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Encyclopedia > Geodesy
An old geodetic pillar (1855) at Ostend, Belgium
A Munich archive with lithography plates of maps of Bavaria

Geodesy (from Greek Γεωδαισία 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 surveying. Look up time in Wiktionary, the free dictionary. ... Surveyor at work with a leveling instrument. ...

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 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 called physical geodesy by some. Cleveland Volcano in the Aleutian Islands of Alaska photographed from the International Space Station For other uses, see Volcano (disambiguation). ... Gravity is a force of attraction that acts between bodies that have mass. ... Dynamic sea surface topography is the average difference between the actual surface of the Earth and a geoid. ... Air redirects here. ... The gravity field is the field of force, caused by the gravitation of the Earth, and influenced by the Earth rotation, the atmosphere and by geological bodies. ... Definition Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy. ...

## History

Main article: History of geodesy

Man has always been interested in the Earth on which he lives. ...

## Geoid and reference ellipsoid

The geoid is essentially the figure of the Earth abstracted from its topographical 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 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 undulation. It varies globally between ±110 m. The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...

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 = (ab)/a, where b is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the Earth (dynamical flattening, symbol J2) 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. In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. ...

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. Definition GRS 80, or Geodetic Reference System 1980, is a geodetic reference system consisting of a global reference ellipsoid and a gravity field model. ... The International Union of Geodesy and Geophysics, or IUGG, is a non-governmental organisation dedicated to the scientific study of the Earth and to the application of the knowledge gained to the needs of society that was established in 1919. ...

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. Fig. ...

Prior to satellite geodesy era, 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. Satellite geodesy is the measurement of the form and dimensions of the Earth, the location of objects on its surface and the figure of the Earths gravity field by means of satellite techniques. ... It has been suggested that this article or section be merged with Geodetic system. ... The geocentric model (in Greek: geo = earth and centron = centre) of the universe is a paradigm which places the Earth at its center. ... Vertical of an alpine point: note its curvature. ... ED 50 (European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of geodetic networks. ... The North American Datum is the official reference ellipsoid used for the primary geodetic network in North America. ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ...

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. GPS redirects here. ...

Geocentric coordinate systems used in geodesy can be divided naturally into two classes:

1. 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
2. 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 closely monitored by geodesists. In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... A fixed star is a celestial object that does not seem to move (in comparison to the other stars of the night sky). ... A gyroscope is a device which demonstrates the principle of conservation of angular momentum, in physics. ... Illumination of Earth by Sun on the day of equinox The vernal equinox (or spring equinox) marks the beginning of astronomical spring. ... The Prime Meridian, Greenwich The Prime Meridian is the meridian (line of longitude) passing through the Royal Greenwich Observatory, Greenwich, England; it is the meridian at which longitude is 0 degrees. ... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... Sidereal time is time measured by the apparent diurnal motion of the vernal equinox, which is very close to, but not identical with, the motion of stars. ... Look up day in Wiktionary, the free dictionary. ... This article needs to be wikified. ...

### 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: Surveyor at work with a leveling instrument. ... The word mapping has several senses: In mathematics and related technical fields, it is some kind of function: see map (mathematics). ...

1. 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 α with respect to a base line or axis;
2. 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. The Mercator projection shows courses of constant bearing as straight lines. ... In mathematics, a conformal map is a function which preserves angles. ...

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. A transverse Mercator projection is a map projection similar to the Mercator projection in that it is a projection of Earth on a tangent cylinder by rays radial with respect to the cylinder. ...

It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be α and s respectively, then we have

$begin{matrix} x &=& s cos alpha y &=& s sin alpha end{matrix}$

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 for regional considerations.[specify] Height is the measurement of distance between a specified point and a corresponding plane of reference. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ...

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. The orthometric height is the distance H along a line of force from a given point P at the physical surface of an object to the geoid. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Geopotential height is a vertical coordinate referenced to Earths mean sea level â€” an adjustment to geometric height (elevation above mean sea level) using the variation of gravity with latitude and elevation. ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ...

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. In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ...

## Geodetic data

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. Normaal Amsterdams Peil (NAP) or Amsterdam Ordnance Datum is a vertical datum in use in large parts of Western Europe. ...

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. ED 50 (European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of geodetic networks. ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ... Potsdam is the capital city of the federal state of Brandenburg in Germany. ...

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 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. â€œISOâ€ redirects here. ... The International Earth Rotation Service (IERS) is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Paramater (EOP) and International Celestial Reference System (ICRS) groups. ...

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. Triangulation can be used to find the distance from the shore to the ship. ... GPS redirects here. ...

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. In fortification, a traverse is a mass of earth or other material employed to protect troops against enfilade. ... A polygon (from the Greek poly, for many, and gonos, for angle) is a closed planar path composed of a finite number of sequential straight line segments. ...

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. GPS redirects here. ... The International Earth Rotation Service (IERS) is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Paramater (EOP) and International Celestial Reference System (ICRS) groups. ...

For surveying mappings, frequently Real Time Kinematic GPS is employed, tying in the unknown points with known terrestrial points close by in real time. Surveyor at work with a leveling instrument. ... Real Time Kinematic (RTK) land survey is based on a differential use of carrier phase measurements of the GPS, Glonass and/or Galileo signals where a single reference station provides the real-time corrections of even to a centimetre level of accuracy. ...

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.

## Geodetic problems

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.

Azimuth is the horizontal component of a direction (compass direction), measured around the horizon, from the north toward the east (i. ...

### Second (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. Wikibooks has a book on the topic of Trigonometry All of the trigonometric functions of an angle Î¸ can be constructed geometrically in terms of a unit circle centered at O. Trigonometry (from Greek trigÅnon triangle + metron measure[1]), informally called trig, is a branch of mathematics that deals with... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the...

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. In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... Visualization of airflow into a duct modelled using the Navier-Stokes equations, a set of partial differential equations. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... Not to be confused with Matlab Upazila in Chandpur District, Bangladesh. ...

## 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 <direction> 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.

Vertical of an alpine point: note its curvature. ... In broad terms, the zenith is the direction pointing directly above a particular location (perpendicular, orthogonal). ... The celestial sphere is divided by the celestial equator. ... For other uses, see Nadir (disambiguation). ... Azimuth is the horizontal component of a direction (compass direction), measured around the horizon, from the north toward the east (i. ... Elevation histogram of the surface of the Earth â€“ approximately 71% of the Earths surface is covered with water. ... The two celestial poles are the imaginary points where the Earths spin axis intersects the imaginary rotating sphere of gigantic radius, called the celestial sphere. ... Precession redirects here. ... Rotation (green), Precession (blue) and Nutation (red) of the Earth Nutation is a slight irregular motion (etymologically a nodding) in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet. ... On the earth, a meridian is a north-south line between the North Pole and the South 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. Look up level in Wiktionary, the free dictionary. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... A spirit level A spirit level or bubble level is an instrument designed to indicate whether a surface is level or plumb. ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ... Definition GRS 80, or Geodetic Reference System 1980, is a geodetic reference system consisting of a global reference ellipsoid and a gravity field model. ...

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 to even robotic in its operations. The method of free station position is widely used. An optical theodolite, manufactured in the Soviet Union in 1958 and used for topographic surveying. ... The tacheometer or tachymeter is a kind of theodolite used for rapid measurments and determines, electronically or electro-optically, the distance to target, and is highly automated in its operations. ...

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) database. GIS redirects here. ... This article is about computing. ...

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 redirects here. ... The geocentric model (in Greek: geo = earth and centron = centre) of the universe is a paradigm which places the Earth at its center. ... WGS 84 is the 1984 revision of the World Geodetic System. ... The International Earth Rotation Service (IERS) is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Paramater (EOP) and International Celestial Reference System (ICRS) groups. ...

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. In satellite laser ranging (SLR) a global network of observation stations measure the round trip time of flight of ultrashort pulses of light to satellites equipped with retroreflectors. ... The Lunar Laser Ranging Experiment from the Apollo 11 mission The ongoing Lunar Laser Ranging Experiment was first made possible by a lunar laser ranging retroreflector array planted on the Moon on July 21, 1969, by the crew of the Apollo 11. ... Very Long Baseline Interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy, in which the data received at each antenna in the array is paired with timing information, usually from a local atomic clock, and then stored for later analysis on magnetic tape or hard disk. ...

## 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. This article is about the geographical term. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. ...

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).

## 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, for instance, petroleum or 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. The tectonic plates of the world were mapped in the second half of the 20th century. ... A glaciation (a created composite term meaning Glacial Period, referring to the Period or Era of, as well as the process of High Glacial Activity), often called an ice age, is a geological phenomenon in which massive ice sheets form in the Arctic and Antarctic and advance toward the equator. ... Petro redirects here. ... An Australian based componey that produces Geothermal Power uning Hot Dry Rocks (HDR) It is supported by the Australian goverment Geodynamics Category: ...

Techniques for studying geodynamic phenomena on the global scale include:

GPS redirects here. ... Very Long Baseline Interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy, in which the data received at each antenna in the array is paired with timing information, usually from a local atomic clock, and then stored for later analysis on magnetic tape or hard disk. ... Lidar (light detection and ranging) is a technology that determines distance to an object or surface using laser pulses. ... For the town in Russia, see Insar. ...

## 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: For the community in Florida, see University, Florida. ... An institute is a permanent organizational body created for a certain purpose. ...

• Facultatea de Geodezie, Universitatea Tehnica de Constructii Bucuresti, Romania
• Surveying & Geomatics Engineering, Palestine Polytechic University, Hebron , Palestine.
• Department of Geodesy and Geomatic Engineering, Institut Teknologi Bandung, Indonesia
• Department of Geodesy and Geomatic Engineering, Gadjah Mada University, Yogyakarta, Indonesia
• Department of Geomatic Engineering, University College London, United Kingdom
• Institut für Erdmessung, Hannover, Germany
• Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden
• Institut für Theoretische Geodäsie, Bonn, Germany
• Institut für Astronomische und Physikalische Geodäsie, Munich, Germany
• Austrian Institute for Geodesy and Geophysics, TU Vienna, Austria
• Swiss Geodetic Institute, the ETH, Zurich, Switzerland
• Moscow State University of Geodesy and Cartography (MIIGAiK), Russia
• Civil Engineering and Geodesy, Ohio State University, Columbus OH, USA
• Department of 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, 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
• 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, Maracaibo, Venezuela
• Geodesy division, Middle East Technical University, Ankara, Turkey
• Department of Land Surveying and Geo-Informatics, (LSGI), Hong Kong Polytechnic University, Hong Kong, SAR, China
• Department of Surveying and Geodesy, Department of Photogrammetry, Cartography, Remote sensing and GIS, Faculty Of Geomatics, Sabaragamuwa University Of Sri Lanka, Belihulloya, Sri Lanka
• Faculty of Geoinformatics, 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
• School of Surveying, University of Otago, Dunedin, New Zealand
• School of Rural and Surveying Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
• School of Civil Engineering and Geosciences, Newcastle University, Newcastle, England

The Royal Institute of Technology or Kungliga tekniska hÃ¶gskolan (KTH) is a university in Stockholm, Sweden. ... The ETH Zurich, often called Swiss Federal Institute of Technology, is a science and technology university in the city of Zurich, Switzerland. ...

## Governmental agencies

• National Geodetic Survey (NGS), Silver Spring MD, USA
• National Geospatial-Intelligence Agency (NGA), Bethesda MD, USA (Previously National Imagery and Mapping Agency NIMA, previously Defense Mapping Agency DMA)
• U.S. Geological Survey (USGS), Reston VA, USA
• Institut Géographique National (IGN), Saint-Mandé, France
• 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
• Geoscience Australia, Australian Federal Agency
• Finnish Geodetic Institute (FGI), Masala, Finland
• Portuguese Geographic Institute (IGEO), Lisbon, Portugal
• Brazilian Institute for Geography and Statistics - IBGE
• Spanish National Geographic Institute (IGN), Madrid, Spain
• Land Information New Zealand.

Note: This list is still largely incomplete. NGS could stand for: the National Garden Scheme a British organisation which promotes the opening of private gardens for charity. ... The National Geospatial-Intelligence Agency (NGA) is an agency of the United States Government with the primary mission of collection, analysis, and distribution of geospatial intelligence (GEOINT) in support of national security. ... The United States Geological Survey (USGS) is a scientific agency of the United States government. ...

Geodesy

Image File history File links Wikibooks-logo-en. ... Survey equipment used in geomatics Geomatics is the discipline of gathering, storing, processing, and delivering of geographic information, or spatially referenced information. ... Definition Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy. ... â€¹ The template below has been proposed for deletion. ... Surveyor at work with a leveling instrument. ... IAG may mean: International Adventure Group, A select group of individuals dedicated to international adventures Louvain School of Management - Institut dAdministration et de Gestion idiopathic adolescent gynecomastia Iraqi Assistance Group, (IAG) Investment Analysis Group at the Leonard N. Stern School of Business, New York University International Association of Geodesy... The European Terrestrial Reference System 1989 is a three-dimensional gedoesic frame of reference. ... GNSS - Global Navigation Satellite System In 1994 in a meeting of the ECAC, a satellite strategy was approved, with as targets: - firstly developing items for an European supplement on the current satellite systems, now called GNSS-1 - secondly designing and defining future satellite systems for civil use (called GNSS-2... // Foundations Principles of Geology Author: Charles Lyell Publication data: 1830â€“1833. ... Man has always been interested in the Earth on which he lives. ... In Geodesy, the term Space techniques includes modern measuring methods which make use of artificial satellites, interplanetary space probes and of quasars. ... The World Geodetic System defines a reference frame for the earth, for use in geodesy and navigation. ... WGS 84 is the 1984 revision of the World Geodetic System. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... In physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force. ...

## Notes

1. ^ OED
2. ^ Vaníček P., Krakiwsky E.J. Geodesy: the Concepts, pp.714, Elsevier (1986)
3. ^ H. Mowlana (2001). "Information in the Arab World", Cooperation South Journal 1.
4. ^ 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).
• 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.)
• "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.

Results from FactBites:

 Geodesy Page by James Q. Jacobs (2057 words) Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG). When an ellipsoid of revolution (semi-major axis a, semi-minor axis b) is defined, it can be made an equipotential surface of normal gravity potential, determined by means of the ellipsoidal surface, the enclosed mass and the angular velocity (independently of the internal density distribution).
 International Association of Geodesy (643 words) The Geodetic Journey is an outreach activity that claims to promote the field of geodesy to the general public by making journeys that focus on geodesy both today and it´s history particularly in the region where the journey take place. The International Association of Geodesy (IAG) is informing all concerned scientists and research Institutes that the post of Director of the International Centre for Earth Tides (ICET) will become vacant on January first 2008. This information is provided by the Communication and Outreach Branch of the International Association of Geodesy, which is hosted by the Department of Geodesy and Surveying of the Budapest University of Technology and Economics, and the Physical Geodesy and Geodynamics Research Group of the Hungarian Academy of Sciences.
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