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'Geodesy' (IPA North American English ; British, Australian English etc. ), also called 'geodetics', is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field, and other geodynamic phenomena, such as crustal motion, oceanic tides, and polar motion.

Contents

Definition

History

Geoid and reference ellipsoid

Coordinate systems in space

Coordinate systems in the plane

Heights

Geodetic data

A note on terminology

Point positioning

Geodetic problems

Geodetic principal problem (also: first geodetic problem)

Geodetic inverse problem (also: second geodetic problem)

Geodetic observational concepts

Geodetic measurements

Units and measures on the ellipsoid

Temporal change

Famous geodesists

Math./ Geodesists before ~1900

20th century

International organizations

University institutes

Governmental agencies

See also

Notes

References

External links

Definition

Geodesy (from Greek ''Γεωδαισία'' lit. division of the Earth) is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of the Earth's magnetic field. Especially in the German speaking world, geodesy is divided in geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the earth on a global scale, and surveying ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface.
The shape of the earth is to a large extent the result of its rotation, which causes its equatorial bulge, and the competition of geologic processes such as the collision of plates and of vulcanism, resisted by the earth's gravity field. 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 field is seen as a part of geodesy, called
physical geodesy.

History

Main articles: History of geodesy

Geoid and reference ellipsoid

The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the 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.
A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial
radius) ''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) is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric 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, $X,\; Y$ and $Z$. Since the advent of satellite positioning, such coordinate systems are typically ''geocentric'': the $Z$ axis is aligned with the Earth's (conventional or instantaneous) rotation axis.
Before the satellite geodesy era, the coordinate systems associated with geodetic datums 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:
# Inertial reference systems, where the coordinate axes retain their orientation relative to the fixed stars, or equivalently, to the rotation axes of ideal gyroscopes; the $X$ 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 $X$ 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 motion into account, a phenomenon currently closely monitored by geodesists.

Coordinate systems in the plane

In surveying and 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 $s$ 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 $x$ and $y$. It is geodetic practice — contrary to the mathematical convention — to let the $x$ axis point to the North and the $y$ axis to the East.
Rectangular coordinates in the plane can be used intuitively with respect to one's current location, in which case the $x$ 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 $x$ and $y$. 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 $s$ respectively, then we have
:$$
egin{matrix}
x &=& s cos lpha\
y &=& s sin lpha
end{matrix}

The reverse translation is slightly more tricky.

Heights

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 $z$, in addition to the horizontal coordinates $x$ and $y$, and though this actually is a good approximation of physical reality in small areas, it quickly becomes invalid in larger areas.
Heights come in the following variants:
# Orthometric heights
# Normal heights
# Geopotential heights
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: $m^2\; s^\{-2\}$) 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.

Geodetic data

Because geodetic point coordinates (and heights) are always obtained in a system that has been constructed itself using real observations, we have to 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, etc.
In case of plane or spatial coordinates, we typically need several datum points. A regional, ellipsoidal datum like ED50 can be fixed by prescribing the undulation of the geoid and the deflection of the vertical in ''one'' datum point, in this case the Helmert Tower in Potsdam. However, an overdetermined ensemble of datum points can also be used.
Changing the coordinates of a point set referring to one datum, 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 transformation has 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

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 triangulation points 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 IERS is used to define a single global, geocentric reference frame which serves as the "zero order" global reference to which national measurements are attached.
For surveying mappings, frequently Real Time Kinematic GPS 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 in the terrain and are documented by the national mapping agencies. Constructors and
surveyors involved in real estate will use these to tie their local measurements to.

Geodetic problems

In geometric geodesy, two standard problems exist:

Geodetic principal problem (also: 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.

Geodetic inverse problem (also: second 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 Vincenty's formulae.
In the general case, the solution is called the geodesic for the surface considered. It may be nonexistent or non-unique. The differential equations for the geodesic can be solved numerically, e.g., in MATLAB.

Geodetic observational concepts

Here we define some basic observational concepts, like angles and
coordinates, defined in geodesy (and astronomy as well), mostly from the
viewpoint 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 sphere where 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.

Geodetic measurements

The level is used for determining height differences and height reference systems, commonly referred to mean sea level. The traditional spirit level produces 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 GRS80 reference ellipsoid. As geoid knowledge accumulates, one may expect use of GPS heighting to spread.
The theodolite is used to measure horizontal and vertical angles to target points. These angles are referred to the local vertical. The tacheometer additionally determines, electronically or electro-optically, the distance to target, and is highly automated in its operations. The method of free station position is 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. More and more, also real time kinematic (RTK) GPS techniques are used. Data collected is tagged and recorded digitally for entry into a Geographic Information System (GIS) data base.
Geodetic GPS receivers produce directly three-dimensional coordinates in a geocentric coordinate 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.
Gravity is measured using gravimeters. There are two basic 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 ocean and atmospheric loading, as well as for verifying the Newtonian constant of gravitation.

Units and measures on the ellipsoid

Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are ''angles'', not metric
measures, and describe the ''direction'' of the local normal to the reference ellipsoid of 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.
A geographic mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. A 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 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. This means that a kilometre is equal to (1/40,000)
★ 360
★ 60 meridional minutes of arc, which equals 0.54 nautical miles. Similarly a nautical mile is on average 1/0.54 = 1.85185... km.

Temporal change

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, plate tectonics

★ 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, e.g., petroleum or water extraction or reservoir construction.
The science of studying deformations and motions in the Earth's crust and the solid Earth as a whole is called geodynamics. Often, also study of the Earth's irregular rotation is included in its definition.
Techniques for studying geodynamic phenomena on the global scale include:

★ satellite positioning by GPS and similar techniques,

★ very long baseline interferometry (VLBI)

★ satellite and lunar laser ranging.

★ Regionally and locally, precise levelling,

★ precise tacheometers

★ monitoring gravity change,

★ Synthetic Aperture Radar Interferometry (InSAR) using satellite images.

Famous geodesists

Math./ Geodesists before ~1900

★ Abu al-Rayhan al-Biruni 973-1048, Khwarezm (Iran/Persia)^[1][2]

★ Sir George Biddell Airy 1801-1892, Cambridge & London

★ Muhammad al-Idrisi 1100-1166, Arabia & Sicily

★ Al-Ma'mun 786-833, Baghdad (Iraq/Mesopotamia)

★ Johann Jacob Baeyer 1794-1885, Berlin

★ Karl Maximilian von Bauernfeind, München (Germany)

★ Friedrich Wilhelm Bessel, Königsberg (Germany)

★ Roger Joseph Boscovich, Rome/ Berlin/ Paris

★ Pierre Bouguer 1698-1758, France & Peru

★ Heinrich Bruns 1848-1919, Berlin

★ Alexis Claude Clairaut 1713-1765, France

★ Alexander Ross Clarke, London

★ Loránd Eötvös 1848-1919, Hungary

★ Eratosthenes, Alexandria (Greece & Egypt)

★ Sir George Everest 1830-1843, England & India

★ Hervé Faye 1814-1902, France

★ Abel Foullon, France

★ Carl Friedrich Gauß 1777-1855, Göttingen (Germany)

★ Friedrich Robert Helmert, Potsdam (Germany)

★ Hipparchos, Nicosia (Greece)

★ Christiaan Huygens 1629-1695, Netherlands

★ Jean Henri Lambert 1728-1777, France

★ Pierre-Simon Laplace 1749-1827, Paris

★ Adrien Marie Legendre 1752-1833, Paris

★ Johann Benedikt Listing 1808-1882, Germany

★ Pierre de Maupertuis 1698-1759, France

★ Gerhard Mercator 1512-1594, Belgium & Germany

★ Friedrich H. C. Paschen, Schwerin (Germany)

★ Henri Poincaré, Paris

★ J. H. Pratt 1809-1871, London

★ Posidonius, Alexandria

★ Ptolemäus, Alexandria

★ Regiomontanus, Germany/Austria

★ Georg von Reichenbach 1771-1826, Bavaria (Germany)

★ Heinrich Christian Schumacher 1780-1850, Germany & Estland

★ Snellius (Willebrord Snel van Royen, Leiden/Netherlands 1580-1626)

★ Johann Georg von Soldner 1776-1833, München (Germany)

★ George Gabriel Stokes, England

20th century

★ Kurt Arnold, Potsdam (Germany)

★ W. Bowie 1872-1940, USA

★ C. F. Baeschlin, Zurich (Swiss)

★ Willem Baarda 1917–2005, Delft (The Netherlands)

★ Arne Bjerhammar 1917 -, Sweden

★ Junyong Chen, Wuhan (China)

★ Yongling Chen, Wuhan China

★ Eduard Dolezal, Wien (Vienna, Austria)

★ Demitris Delikaraoglou, Athens (Greece)

★ David Doyle, USA

★ Wilhelm Embacher 1911-20.., Innsbruck (Austria)

★ Richard Finsterwalder, München/Hannover

★ Sebastian Finsterwalder 1862-1951, Bavaria (Germany)

★ Irene K. Fischer, USA

★ Erik Grafarend, Stuttgart (Germany)

★ Erwin Groten, Germany

★ John Fillmore Hayford, USA

★ Weikko A. Heiskanen 1895-1971, Finland

★ Siegfried Heitz, Bonn (Germany)

★ Martin Hotine 1898-1968

★ Friedrich Hopfner, Wien (Austria)

★ L. Hradilek, Czechoslovakia

★ W. K. Hristow, Bulgaria

★ Sir Harold Jeffreys, London

★ Martin Hotine 1898-1968

★ W. Jordan, Germany

★ Ladislav Feil, Croatia

★ Karl Jung, Germany

★ Heribert Kahmen, Hannover/Wien (Germany/Austria)

★ William Mason Kaula 1926-2000, USA

★ John A. O'Keefe 1916-2000, USA

★ Max Kneissl, München (Germany)

★ Karl-Rudolf Koch, Bonn (Germany)

★ Yoshihide Kozai, Boston, USA

★ Th. N. Krassowski, Russia

★ Johann Heinrich Louis Krüger, Berlin

★ Jean-Jacques Levallois 1911-2001, IGN Paris, France

★ Antonio Marussi 1908-1984]], Florence (Italy)

★ Mikhail Sergeevich Molodenskii 1909-1991, Russia

★ Helmut Moritz, Graz (Austria)

★ Theodor Niethammer, Schweiz

★ Wolfgang Pillewizer, Dresden/Wien (Germany/Austria)

★ Karl Ramsayer, Stuttgart

★ Christoph Reigber, Potsdam

★ Karl Rinner, Germany and Graz (Austria)

★ Alwyn R. Robbins 1920-2002, Oxford (Geodetic Astronomy)

★ Reiner Rummel, München

★ Fernando Sanso, Milano (Italy)

★ Hellmut Schmid, Schweiz

★ Rudolf Sigl 1928-1998, München (Germany)

★ David G. Smith, USA

★ L. Tanni, Helsinki

★ Wolfgang Torge, Hannover (Germany)

★ Werner Uhink, Potsdam (Germany)

★ Petr Vaníček, Fredericton (Canada)

★ Yrjö Väisälä 1889-1971, Finland (brother in law of W.A. Heiskanen)

★ Felix Andries Vening-Meinesz 1887-1966 Netherlands

★ Thaddeus Vincenty, Poland

★ Alfred Wegener 1880-1930, Germany & Greenland

★ Helmut Wolf, Bonn (Germany)

★ Thomas Wunderlich, Wien/Munich (Germany)

★ Carl Christian Tscherning, Copenhagen (Denmark)

★ Rene Forsberg, Copenhagen (Denmark)

★ Per Knudsen, Copenhagen (Denmark)

★ Lars Sjöberg, Stockholm (Sweden)

International organizations

★ International Association of Geodesy (IAG)

★ International Union of Geodesy and Geophysics (IUGG)

★ Fédération Internationale des Géomètres (FIG)

University institutes

Some university institutes engaged in geodesy include:

★ Department of Geomatic Engineering, University College London

★ The ''Institut für Erdmessung'' in Hannover, Germany - which specialises in astro-geodetic zenith cameras and geoid computations for many European countries

★ Division of Geodesy - Royal Institute of Technology (KTH) Stockholm, Sweden

★ The ''Institut für Theoretische Geodäsie'' in Bonn (Geodesy, Radio astronomy and GPS)

★ The ''Institut für Astronomische und Physikalische Geodäsie'' in Munich, southern Germany.

★ The Austrian ''Institute for Geodesy and Geophysics'' at the TU Vienna (astro-geological geoid, IGS and VLBI)

★ The Swiss ''Geodetic Institute'' at the ETH Zürich (geophysical geodesy, GPS etc.)

★ Moscow State University of Geodesy and Cartography (MIIGAiK)

★ Geodesy at Ohio State University, Columbus OH, USA

★ Geodesy and Geomatics Engineering, University of New Brunswick, Canada

★ Department of Geodesy and Geomatics, Zanjan University, Zanjan, Iran

★ Department of Surveying at Helsinki University of Technology, Espoo, Finland

★ Geomatics Engineering at the University of Calgary, Alberta, Canada

★ Wuhan Technical University of Surveying and Mapping (WTUSM), Wuhan, China

★ Department of Spatial Sciences, Curtin University of Technology, Perth, Australia

★ Faculty of Geodesy and Geoinformatics, University of Zagreb, Zagreb, Croatia

★ Department of Geodesy and Geoinformatics, University of Belgrade, Belgrade, Serbia

★ Faculty of Geoinformation Science & Engineering, Malaysian University of Technology, Johor Bahru, Malaysia

★ Department of Geomatic Engineering, University Of Melbourne, Australia

★ Escuela de Ingenieria Geodesica de La Universidad del Zulia'' (LUZ-INGENIERIA GEODESICA) at Maracaibo, Venezuela

★ Geodesy division, Middle East Technical University Ankara, Turkey

★ Department of Land Surveying and Geo-Informatics, LSGI, The Hong Kong Polytechnic University Hong Kong, SAR, China

★ Faculty Of Geomatics,Sabaragamuwa University Of Sri Lanka,Belihulloya Department of Surveying and Geodesy, Department of Photogrammetry,Cartography,Remotesensing and GIS

★ Faculty of Geoinformatics, The University of West Hungary Székesfehérvár, Hungary

★ Faculty of Civil and Geodetic Engineering, University of Ljubljana, Slovenia

★ Faculty of Geodesy and Cartography, Warsaw University of Technology, Warsaw, Poland

★ School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia

Governmental agencies

★ National Geodetic Survey (NGS) in Silver Spring MD, USA

★ National Geospatial-Intelligence Agency (NGA) in Bethesda MD, USA (Previously National Imagery and Mapping Agency NIMA, previously Defense Mapping Agency DMA)

★ U.S. Geological Survey (USGS) in Reston VA, USA

★ Institut Géographique National (IGN) in Saint-Mandé, France

★ Bundesamt für Kartographie und Geodäsie (BKG) In Frankfurt a.M., Germany (Previously Institut für Angewandte Geodäsie, IfAG)

★ ''Central Research Institute for Geodesy, Remote Sensing and Cartography'' (CNIIGAIK), Moscow, Russia

★ Geodetic Survey Division, Natural Resources Canada

★ Geoscience Australia, Australian Federal Agency

★ ''Finnish Geodetic Institute'' (FGI) at Masala, Finland

★ ''Portuguese Geographic Institute'' (IGEO) at Lisbon, Portugal

★ [1] Brazilian Institute for Geography and Statistics - IBGE

★ Spanish National Geographic Institute. IGN Madrid, Spain
''Note: This list is still largely incomplete.''

See also

★ IAG

★ ETRS89

★ GNSS

★ Important publications in geodesy

★ History of geodesy, Space techniques

★ World Geodetic System, WGS 84

★ Geodesic (in mathematics)

★ Geodesic (in physics)

Notes

1. H. Mowlana (2001). "Information in the Arab World", ''Cooperation South Journal'' '1'.
2. A. S. Ahmed (1984). "Al-Beruni: The First Anthropologist", ''RAIN'' '60', p. 9-10.

References

★ 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).

★ 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''.)

★
★ "Part I: Introduction" ''SaLIS'' Vol. 64, No. 4, pages 223-233, December 2004.

★
★ "Part II: Physics and gravity" ''SaLIS'' Vol. 65, No. 1, pages 5-15, March 2005.

★
★ "Part III: Height systems" ''SaLIS'' Vol. 66, No. 2, pages 149-160, June 2006.

★
★ "Part IV: GPS heighting" ''SaLIS'' Vol. 66, No. 3, pages 165-183, September 2006.

External links

★ International Association of Geodesy (IAG).

★ The Geodesy Page.

★ Welcome to Geodesy

★ MapRef.org: The Collection of Map Projections and Reference Systems for Europe

★ Geodesy on the World Wide Web

★ Pennsylvania Geospatial Data Sharing Standard - Geodesy and Geodetic Monumentation

★ References on Absolute Gravimeters

★ Geodesy tutorial at University of New Brunswick

★ Vincenty's Direct and Inverse Solutions of Geodesics on the Ellipsoid, in JavaScript

★ EarthScope Project

★ UNAVCO - EarthScope - Plate Boundary Observatory

★ [2]

★ Polish Internet Informant of Geodesy

★ Geodesy and Geomatics Home page of Ramin Kiamehr