ɪsi [OED] ), also called geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal motion, tides, and polar motion. For this they design global and national control networks, using space and terrestrial techniques while relying on datums and coordinate systems.Geodesy or geodetics is that branch of earth science which deals with the measurement and representation of Earth,including its gravitational field,in a three-dimensional time-varying space,and also geodynamics.
Geodesy (from Greek "γεωδαισία" - "geodaisia", lit. "division of the Earth") is primarily concerned with positioning within the temporally varying gravity field. Somewhat obsolete nowadays, geodesy in the German speaking world is divided into "Higher Geodesy" ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the Earth on the global scale, and "Practical Geodesy" or "Engineering Geodesy" ("Ingenieurgeodäsie"), which is concerned with measuring specific parts or regions of the Earth, and which includes
The shape of the Earth is to a large extent the result of its rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates and of vulcanism, resisted by the Earth's
gravityfield. This applies to the solid surface, the liquid surface ( dynamic sea surface topography) and the Earth's atmosphere. For this reason, the study of the Earth's gravity fieldis called physical geodesyby some.
Geoid and reference ellipsoid
geoidis essentially the figure of the Earth abstracted from its topographical features. It is an idealized equilibrium surface of sea water, the mean sea levelsurface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike 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 it and the reference ellipsoid is called the geoidal . It varies globally between ±110 m.
reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorialradius) "a" and flattening "f". The quantity "f" = ("a"−"b")/"a", where "b" is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the Earth (dynamical flattening, symbol "J"2) can be determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometrical flattening is indirect. The relationship depends on the internal density distribution, or, in simplest terms, the degree of central concentration of mass.
The 1980 Geodetic Reference System (
GRS80) posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics ( IUGG). It is essentially the basis for geodetic positioning by the Global Positioning System and is thus also in extremely widespread use outside the geodetic community.
The numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid.
Coordinate systems in space
The locations of points in three-dimensional space are most conveniently described by three cartesian or rectangular coordinates, and . Since the advent of satellite positioning, such coordinate systems are typically
geocentric: the axis is aligned with the Earth's (conventional or instantaneous) rotation axis.
satellite geodesyera, the coordinate systems associated with a geodetic datum attempted to be geocentric, but their origins differed from the geocentre by hundreds of metres, due to regional deviations in the direction of the plumbline(vertical). These regional geodetic datums, such as ED50(European Datum 1950) or NAD83(North American Datum 1983) have ellipsoids associated with them that are regional 'best fits' to the geoids within their areas of validity, minimising the deflections of the vertical over these areas.
It is only because GPS satellites orbit about the geocentre, that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space are themselves computed in such a system.
Geocentric coordinate systems used in geodesy can be divided naturally into two classes:
Inertialreference systems, where the coordinate axes retain their orientation relative to the fixed stars, or equivalently, to the rotation axes of ideal gyroscopes; the axis points to the vernal equinox
# Co-rotating, also ECEF ("Earth Centred, Earth Fixed"), where the axes are attached to the solid body of the Earth. The axis lies within the Greenwich observatory's meridian plane.
The coordinate transformation between these two systems is described to good approximation by (apparent)
sidereal time, which takes into account variations in the Earth's axial rotation (length-of-day variations). A more accurate description also takes polar motioninto account, a phenomenon closely monitored by geodesists.
Coordinate systems in the plane
surveyingand mapping, important fields of application of geodesy, two general types of coordinate systems are used in the plane:
# Plano-polar, in which points in a plane are defined by a distance from a specified point along a ray having a specified direction with respect to a base line or axis;
# Rectangular, points are defined by distances from two perpendicular axes called and . It is geodetic practice — contrary to the mathematical convention — to let the axis point to the North and the axis to the East.
Rectangular coordinates in the plane can be used intuitively with respect to one's current location, in which case the axis will point to the local North. More formally, such coordinates can be obtained from three-dimensional coordinates using the artifice of a
map projection. It is "not" possible to map the curved surface of the Earth onto a flat map surface without deformation. The compromise most often chosen — called a conformal projection— preserves angles and length ratios, so that small circles are mapped as small circles and small squares as squares.
An example of such a projection is UTM (
Universal Transverse Mercator). Within the map plane, we have rectangular coordinates and . In this case the North direction used for reference is the "map" North, not the "local" North. The difference between the two is called " meridian convergence".
It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be and respectively, then we have
The reverse transformation is given by:
In geodesy, point or terrain "
heights" are "above sea level", an irregular, physically defined surface. Therefore a height should ideally "not" be referred to as a coordinate. It is more like a physical quantity, and though it can be tempting to treat height as the vertical coordinate , in addition to the horizontal coordinates and , and though this actually is a good approximation of physical reality in small areas, it quickly becomes invalid for regional considerations. Specify|date=December 2006
Heights come in the following variants:
Each has its advantages and disadvantages. Both orthometric and normal heights are heights in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m² s−2) and not metric. Orthometric and normal heights differ in the precise way in which mean sea level is conceptually continued under the continental masses. The reference surface for orthometric heights is the
geoid, an equipotential surface approximating mean sea level.
"None" of these heights is in any way related to geodetic or ellipsoidial heights, which express the height of a point above the
reference ellipsoid. Satellite positioning receivers typically provide ellipsoidal heights, unless they are fitted with special conversion software based on a model of the geoid.
Because geodetic point coordinates (and heights) are always obtained in a system that has been constructed itself using real observations, geodesists introduce the concept of a "geodetic datum": a physical realization of a coordinate system used for describing point locations. The realization is the result of "choosing" conventional coordinate values for one or more "datum points".
In the case of height datums, it suffices to choose "one" datum point: the reference bench mark, typically a tide gauge at the shore. Thus we have vertical datums like the NAP (
Normaal Amsterdams Peil), the North American Vertical Datum 1988 (NAVD88), the Kronstadt datum, the Trieste datum, and so on.
In case of plane or spatial coordinates, we typically need several datum points. A regional, ellipsoidal datum like
ED50can be fixed by prescribing the undulation of the geoidand the deflection of the vertical in "one" datum point, in this case the Helmert Towerin Potsdam. However, an overdetermined ensemble of datum points can also be used.
Changing the coordinates of a point set referring to one datum, so to make them refer to another datum, is called a "datum transformation". In the case of vertical datums, this consists of simply adding a constant shift to all height values. In the case of plane or spatial coordinates, datum transformation takes the form of a similarity or "Helmert transformation", consisting of a rotation and scaling operation in addition to a simple translation. In the plane, a
Helmert transformationhas four parameters, in space, seven.
A note on terminology
In the abstract, a coordinate system as used in mathematics and geodesy is, e.g., in ISO terminology, referred to as a "coordinate system". International geodetic organizations like the
IERS(International Earth Rotation and Reference Systems Service) speak of a "reference system".
When these coordinates are realized by choosing datum points and fixing a geodetic datum, ISO uses the terminology "coordinate reference system", while IERS speaks of a "reference frame". A datum transformation again is referred to by ISO as a "coordinate transformation". (ISO 19111: Spatial referencing by coordinates).
Point positioning is the determination of the coordinates of a point on land, at sea, or in space with respect to a coordinate system. Point position is solved by computation from measurements linking the known positions of terrestrial or extraterrestrial points with the unknown terrestrial position. This may involve transformations between or among astronomical and terrestrial coordinate systems.
The known points used for point positioning can be
triangulationpoints of a higher order network, or GPS satellites.
Traditionally, a hierarchy of networks has been built to allow point positioning within a country. Highest in the hierarchy were triangulation networks. These were densified into networks of
traverses ( polygons), into which local mapping surveying measurements, usually with measuring tape, corner prism and the familiar red and white poles, are tied.
Nowadays all but special measurements (e.g., underground or high precision engineering measurements) are performed with GPS. The higher order networks are measured with
static GPS, using differential measurement to determine vectors between terrestrial points. These vectors are then adjusted in traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the IERSis used to define a single global, geocentric reference frame which serves as the "zero order" global reference to which national measurements are attached.
surveyingmappings, frequently Real Time KinematicGPS is employed, tying in the unknown points with known terrestrial points close by in real time.
One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control.In every country, thousands of such known points exist and are normally documented by the national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements to.
In geometric geodesy, two standard problems exist:
First geodetic problem
: Given a point (in terms of its coordinates) and the direction (
azimuth) and distance from that point to a second point, determine (the coordinates of) that second point.
econd (inverse) geodetic problem
: Given two points, determine the azimuth and length of the line (straight line, arc or geodesic) that connects them.
In the case of plane geometry (valid for small areas on the Earth's surface) the solutions to both problems reduce to simple
trigonometry.On the sphere, the solution is significantly more complex, e.g., in the inverse problem the azimuths will differ between the two end points of the connecting great circle, arc, i.e. the geodesic.
On the ellipsoid of revolution, solutions in closed form do not exist, so rapidly converging series expansions have traditionally been used, such as
In the general case, the solution is called the
geodesicfor the surface considered. It may be nonexistent or non-unique. The differential equations for the geodesiccan be solved numerically, e.g., in Mathematica[ [http://reference.wolfram.com/mathematica/Geodesy/guide/GeodesyPackage.html Geodesy Package] Mathematica documentation] .
Geodetic observational concepts
Here we define some basic observational concepts, like angles andcoordinates, defined in geodesy (and astronomy as well), mostly from theviewpoint of the local observer.
* The "
plumbline" or "vertical" is the direction of local gravity, or the line that results by following it. It is slightly curved.
* The "
zenith" is the point on the celestial spherewhere the direction of the gravity vector in a point, extended upwards, intersects it. More correct is to call it a rather than a point.
* The "
nadir" is the opposite point (or rather, direction), where the direction of gravity extended downward intersects the (invisible) celestial sphere.
* The celestial "horizon" is a plane perpendicular to a point's gravity vector.
Azimuth" is the direction angle within the plane of the horizon, typically counted clockwise from the North (in geodesy and astronomy) or South (in France).
Elevation" is the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90 degrees minus elevation.
* "Local topocentric coordinates" are azimuth (direction angle within the plane of the horizon) and elevation angle (or zenith angle) and distance.
* The North "
celestial pole" is the extension of the Earth's (precessing and nutating) instantaneous spin axis extended Northward to intersect the celestial sphere. (Similarly for the South celestial pole.)
* The "celestial equator" is the intersection of the (instantaneous) Earth equatorial plane with the celestial sphere.
* A "meridian plane" is any plane perpendicular to the celestial equator and containing the celestial poles.
* The "local meridian" is the plane containing the direction to the zenith and the direction to the celestial pole.
levelis used for determining height differences and height reference systems, commonly referred to mean sea level. The traditional spirit levelproduces these practically most useful heights above sea level directly; the more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid, as GPS only gives heights above the GRS80reference ellipsoid. As geoid knowledge accumulates, one may expect use of GPS heighting to spread.
theodoliteis used to measure horizontal and vertical angles to target points. These angles are referred to the local vertical. The tacheometeradditionally determines, electronically or electro-optically, the distance to target, and is highly automated to even robotic in its operations. The method of free station positionis widely used.
For local detail surveys, tacheometers are commonly employed although the old-fashioned rectangular technique using angle prism and steel tape is still an inexpensive alternative. Real-time kinematic (RTK) GPS techniques are used as well. Data collected are tagged and recorded digitally for entry into a Geographic Information System (GIS)
Geodetic GPS receivers produce directly three-dimensional coordinates in a
geocentriccoordinate frame. Such a frame is, e.g., WGS84, or the frames that are regularly produced and published by the International Earth Rotation and Reference Systems Service ( IERS).
GPS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. For Planet-wide geodetic surveys, previously impossible, we can still mention Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR) and
Very Long Baseline Interferometry(VLBI) techniques. All these techniques also serve to monitor Earth rotation irregularities as well as plate tectonic motions. Gravityis measured using gravimeters. Basically, there are two kinds of gravimeters. "Absolute" gravimeters, which nowadays can also be used in the field, are based directly on measuring the acceleration of free fall (for example, of a reflecting prism in a vacuum tube). They are used for establishing the vertical geospatial control. Most common "relative" gravimeters are spring based. They are used in gravity surveys over large areas for establishing the figure of the geoid over these areas. Most accurate relative gravimeters are "superconducting" gravimeters, and these are sensitive to one thousandth of one billionth of the Earth surface gravity. Twenty-some superconducting gravimeters are used worldwide for studying Earth tides, rotation, interior, and oceanand atmospheric loading, as well as for verifying the Newtonian constant of gravitation.
Units and measures on the ellipsoid
latitudeand longitudeare stated in the units degree, minute of arc, and second of arc. They are "angles", not metricmeasures, and describe the "direction" of the local normal to the reference ellipsoidof revolution. This is "approximately" the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination - measuring the direction of the plumbline by astronomical means - works fairly well provided an ellipsoidal model of the figure of the Earth is used.
One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One nautical mile is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator as is the nautical mile.
A metre was originally defined as the 40-millionth part of the length of a meridian (the target wasn't quite reached in actual implementation, so that is off by 0.02% in the current definitions). This means that one kilometre is roughly equal to (1/40,000) * 360 * 60 meridional minutes of arc, which equals 0.54 nautical mile, though this is not exact because the two units are defined on different bases (the international nautical mile is defined as exactly 1,852 m, corresponding to a rounding of 1000/0.54 m to four digits).
In geodesy, temporal change can be studied by a variety of techniques. Points on the Earth's surface change their location due to a variety of mechanisms:
* Continental plate motion,
* Episodic motion of tectonic origin, esp. close to fault lines
* Periodic effects due to Earth tides
* Postglacial land uplift due to isostatic adjustment
* Various anthropogenic movements due to, for instance,
petroleumor water extraction or reservoir construction.
The science of studying deformations and motions of the Earth's crust and the solid Earth as a whole is called
geodynamics. Often, study of the Earth's irregular rotation is also included in its definition.
Techniques for studying geodynamic phenomena on the global scale include:
*satellite positioning by GPS and other such systems,
Very Long Baseline Interferometry(VLBI)
*satellite and lunar
*Regionally and locally, precise levelling,
*monitoring of gravity change,
Interferometric synthetic aperture radar(InSAR) using satellite images, etc.
Mathematical Geodesists before 1900
* Abu Rayhan Biruni 973-1048,
Khwarezm(Iran/Persia) [H. Mowlana (2001). "Information in the Arab World", "Cooperation South Journal" 1.] [A. S. Ahmed (1984). "Al-Beruni: The First Anthropologist", "RAIN" 60, p. 9-10.]
George Biddell Airy1801-1892, Cambridge & London
Muhammad al-Idrisi1100-1166, ( Arabia& Sicily)
Al-Ma'mun786-833, Baghdad(Iraq/ Mesopotamia)
Johann Jacob Baeyer1794-1885, Berlin (Germany)
Karl Maximilian von Bauernfeind, Munich (Germany)
Friedrich Wilhelm Bessel, Königsberg (Germany)
Roger Joseph Boscovich, Rome/ Berlin/ Paris
Pierre Bouguer1698-1758, (France & Peru)
Heinrich Bruns1848-1919, Berlin (Germany)
Alexis Claude Clairaut1713-1765 (France)
Alexander Ross Clarke, London (England)
Loránd Eötvös1848-1919 (Hungary)
Eratosthenes, Alexandria (Greece & Egypt)
George Everest1830-1843 (England & India)
Hervé Faye1814-1902 (France)
Carl Friedrich Gauß1777-1855, Göttingen (Germany)
Friedrich Robert Helmert, Potsdam (Germany)
* Hipparchos, Nicosia (Greece)
Christiaan Huygens1629-1695 (Netherlands)
Jean Henri Lambert1728-1777 (France)
Pierre-Simon Laplace1749-1827, Paris (France)
* Adrien Marie Legendre 1752-1833, Paris (France)
Johann Benedikt Listing1808-1882 (Germany)
Pierre de Maupertuis1698-1759 (France)
* Gerhard Mercator 1512-1594 (Belgium & Germany)
Friedrich H. C. Paschen, Schwerin (Germany)
Charles S. Peirce1839-1914 (United States)
Henri Poincaré, Paris (France)
J. H. Pratt1809-1871, London (England)
Posidonius, Alexandria (Greece & Egypt)
Ptolemäus, Alexandria (Greece & Egypt)
Georg von Reichenbach1771-1826, Bavaria (Germany)
Heinrich Christian Schumacher1780-1850 (Germany & Estonia)
Snellius(Willebrord Snel van Royen) 1580-1626, Leiden (Netherlands)
Johann Georg von Soldner1776-1833, Munich (Germany)
George Gabriel Stokes(England)
Friedrich Georg Wilhelm Struve1793-1864, Dorpat and Pulkowa/St.-Petersburg (Russia)
Arne Bjerhammar,KTH, Stockholm(Sweden)
* W. Bowie 1872-1940 (USA)
John Fillmore Hayford(USA)
Friedrich Hopfner, Vienna(Austria)
Harold Jeffreys, London(England)
John A. O'Keefe1916-2000 (USA)
Karl-Rudolf Koch, Bonn(Germany)
* Mikhail Sergeevich Molodenskii 1909-1991 (Russia)
Hellmut Schmid, (Switzerland)
Petr Vaníček, Fredericton(Canada)
Yrjö Väisälä1889-1971, (Finland)
* Felix Andries Vening-Meinesz 1887-1966 (Netherlands)
Thaddeus Vincenty, (Poland)
Alfred Wegener1880-1930, (Germany & Greenland)
* [http://www.iag-aig.org/ International Association of Geodesy (IAG)]
* [http://www.iugg.org/ International Union of Geodesy and Geophysics (IUGG)]
* [http://www.fig.net/ Fédération Internationale des Géomètres (FIG)]
* European Petroleum Survey Group (EPSG) (which despite being officially disbanded in 2005 continues to refine a well tested set of Geodetic Parameters)
* [http://www.ngs.noaa.gov/ National Geodetic Survey] (
NGS), Silver Spring MD, USA
* [http://www.nga.mil/portal/site/nga01/ National Geospatial-Intelligence Agency] (NGA), Bethesda MD, USA (Previously National Imagery and Mapping Agency NIMA, previously Defense Mapping Agency DMA)
* [http://www.usgs.gov/ U.S. Geological Survey] (
USGS), Reston VA, USA
* [http://www.ign.fr/rubrique.asp?rbr_id=1&lng_id=EN Institut Géographique National (IGN)] , Saint-Mandé, France
* [http://www.bkg.bund.de Bundesamt für Kartographie und Geodäsie] (BKG), Frankfurt a. M., Germany (Previously Institut für Angewandte Geodäsie, IfAG)
* Central Research Institute for Geodesy, Remote Sensing and Cartography (CNIIGAIK), Moscow, Russia
* [http://www.geod.nrcan.gc.ca/index_e/geodesy_e/geodesy_e.html Geodetic Survey Division] , Natural Resources Canada, Ottawa, Canada
* [http://www.ga.gov.au/geodesy/ Geoscience Australia] , Australian Federal Agency
* [http://www.fgi.fi Finnish Geodetic Institute] (FGI), Masala, Finland
* [http://www.igeo.pt Portuguese Geographic Institute] (IGEO), Lisbon, Portugal
* [http://www.ibge.gov.br/english/ Brazilian Institute for Geography and Statistics - IBGE]
* [http://www.ign.es Spanish National Geographic Institute (IGN)] , Madrid, Spain
* [http://www.linz.govt.nz Land Information New Zealand] .
"Note: This list is still largely incomplete."
* Important publications in geodesy
History of geodesy
World Geodetic System, WGS 84
* Geodesic (in physics)
* B. Hofmann-Wellenhof and H. Moritz, "Physical Geodesy", Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).
* Vaníček P. and E.J. Krakiwsky, "Geodesy: the Concepts", pp.714, Elsevier, 1986.
* Thomas H. Meyer, Daniel R. Roman, and David B. Zilkoski. "What does "height" really mean?" (This is a series of four articles published in "Surveying and Land Information Science, SaLIS".)
** [http://digitalcommons.uconn.edu/thmeyer_articles/2 "Part I: Introduction"] "SaLIS" Vol. 64, No. 4, pages 223-233, December 2004.
** [http://digitalcommons.uconn.edu/thmeyer_articles/3 "Part II: Physics and gravity"] "SaLIS" Vol. 65, No. 1, pages 5-15, March 2005.
** [http://digitalcommons.uconn.edu/nrme_articles/2 "Part III: Height systems"] "SaLIS" Vol. 66, No. 2, pages 149-160, June 2006.
** [http://digitalcommons.uconn.edu/nrme_articles/5 "Part IV: GPS heighting"] "SaLIS" Vol. 66, No. 3, pages 165-183, September 2006.
* [http://www.iag-aig.org/ International Association of Geodesy (IAG)] .
* [http://www.jqjacobs.net/astro/geodesy.html The Geodesy Page.]
* [http://www.kiamehr.tk Geodesy and Geomatics Home Page]
* [http://www.oceanservice.noaa.gov/education/geodesy/welcome.html Welcome to Geodesy]
* [http://www.mapref.org MapRef.org: The Collection of Map Projections and Reference Systems for Europe]
* [http://www.wolfram.com/products/applications/geodesy/ GeometricalGeodesy] software for Geodesy calculations
* [http://www.znu.ac.ir/members/kiamehr_ramin/znu/INDEX.HTM Department of Geodesy and Geomatics Zanjan University - Iran]
* [http://www.pamagic.org/pamagic/lib/pamagic/Geodetic_Ver1_5.pdf Pennsylvania Geospatial Data Sharing Standard - Geodesy and Geodetic Monumentation]
* [http://cires.colorado.edu/~bilham/FG5references.html References on Absolute Gravimeters]
* [http://gge.unb.ca/Research/GRL/GeodesyGroup/tutorial/tutorial.htm Geodesy tutorial at University of New Brunswick]
* [http://www.codeproject.com/KB/cs/Vincentys_Formula.aspx Vincenty's Solution of Geodesics on the Ellipsoid, in C#]
* [http://www.gavaghan.org/blog/free-source-code/geodesy-library-vincentys-formula-java/ Vincenty's Solution of Geodesics on the Ellipsoid, in Java]
* [http://www.earthscope.org/ EarthScope Project]
* [http://pboweb.unavco.org/ UNAVCO - EarthScope - Plate Boundary Observatory]
* [http://www.geodezja.pl/eng/ Polish Internet Informant of Geodesy]
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Look at other dictionaries:
Geodesy — Ge*od e*sy, n. [Gr. ?; ge a, gh^, the earth + ? to divide: cf. F. g[ e]od[ e]sie.] (Math.) That branch of applied mathematics which determines, by means of observations and measurements, the figures and areas of large portions of the earth s… … The Collaborative International Dictionary of English
geodesy — 1560s, surveying, from Mod.L. geodaesia, from Gk. geodaisia division of the earth; ultimately from ge earth + stem of daiein divide … Etymology dictionary
geodesy — ► NOUN ▪ the branch of mathematics concerned with the shape and area of the earth or large portions of it. DERIVATIVES geodesist noun. ORIGIN Greek ge daisia, from g earth + daiein to divide … English terms dictionary
geodesy — [jē äd′ə sē] n. [Gr geōdaisia < gē, the earth + daiein, to divide < IE base * dā , dā(i) , to divide > TIDE1] the branch of applied mathematics concerned with measuring, or determining the shape of, the earth or a large part of its… … English World dictionary
geodesy — geodesist, n. /jee od euh see/, n. the branch of applied mathematics that deals with the measurement of the shape and area of large tracts of country, the exact position of geographical points, and the curvature, shape, and dimensions of the… … Universalium
geodesy — n. mathematical study of the earth, its shape, measurements, etc., and the position and area of points and parts of its surface. ♦ geodete, geodesist, n. student of geodesy. ♦ geodetic, ♦ geodesic, a. making allowance for earth s… … Dictionary of difficult words
geodesy — geodezija statusas Aprobuotas sritis geodezija apibrėžtis Mokslo ir gamybinės veiklos sritis, apimanti visos Žemės ar jos dalies formos bei dydžio tikslinimą, gravitacinio lauko bei erdvinės taškų padėties Žemės paviršiuje (virš ar žemiau šio… … Lithuanian dictionary (lietuvių žodynas)
geodesy — geodezija statusas T sritis ekologija ir aplinkotyra apibrėžtis Mokslas, tiriantis išorinį gravitacijos lauką, Žemės formą ir su jos tyrimu susijusius matavimus bei jų taikymą inžineriniams uždaviniams spręsti, kitų Saulės sistemos kūnų… … Ekologijos terminų aiškinamasis žodynas
geodesy — noun Etymology: Greek geōdaisia, from geō ge + daiesthai to divide more at tide Date: 1853 a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and… … New Collegiate Dictionary
Geodesy — Die Höhere Geodäsie ist jener grundlegende Teil der Geodäsie, der sich mit der großräumigen Erdfigur (Form der Erde, Geoid, Rotation) und dem Erdschwerefeld befasst. Der Begriff wurde von Friedrich Robert Helmert geprägt. Die zugehörigen… … Deutsch Wikipedia