WikiMili The Free Encyclopedia

This article has multiple issues. Please help improve it or discuss these issues on the talk page . (Learn how and when to remove these template messages)
(Learn how and when to remove this template message) |

Geodesy | ||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Fundamentals | ||||||||||||||||||||||||||

Concepts | ||||||||||||||||||||||||||

Standards (history)
| ||||||||||||||||||||||||||

**Geodesy** ( /dʒiːˈɒdɪsi/ )^{ [1] } is the Earth science of accurately measuring and understanding Earth's geometric shape, orientation in space and gravitational field.^{ [2] } The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as planetary geodesy). Geodynamical phenomena include crustal motion, tides and polar motion, which can be studied by designing global and national control networks, applying space and terrestrial techniques and relying on datums and coordinate systems.

**Earth science** or **geoscience** includes all fields of natural science related to the planet Earth. This is a branch of science dealing with the physical constitution of the Earth and its atmosphere. Earth science is the study of our planet's physical characteristics, from earthquakes to raindrops, and floods to fossils. Earth science can be considered to be a branch of planetary science, but with a much older history. Earth science encompasses four main branches of study, the lithosphere, the hydrosphere, the atmosphere, and the biosphere, each of which is further broken down into more specialized fields.

In physics, a **gravitational field** is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). In its original concept, gravity was a force between point masses. Following Isaac Newton, Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been taught in terms of a field model, rather than a point attraction.

A **planet** is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.

- Definition
- History
- Geoid and reference ellipsoid
- Coordinate systems in space
- Coordinate systems in the plane
- Heights
- Geodetic data
- Point positioning
- Geodetic problems
- Observational concepts
- Measurements
- Units and measures on the ellipsoid
- Temporal change
- Notable geodesists
- Mathematical geodesists before 1900
- 20th century geodesists
- Unlisted
- See also
- References
- Further reading
- External links

The word "geodesy" comes from the Ancient Greek word γεωδαισία*geodaisia* (literally, "division of Earth").

The **ancient Greek** language includes the forms of Greek used in Ancient Greece and the ancient world from around the 9th century BCE to the 6th century CE. It is often roughly divided into the Archaic period, Classical period, and Hellenistic period. It is antedated in the second millennium BCE by Mycenaean Greek and succeeded by Medieval Greek.

It is primarily concerned with positioning within the temporally varying gravity field. Geodesy in the German-speaking world is divided into "higher geodesy" ("*Erdmessung*" or "*höhere Geodäsie*"), which is concerned with measuring Earth on the global scale, and "practical geodesy" or "engineering geodesy" ("*Ingenieurgeodäsie*"), which is concerned with measuring specific parts or regions of Earth, and which includes surveying. Such geodetic operations are also applied to other astronomical bodies in the solar system. It is also the science of measuring and understanding Earth's geometric shape, orientation in space, and gravity field.

**Time** is the indefinite continued progress of existence and events that occur in an apparently irreversible succession from the past, through the present, to the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.

**German** is a West Germanic language that is mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, South Tyrol in Italy, the German-speaking Community of Belgium and Liechtenstein. It is one of the three official languages of Luxembourg and a co-official language in the Opole Voivodeship in Poland. The languages that are most similar to the German are the other members of the West Germanic language branch, including Afrikaans, Dutch, English, the Frisian languages, Low German/Low Saxon, Luxembourgish, and Yiddish. There are strong similarities in vocabulary with Danish, Norwegian and Swedish, although those belong to the North Germanic group. German is the second most widely spoken Germanic language, after English.

**Surveying** or **land surveying** is the technique, profession, art and science of determining the terrestrial or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a **land surveyor**. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as building corners or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.

To a large extent, the shape of Earth is the result of rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates and of volcanism, resisted by Earth's gravity field. This applies to the solid surface, the liquid surface (dynamic sea surface topography) and Earth's atmosphere. For this reason, the study of Earth's gravity field is called physical geodesy.

**Earth's rotation** is the rotation of Planet Earth around its own axis. Earth rotates eastward, in prograde motion. As viewed from the north pole star Polaris, Earth turns counterclockwise.

An **equatorial bulge** is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

**Continental collision** is a phenomenon of the plate tectonics of Earth that occurs at convergent boundaries. Continental collision is a variation on the fundamental process of subduction, whereby the subduction zone is destroyed, mountains produced, and two continents sutured together. Continental collision is known only to occur on Earth.

The geoid is essentially the figure of 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 and air pressure variations, and continued under the continental masses. The geoid, unlike the reference 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 the geoid and the reference ellipsoid is called the geoidal undulation. It varies globally between ±110 m, when referred to the GRS 80 ellipsoid.

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

An **ocean current** is a continuous, directed movement of sea water generated by a number of forces acting upon the water, including wind, the Coriolis effect, breaking waves, cabbeling, and temperature and salinity differences. Depth contours, shoreline configurations, and interactions with other currents influence a current's direction and strength. Ocean currents are primarily horizontal water movements.

**Atmospheric pressure**, sometimes also called **barometric pressure**, is the pressure within the atmosphere of Earth. The standard atmosphere is a unit of pressure defined as 1,013.25 mbar, equivalent to 760 mm Hg, 29.9212 inches Hg, or 14.696 psi. The atm unit is roughly equivalent to the mean sea-level atmospheric pressure on Earth, that is, the Earth's atmospheric pressure at sea level is approximately 1 atm.

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 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.

In geodesy, a **reference ellipsoid** is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined.

The 1980 Geodetic Reference System (GRS 80) 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 (GPS) and is thus also in widespread use outside the geodetic community. The numerous systems that countries have used to create maps and charts are becoming obsolete as countries increasingly move to global, geocentric reference systems using the GRS 80 reference ellipsoid.

The geoid is "realizable", meaning it can be consistently located on Earth by suitable simple measurements from physical objects like a tide gauge. The geoid can, therefore, be considered a real surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, therefore it is an abstract surface. The third primary surface of geodetic interest—the topographic surface of Earth—is a realizable surface.

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 Earth's (conventional or instantaneous) rotation axis.

Prior to the era of satellite geodesy, the coordinate systems associated with a geodetic datum attempted to be geocentric, but their origins differed from the geocenter by hundreds of meters, due to regional deviations in the direction of the plumbline (vertical). These regional geodetic data, such as ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927) have ellipsoids associated with them that are regional "best fits" to the geoids within their areas of validity, minimizing the deflections of the vertical over these areas.

It is only because GPS satellites orbit about the geocenter, 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 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 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 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*α*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 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 *α* and *s* 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. 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: 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.

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 data, it suffices to choose *one* datum point: the reference benchmark, typically a tide gauge at the shore. Thus we have vertical data like the NAP (Normaal Amsterdams Peil), the North American Vertical Datum 1988 (NAVD 88), 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 ED 50 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, so to make them refer to another datum, is called a *datum transformation*. In the case of vertical data, 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 called a "coordinate system" in ISO terminology, whereas the International Earth Rotation and Reference Systems Service (IERS) uses the term "reference system". When these coordinates are realized by choosing datum points and fixing a geodetic datum, ISO says "coordinate reference system", while IERS says "reference frame". The ISO term for a datum transformation again is a "coordinate transformation".^{ [3] }

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^{[ where? ]} 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 and are normally documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements.

In geometric geodesy, two standard problems exist—the first (direct or forward) and the second (inverse or reverse).

- First (direct or forward) 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.

- Second (inverse or reverse) geodetic problem

- Given two points, determine the azimuth and length of the line (straight line, arc or geodesic) that connects them.

In plane geometry (valid for small areas on Earth's surface), the solutions to both problems reduce to simple trigonometry. On a sphere, however, the solution is significantly more complex, because in the inverse problem the azimuths will differ between the two end points of the connecting great circle, arc.

On the ellipsoid of revolution, geodesics may be written in terms of elliptic integrals, which are usually evaluated in terms of a series expansion—see, for example, Vincenty's formulae. In the general case, the solution is called the geodesic for the surface considered. The differential equations for the geodesic can be solved numerically.

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.

**Plumbline**or**vertical**: the direction of local gravity, or the line that results by following it.**Zenith**: the point on the celestial sphere where the direction of the gravity vector in a point, extended upwards, intersects it. It is more correct to call it a**direction**rather than a point.**Nadir**: the opposite point—or rather, direction—where the direction of gravity extended downward intersects the (obscured) celestial sphere.**Celestial horizon**: a plane perpendicular to a point's gravity vector.**Azimuth**: the direction angle within the plane of the horizon, typically counted clockwise from the north (in geodesy and astronomy) or the south (in France).**Elevation**: the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90 degrees minus elevation.**Local topocentric coordinates**: azimuth (direction angle within the plane of the horizon), elevation angle (or zenith angle), distance.**North celestial pole**: the extension of Earth's (precessing and nutating) instantaneous spin axis extended northward to intersect the celestial sphere. (Similarly for the south celestial pole.)**Celestial equator**: the (instantaneous) intersection of Earth's equatorial plane with the celestial sphere.**Meridian plane**: any plane perpendicular to the celestial equator and containing the celestial poles.**Local meridian**: the plane containing the direction to the zenith and the direction to the celestial pole.

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 the 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 to even robotic 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. 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.

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 irregularities in Earth's rotation as well as plate tectonic motions.

Gravity is measured using gravimeters, of which there are two kinds. First, "absolute gravimeters" are based on measuring the acceleration of free fall (e.g., of a reflecting prism in a vacuum tube). They are used to establish the vertical geospatial control and can be used in the field. Second, "relative gravimeters" are spring-based and are more common. They are used in gravity surveys over large areas for establishing the figure of the geoid over these areas. The most accurate relative gravimeters are called "superconducting" gravimeters, which are sensitive to one-thousandth of one-billionth of Earth-surface gravity. Twenty-some superconducting gravimeters are used worldwide for studying Earth's tides, rotation, interior, and ocean and atmospheric loading, as well as for verifying the Newtonian constant of gravitation.

In the future, gravity and altitude, will be measured by relativistic time dilation measured by strontium optical clocks.

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 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 10-millionth part of the length from equator to North Pole along the meridian through Paris (the target was not quite reached in actual implementation, so that is off by 200 ppm 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 1,000/0.54 m to four digits).

In geodesy, temporal change can be studied by a variety of techniques. Points on Earth's surface change their location due to a variety of mechanisms:

- Continental plate motion, plate tectonics
- Episodic motion of tectonic origin, especially close to fault lines
- Periodic effects due to tides
- Postglacial land uplift due to isostatic adjustment
- Mass variations due to hydrological changes
- Anthropogenic movements such as reservoir construction or petroleum or water extraction

The science of studying deformations and motions of Earth's crust and its solidity as a whole is called geodynamics. Often, study of Earth's irregular rotation is also included in its definition.

Techniques for studying geodynamic phenomena on the global scale include:

- Satellite positioning by GPS
- Very-long-baseline interferometry (VLBI)
- Satellite and lunar laser ranging
- Regionally and locally precise levelling
- Precise tacheometers
- Monitoring of gravity change
- Interferometric synthetic aperture radar (InSAR) using satellite images

- Pythagoras 580–490 BC, ancient Greece
^{ [4] } - Eratosthenes 276–194 BC, ancient Greece
- Hipparchus c. 190–120 BC, ancient Greece
- Posidonius c. 135–51 BC, ancient Greece
- Claudius Ptolemy c. AD 83–168, Roman Empire (Roman Egypt)
- Al-Ma'mun 786–833, Baghdad (Iraq/Mesopotamia)
- Abu Rayhan Biruni 973–1048, Khorasan (Iran/Samanid Dynasty)
- Muhammad al-Idrisi 1100–1166, (Arabia & Sicily)
- Regiomontanus 1436–1476, (Germany/Austria)
- Abel Foullon 1513–1563 or 1565, (France)
- Pedro Nunes 1502–1578 (Portugal)
- Gerhard Mercator 1512–1594 (Belgium & Germany)
- Snellius (Willebrord Snel van Royen) 1580–1626, Leiden (Netherlands)
- Christiaan Huygens 1629–1695 (Netherlands)
- Pierre Bouguer 1698–1758, (France & Peru)
- Pierre de Maupertuis 1698–1759 (France)
- Alexis Clairaut 1713–1765 (France)
- Johann Heinrich Lambert 1728–1777 (France)
- Roger Joseph Boscovich 1711–1787, (Rome/ Berlin/ Paris)
- Ino Tadataka 1745–1818, (Tokyo)
- Georg von Reichenbach 1771–1826, Bavaria (Germany)
- Pierre-Simon Laplace 1749–1827, Paris (France)
- Adrien Marie Legendre 1752–1833, Paris (France)
- Johann Georg von Soldner 1776–1833, Munich (Germany)
- George Everest 1790–1866 (England and India)
- Friedrich Wilhelm Bessel 1784–1846, Königsberg (Germany)
- Heinrich Christian Schumacher 1780–1850 (Germany & Estonia)
- Carl Friedrich Gauss 1777–1855, Göttingen (Germany)
- Friedrich Georg Wilhelm Struve 1793–1864, Dorpat and Pulkovo (Russian Empire)
- J. H. Pratt 1809–1871, London (England)
- Friedrich H. C. Paschen 1804–1873, Schwerin (Germany)
- Johann Benedikt Listing 1808–1882 (Germany)
- Johann Jacob Baeyer 1794–1885, Berlin (Germany)
- Sir George Biddell Airy 1801–1892, Cambridge & London
- Karl Maximilian von Bauernfeind 1818–1894, Munich (Germany)
- Wilhelm Jordan 1842–1899, (Germany)
- Hervé Faye 1814–1902 (France)
- George Gabriel Stokes 1819–1903 (England)
- Carlos Ibáñez e Ibáñez de Ibero 1825–1891, Barcelona (Spain)
- Henri Poincaré 1854–1912, Paris (France)
- Alexander Ross Clarke 1828–1914, London (England)
- Charles Sanders Peirce 1839–1914 (United States)
- Friedrich Robert Helmert 1843–1917, Potsdam (Germany)
- Heinrich Bruns 1848–1919, Berlin (Germany)
- Loránd Eötvös 1848–1919 (Hungary)

- John Fillmore Hayford, 1868–1925, (US)
- Feodosy Nikolaevich Krasovsky, 1878–1948, (Russian Empire, USSR)
- Alfred Wegener, 1880–1930, (Germany and Greenland)
- William Bowie, 1872–1940, (US)
- Friedrich Hopfner, 1881–1949, Vienna, (Austria)
- Tadeusz Banachiewicz, 1882–1954, (Poland)
- Felix Andries Vening-Meinesz, 1887–1966, (Netherlands)
- Martin Hotine, 1898–1968, (England)
- Yrjö Väisälä, 1889–1971, (Finland)
- Veikko Aleksanteri Heiskanen, 1895–1971, (Finland and US)
- Karl Ramsayer, 1911–1982, Stuttgart, (Germany)
- Buckminster Fuller, 1895–1983 (United States)
- Harold Jeffreys, 1891–1989, London, (England)
- Reino Antero Hirvonen, 1908–1989, (Finland)
- Mikhail Sergeevich Molodenskii, 1909–1991, (Russia)
- Maria Ivanovna Yurkina, 1923-2010, (Russia)
- Guy Bomford, 1899–1996, (India?)
^{ [5] } - Antonio Marussi, 1908–1984, (Italy)
- Hellmut Schmid, 1914–1998, (Switzerland)
- William M. Kaula, 1926–2000, Los Angeles, (US)
- John A. O'Keefe, 1916–2000, (US)
- Thaddeus Vincenty, 1920–2002, (Poland)
- Willem Baarda, 1917–2005, (Netherlands)
- Irene Kaminka Fischer, 1907–2009, (US)
- Arne Bjerhammar, 1917–2011, (Sweden)
- Karl-Rudolf Koch 1935, Bonn, (Germany)
- Helmut Moritz, 1933, Graz, (Austria)
- Petr Vaníček, 1935, Fredericton, (Canada)
- Erik Grafarend, 1939, Stuttgart, (Germany)
- Hans-Georg Wenzel (1949–1999), (Germany)

- Fundamentals

- Governmental agencies

- U.S. National Geodetic Survey
- National Geospatial-Intelligence Agency
- United States Geological Survey

- International organizations

- International Association of Geodesy
- International Federation of Surveyors
- International Geodetic Student Organisation

- Other

In geography, **latitude** is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles. Lines of constant latitude, or *parallels*, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the *geodetic latitude* as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six *auxiliary latitudes* which are used in special applications.

A **geographic coordinate system** is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector. A common choice of coordinates is latitude, longitude and elevation. To specify a location on a plane requires a map projection.

**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.

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

**Figure of the Earth** is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. The sphere is an approximation of the figure of the Earth that is satisfactory for many purposes. Several models with greater accuracy have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.

The **vertical deflection** at a point on the Earth is a measure of how far the gravity direction has been shifted by local anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes.

A **geodetic datum** or **geodetic system** is a coordinate system, and a set of reference points, used to locate places on the Earth. An approximate definition of sea level is the datum WGS 84, an ellipsoid, whereas a more accurate definition is Earth Gravitational Model 2008 (EGM2008), using at least 2,159 spherical harmonics. Other datums are defined for other areas or at other times; ED50 was defined in 1950 over Europe and differs from WGS 84 by a few hundred meters depending on where in Europe you look. Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there.

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

The **orthometric height** of a point is the distance H along a plumb line from the point to a reference height. When the reference height is a geoid model, orthometric height is for practical purposes "height above sea level".

**Mikhail Sergeevich Molodenskii** was a famous Soviet physical geodesist. He was once said to be "probably the only geodesist who would have deserved a Nobel prize"

**ECEF**, also known as **ECR**, is a geographic and Cartesian coordinate system and is sometimes known as a "conventional terrestrial" system. It represents positions as X, Y, and Z coordinates. The point is defined as the center of mass of Earth, hence the term **geocentric coordinates**. The distance from a given point of interest to the center of Earth is called the **geocentric radius** or **geocentric distance**.

The **North American Vertical Datum of 1988** is the vertical datum for orthometric heights established for vertical control surveying in the United States of America based upon the General Adjustment of the North American Datum of 1988.

The **Helmert transformation** is a transformation method within a three-dimensional space. It is frequently used in geodesy to produce distortion-free transformations from one datum to another. The Helmert transformation is also called a **seven-parameter transformation** and is a similarity transformation.

The **Bessel ellipsoid** is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.

An **Earth ellipsoid** is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.

The term **fundamental station** is used for special observatories which combine several space positioning techniques like VLBI, satellite laser ranging, GPS, Glonass, etc. They are the basis of plate tectonic analysis, allowing the monitoring of continental drift rates with milimetre accuracies. A **fundamental point** is the geometric origin of a geodetic network and defines the geodetic datum of a national survey.

A **vertical datum** or **height datum** is a reference surface for vertical positions, such as the elevations of Earth features including terrain, bathymetry, water level, and man-made structures. Vertical datums are either: tidal, based on sea levels; gravimetric, based on a geoid; or geodetic, based on the same ellipsoid models of the Earth used for computing horizontal datums.

*Normalhöhennull* or

- ↑ "geodesy | Definition of geodesy in English by Lexico Dictionaries".
*Lexico Dictionaries | English*. Retrieved 2019-08-15. - ↑ "What Is Geodesy".
*National Ocean Service*. Retrieved 8 February 2018. - ↑ (ISO 19111: Spatial referencing by coordinates).
- ↑ "DEFENSE MAPPING AGENCY TECHNICAL REPORT 80-003".
*Ngs.noaa.gov*. Retrieved 8 December 2018. - ↑ "Guy Bomford tribute".
*Bomford.net*. Retrieved 8 December 2018.

- F. R. Helmert,
*Mathematical and Physical Theories of Higher Geodesy*, Part 1, ACIC (St. Louis, 1964). This is an English translation of*Die mathematischen und physikalischen Theorieen der höheren Geodäsie*, Vol 1 (Teubner, Leipzig, 1880). - F. R. Helmert,
*Mathematical and Physical Theories of Higher Geodesy*, Part 2, ACIC (St. Louis, 1964). This is an English translation of*Die mathematischen und physikalischen Theorieen der höheren Geodäsie*, Vol 2 (Teubner, Leipzig, 1884). - 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). - W. Kaula,
*Theory of Satellite Geodesy : Applications of Satellites to Geodesy*, Dover Publications, 2000. (This text is a reprint of the 1966 classic). - Vaníček P. and E.J. Krakiwsky,
*Geodesy: the Concepts*, pp. 714, Elsevier, 1986. - Torge, W (2001),
*Geodesy*(3rd edition), published by de Gruyter, ISBN 3-11-017072-8. - 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.

- "Part I: Introduction"

- Geodetic awareness guidance note, Geodesy Subcommittee, Geomatics Committee, International Association of Oil & Gas Producers
*Encyclopædia Britannica*.**11**(11th ed.). 1911. pp. 607–615. .

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.