National Geospatial-Intelligence Agency. Archived from the original on April 2, 2012.
  3. ^ "The EGM96 Geoid Undulation with Respect to the WGS84 Ellipsoid". NASA.
  4. ^ a b European Organisation for the Safety of Air Navigation and IfEN: WGS 84 Implementation Manual, p. 13. 1998
  5. ^ "Greenwich Meridan, Tracing its History". Gpsinformation.net. Retrieved 2017-05-24.
  6. ^ Malys, Stephen; Seago, John H.; Palvis, Nikolaos K.; Seidelmann, P. Kenneth; Kaplan, George H. (1 August 2015). "Why the Greenwich meridian moved". Journal of Geodesy. doi:10.1007/s00190-015-0844-y.
  7. ^ a b "Department of Defense World Geodetic System 1984". National Imagery and Mapping Agency Technical Report TR 8350.2 Third Edition, Amendment 1, 1 Jan 2000.
  8. ^ "NGA Geomatics - WGS 84". earth-info.nga.mil. Retrieved 2019-03-19.
  9. ^ "NGA: NGA/NASA EGM96, N=M=360 Earth Gravitational Model". Earth-info.nga.mil. 2014-10-24. Retrieved 2017-05-24.
  10. ^ "Archived copy". Archived from the original on 2008-09-23. Retrieved 2008-10-24.CS1 maint: archived copy as title (link)
  11. ^ "World Magnetic Model | NCEI". www.ngdc.noaa.gov. Retrieved 2019-03-19.
  12. ^ "NOAA History - Stories and Tales of the Coast & Geodetic Survey - Personal Tales/Earth Measurer/Aslakson Bio". History.noaa.gov. Retrieved 2017-05-24.
  13. ^ "Earth Gravitational Model 2008 (EGM2008)". Earth-info.nga.mil. 2013-05-06. Retrieved 2017-05-24.

External links

 This article incorporates public domain material from websites or documents of the National Geodetic Survey.

Decimal degrees

Decimal degrees (DD) express latitude and longitude geographic coordinates as decimal fractions and are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap, and GPS devices. Decimal degrees are an alternative to using degrees, minutes, and seconds (DMS). As with latitude and longitude, the values are bounded by ±90° and ±180° respectively.

Positive latitudes are north of the equator, negative latitudes are south of the equator. Positive longitudes are east of Prime meridian, negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence, latitude before longitude.

Earth Gravitational Model

The Earth Gravitational Models (EGMs) are geopotential models of the Earth consisting of spherical harmonic coefficients published by the Office of Geomatics at National Geospatial-Intelligence Agency (NGA). EGM96 from 1996 is used as the geoid reference of the World Geodetic System. Three versions of EGM are published: EGM84 with n=m=180, EGM96 with n=m=360, and EGM2008 with n=m=2160. n and m are the degree and orders of harmonic coefficients; the higher they are, the more parameters the models have, and the precise they are. EGM2008 also contains expansions to n=2190. Developmental versions of EGMs are referred to as PGMs, Preliminary Gravitational Models.The NGA provides the model in two formats: in a raster image recording the geoid height at each coordinate at a given resolution, or in a format providing the numerical parameters – the coefficients – defining the model.

Extreme points of Norway

The extreme points of Norway include the coordinates that are farther north, south, east or west than any other location in Norway; and the highest and the lowest altitudes in the country. The northernmost point is Rossøya on Svalbard, the southernmost is Pysen in Mandal, the easternmost is Kræmerpynten on Svalbard, and the westernmost is Høybergodden on Jan Mayen. The highest peak is Galdhøpiggen, standing at 2,469 m (8,100 ft) above mean sea level, while the lowest elevation is sea level at the coast.The Norwegian Antarctic Territory—consisting of Queen Maud Land, Peter I Island and Bouvet Island—are not part of the Kingdom of Norway. Norway administrates the claims based on the Antarctic Treaty System; therefore they are sometimes considered part of a wider definition of Norway. If included, the Norwegian Antarctic Territory accounts the southernmost, easternmost, westernmost and highest extreme points.The latitude and longitude are expressed in degrees, minutes and seconds, in which an "N" value refers to the northern hemisphere, and an "S" value refers to the southern hemisphere. Similarly, a "E" longitude value refers to the eastern hemisphere, and a "W" refers to the western hemisphere. The extreme points of latitude and longitude are published by the Norwegian Mapping Authority, while the elevations are published by the World Fact Book. Both make use of the World Geodetic System (WGS) 84, a geodetic reference system.

Extreme points of the Faroe Islands

The extreme points of the Faroe Islands include the coordinates that are further north, south, east or west than any other location in the Faroe Islands; and the highest and the lowest elevations in the territory.

The latitude and longitude are expressed in decimal degree notation, in which a positive latitude value refers to the northern hemisphere, and a negative value refers to the southern hemisphere. Similarly, a positive longitude value refers to the eastern hemisphere, and a negative value refers to the western hemisphere. The coordinates used in this article are sourced from Google Earth, which makes use of the World Geodetic System (WGS) 84, a geodetic reference system.

GeoNames

GeoNames is a geographical database available and accessible through various web services, under a Creative Commons attribution license.

Geodetic Reference System 1980

The Geodetic Reference System 1980 (GRS 80) is a geodetic reference system consisting of a global reference ellipsoid and a gravity field model.

Geodetic datum

A geodetic datum or geodetic system (also: geodetic reference datum or geodetic reference system) is a coordinate system, and a set of reference points, used to locate places on the Earth (or similar objects). An approximate definition of sea level is the datum WGS 84, an ellipsoid, whereas a more accurate definition is Earth Gravitational Model 2008 (EGM2008), using at least 2,159 spherical harmonics. Other datums are defined for other areas or at other times; ED50 was defined in 1950 over Europe and differs from WGS 84 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 and satellite navigation systems to translate positions indicated on maps (paper or digital) to their real position on Earth. Each starts with an ellipsoid (stretched sphere), and then defines latitude, longitude and altitude coordinates. One or more locations on the Earth's 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, and can be anything from zero to hundreds of meters (or several kilometers for some remote islands). 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 precise shape and size of the Earth (reference ellipsoids).

Because the Earth is an imperfect ellipsoid, localised datums can give a more accurate representation of the area of coverage than WGS 84. OSGB36, for example, is a better approximation to the geoid covering the British Isles than the global WGS 84 ellipsoid. However, as the benefits of a global system outweigh the greater accuracy, the global WGS 84 datum is becoming increasingly adopted.Horizontal datums are used for describing a point on the Earth's surface, in latitude and longitude or another coordinate system. Vertical datums measure elevations or depths.

Geographical mile

The geographical mile is a unit of length determined by 1 minute of arc along the Earth's equator. For the 1924 International Spheroid this equalled 1855.4 metres. The American Practical Navigator 2017 defines the geographical mile as 6087.08 feet (1855.342 m). Greater precision depends more on choice of ellipsoid than on more careful measurement: the length of the equator in the World Geodetic System WGS-84 is 40075016.6856 m which makes the geographical mile 1855.3248 m, while the IERS Conventions (2010) takes the equator to be 40075020.4555 m making the geographical mile 1855.3250 m, 1.2 millimetres longer. In any ellipsoid, the length of a degree of longitude at the equator is thus exactly 60 geographical miles.

The shape of the Earth is a slightly flattened sphere, which results in the Earth's circumference being 0.168% larger when measured around the equator as compared to through the poles. The geographical mile is slightly larger than the nautical mile (which was historically linked to the circumference measured through both poles); one geographic mile is equivalent to approximately 1.00178 nautical miles.

Geoid

The geoid () is the shape that the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent. This surface is extended through the continents (such as with very narrow hypothetical canals). According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.

All points on a geoid surface have the same effective potential (the sum of gravitational potential energy and centrifugal potential energy). The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid if only gravity and rotational acceleration were at work. The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly (mass deficit).

List of extreme points of Bulgaria

The extreme points of Bulgaria include the coordinates that are further north, south, east or west than any other location in Bulgaria; and the highest and the lowest elevations in the country. This list excludes Bulgaria's station in Antarctica. With the exception of Cape Shabla, the easternmost location of Bulgaria, all other extreme points are uninhabited.

The latitude and longitude are expressed in decimal degree notation, in which a positive latitude value refers to the northern hemisphere, and a negative value refers to the southern hemisphere. Similarly, a positive longitude value refers to the eastern hemisphere, and a negative value refers to the western hemisphere. The coordinates used in this article are sourced from Google Earth, which makes use of the World Geodetic System (WGS) 84, a geodetic reference system.

List of extreme points of Japan

The extreme points of Japan include the coordinates that are farthest north, south, east and west in Japan, and the ones that are at the highest and the lowest elevations in the country. Japan's northernmost point is disputed, because Japan considers it to be on Iturup, an island de facto governed by Russia. The southernmost point is Okinotorishima; the westernmost is Cape Irizaki in Okinawa Prefecture, and the easternmost is Minami Torishima. The highest point in Japan is the summit of Mount Fuji at 3,776.24 m (12,389 ft). At 150 m (492 ft) below sea level, the bottom of Hachinohe mine is the country's lowest point. The surface of Hachirōgata is Japan's lowest natural point at 4 m (13 ft) below sea level. With the exception of Cape Irizaki, the western-most location of Japan, all other extreme locations are uninhabited.

Japan extends from 20° to 45° north latitude (Okinotorishima to Benten-jima) and from 122° to 153° east longitude (Yonaguni to Minami Torishima). The coordinates used in this article are sourced from Google Earth, which makes use of the World Geodetic System (WGS) 84.

Location

In geography, location and place are used to identify a point or an area on the Earth's surface or elsewhere. The term location generally implies a higher degree of certainty than place, the latter often indicating an entity with an ambiguous boundary, relying more on human or social attributes of place identity and sense of place than on geometry.

North American Datum

The North American Datum (NAD) is the datum now used to define the geodetic network in North America. A datum is a formal 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 (NAD 27) and the North American Datum of 1983 (NAD 83). Both are geodetic reference systems based on slightly different assumptions and measurements.

OpenCRG

OpenCRG is a complete free and open-source project for the creation, modification and evaluation of road surfaces, and an open file format specification CRG (curved regular grid). Its objective is to standardize a detailed road surface description and it may be used for applications like tire-, vibration- or driving-simulation.

The initial release of OpenCRG was a beta version 0.3 in early 2009; as of August 2015, the current stable release of the OpenCRG C-API and MATLAB tool suite is version 1.0.6.

Reference ellipsoid

In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.

Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined.

In the context of standardization and geographic applications, a geodesic reference ellipsoid is the mathematical model used as foundation by Spatial reference system or Geodetic datum definitions.

Satellite geodesy

Satellite geodesy is geodesy by means of artificial satellites — the measurement of the form and dimensions of Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques. It belongs to the broader field of space geodesy. Traditional astronomical geodesy is not commonly considered a part of satellite geodesy, although there is considerable overlap between the techniques.The main goals of satellite geodesy are:

Determination of the figure of the Earth, positioning, and navigation (geometric satellite geodesy)

Determination of geoid, Earth's gravity field and its temporal variations (dynamical satellite geodesy)

Measurement of geodynamical phenomena, such as crustal dynamics and polar motionSatellite geodetic data and methods can be applied to diverse fields such as navigation, hydrography, oceanography and geophysics. Satellite geodesy relies heavily on orbital mechanics.

Spheroid

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. A spheroid has circular symmetry.

If the ellipse is rotated about its major axis, the result is a prolate (elongated) spheroid, shaped like an American football or rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate (flattened) spheroid, shaped like a lentil. If the generating ellipse is a circle, the result is a sphere.

Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) 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 (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles.

The word spheroid originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape, and that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of the Earth).

Theoretical gravity

In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on Earth's surface by means of a mathematical model representing (a physically smoothed) Earth. The most common model of a smoothed Earth is an Earth ellipsoid, or, more specifically, an Earth spheroid (i.e., an ellipsoid of revolution).

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