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Geodesy ( ) is the
Earth science 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, chemical, and biological complex constitutions and synergistic linkages of Earth's four spher ...
of accurately measuring and understanding Earth's figure (
geometric shape A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type. A plane shape or plane figure is constrained to lie ...
and size), orientation in space, and
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
. The field also incorporates studies of how these properties change over time and equivalent measurements for other
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
s (known as '' planetary geodesy''). Geodynamical phenomena, including crustal motion,
tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can ...
s and
polar motion Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called ''Earth-centered, Earth-fixed'' or ECEF reference ...
, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques and relying on datums and coordinate systems. The job title is geodesist or geodetic surveyor.


History


Definition

The word geodesy comes from the
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic p ...
word ''geodaisia'' (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying gravitational field. Geodesy in the
German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...
-speaking world is divided into "higher geodesy" ( or ), which is concerned with measuring Earth on the global scale, and "practical geodesy" or "engineering geodesy" (), which is concerned with measuring specific parts or regions of Earth, and which includes
surveying Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...
. Such geodetic operations are also applied to other astronomical bodies in the
Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
. It is also the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field. To a large extent, the shape of Earth is the result of
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
, which causes its
equatorial bulge 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. On Ear ...
, and the competition of geological processes such as the collision of plates and of
volcanism Volcanism, vulcanism or volcanicity is the phenomenon of eruption of molten rock (magma) onto the Earth#Surface, surface of the Earth or a solid-surface planet or moon, where lava, pyroclastics, and volcanic gases erupt through a break in the su ...
, resisted by Earth's gravitational field. This applies to the solid surface, the liquid surface ( dynamic sea surface topography) and
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
. For this reason, the study of Earth's gravitational field is called physical geodesy.


Geoid and reference ellipsoid

The
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exten ...
is essentially the figure of Earth abstracted from its
topographical Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary scie ...
features. It is an idealized equilibrium surface of
sea water Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has appro ...
, the
mean sea level There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ari ...
surface in the absence of currents and
air pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, ...
variations, and continued under the continental masses. The geoid, unlike the
reference ellipsoid An Earth ellipsoid or Earth spheroid 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 approximatio ...
, 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. 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'' = , 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. 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 A tide gauge is a device for measuring the change in sea level relative to a vertical datum. It its also known as mareograph, marigraph, sea-level recorder and limnimeter. When applied to freshwater continental water bodies, the instrument m ...
. 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.


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 In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
: the ''Z''-axis is aligned with Earth's (conventional or instantaneous) rotation axis. Prior to the era of
satellite geodesy Satellite geodesy is geodesy by means of artificial satellites—the measurement of the form and dimensions of Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniqu ...
, the coordinate systems associated with a geodetic datum attempted to be
geocentric In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
, but their origins differed from the geocenter by hundreds of meters, due to regional deviations in the direction of the
plumbline A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is a precursor to the spirit level and used to establish a verti ...
(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
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exten ...
s 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 In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
reference systems, where the coordinate axes retain their orientation relative to the fixed stars, or equivalently, to the rotation axes of ideal
gyroscopes A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotat ...
; the ''X''-axis points to the
vernal equinox Spring equinox or vernal equinox or variations may refer to: * March equinox, the spring equinox in the Northern Hemisphere * September equinox, the spring equinox in the Southern Hemisphere Other uses * Nowruz, Persian/Iranian new year which be ...
# 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 Greenwich ( , ,) is a town in south-east London, England, within the ceremonial county of Greater London. It is situated east-southeast of Charing Cross. Greenwich is notable for its maritime history and for giving its name to the Greenwic ...
observatory's
meridian Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...
plane. The coordinate transformation between these two systems is described to good approximation by (apparent)
sidereal time Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coor ...
, which takes into account variations in Earth's axial rotation ( length-of-day variations). A more accurate description also takes
polar motion Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called ''Earth-centered, Earth-fixed'' or ECEF reference ...
into account, a phenomenon closely monitored by geodesists.


Coordinate systems in the plane

In
surveying Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...
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 In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...
. It is impossible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen—called a
conformal projection In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in ...
—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 The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, which mean ...
). 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 :\begin x &= s \cos \alpha\\ y &= s \sin \alpha \end The reverse transformation is given by: :\begin s &= \sqrt\\ \alpha &= \arctan\frac. \end


Heights

In geodesy, point or terrain ''
height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is ab ...
s'' are "
above sea level Height above mean sea level is a measure of the vertical distance (height, elevation or altitude) of a location in reference to a historic mean sea level taken as a vertical datum. In geodesy, it is formalized as '' orthometric heights''. The ...
", an irregular, physically defined surface. Heights come in the following variants: #
Orthometric height The orthometric height is the vertical distance ''H'' along the plumb line from a point of interest to a reference surface known as the ''geoid'', the vertical datum that approximates mean sea level. Orthometric height is one of the scientific f ...
s # Dynamic heights #
Geopotential height Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level, an adjustment to geometric height (altitude above mean sea level) that accounts for the variation of gravity with latitude and altitude. Thu ...
s #
Normal height Normal heights is a type of height above sea level introduced by Mikhail Molodenskii. The normal height H^* (or H^N) of a point is computed as the ratio of a point's geopotential number (i.e. its geopotential difference with that of sea level), by ...
s 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. The reference surface is the
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exten ...
, an equipotential surface approximating mean sea level. (For normal heights, the reference surface is actually the so-called quasi-geoid, which has a few metre separation from the geoid, because of the density assumption in its continuation under the continental masses.) These heights can be related to '' ellipsoidal height'' (also known as ''geodetic height''), which express the height of a point above the
reference ellipsoid An Earth ellipsoid or Earth spheroid 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 approximatio ...
, by means of the
geoid undulation The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exten ...
.
Satellite positioning receiver A satellite navigation device (satnav device) is a user equipment that uses one or more of several global navigation satellite systems (GNSS) to calculate the device's geographical position and provide navigational advice. Depending on the s ...
s 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, 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 Amsterdam Ordnance Datum or ' (NAP) is a vertical datum in use in large parts of Western Europe. Originally created for use in the Netherlands, its height was used by Prussia in 1879 for defining ', and in 1955 by other European countries. In ...
), 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 Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of B ...
. 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 The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917) is a geometric transformation method within a three-dimensional space. It is frequently used in geodesy to produce datum transformations between datums. The H ...
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 The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation P ...
(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".


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 In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle ...
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 The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Pa ...
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 Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...
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.


Geodetic problems

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 An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...
) and
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
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 In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
) that connects them. In plane geometry (valid for small areas on Earth's surface), the solutions to both problems reduce to simple
trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
. 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 In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry ...
, 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 Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth i ...
. In the general case, the solution is called the
geodesic In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
for the surface considered. The
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...
s for the
geodesic In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
can be solved numerically.


Observational concepts

Here we define some basic observational concepts, like angles and coordinates, defined in geodesy (and
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
as well), mostly from the viewpoint of the local observer. *
Plumbline A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is a precursor to the spirit level and used to establish a verti ...
or vertical: the direction of local gravity, or the line that results by following it. *
Zenith The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction ( plumb line) opposite to the gravity direction at that location ( nadir). The zenith is the "high ...
: the point on the
celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of 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 nadir (, ; ar, نظير, naẓīr, counterpart) is the direction pointing directly ''below'' a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface. The direc ...
: 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 An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...
: 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 elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § ...
: 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 north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers a ...
: the extension of Earth's (
precessing Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
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 Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...
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.


Measurements

The level is used for determining height differences and height reference systems, commonly referred to
mean sea level There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ari ...
. The traditional
spirit level A spirit level, bubble level, or simply a level, is an instrument designed to indicate whether a surface is horizontal (level) or vertical ( plumb). Different types of spirit levels may be used by carpenters, stonemasons, bricklayers, oth ...
produces these practically most useful heights above
sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardise ...
directly; the more economical use of GPS instruments for height determination requires precise knowledge of the figure of the
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exten ...
, 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 A theodolite () is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and ...
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 Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure ...
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 A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a ...
(GIS) database. Geodetic GPS receivers produce directly three-dimensional coordinates in a
geocentric In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
coordinate frame. Such a frame is, e.g.,
WGS84 The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also desc ...
, or the frames that are regularly produced and published by the International Earth Rotation and Reference Systems Service (
IERS The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Pa ...
). 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 In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
is measured using gravimeters, of which there are two kinds. First, "absolute gravimeters" are based on measuring the acceleration of
free fall In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on i ...
(e.g., of a reflecting prism in a
vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
). 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
tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can ...
s,
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
, interior, and
ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wo ...
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 In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
measured by optical clocks.


Units and measures on the ellipsoid

Geographical
latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north po ...
and
longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...
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 An Earth ellipsoid or Earth spheroid 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 approximatio ...
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 A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of territorial waters. Historically, it was defined as the meridian arc length corresponding to one minute ( of a degree) of latitude. Today t ...
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).


Temporal change

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 Plate tectonics (from the la, label= Late Latin, tectonicus, from the grc, τεκτονικός, lit=pertaining to building) is the generally accepted scientific theory that considers the Earth's lithosphere to comprise a number of large t ...
* Episodic motion of tectonic origin, especially close to
fault line In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant displacement as a result of rock-mass movements. Large faults within Earth's crust result from the action of plate tectonic ...
s * Periodic effects due to tides and tidal loading *
Postglacial The Holocene ( ) is the current geological epoch. It began approximately 11,650 cal years Before Present (), after the Last Glacial Period, which concluded with the Holocene glacial retreat. The Holocene and the preceding Pleistocene together ...
land uplift due to isostatic adjustment * Mass variations due to hydrological changes, including the atmosphere, cryosphere, land hydrology and oceans * Sub-daily polar motion * Length-of-day variability * Earth's center-of-mass (geocenter) variations * Anthropogenic movements such as reservoir construction or
petroleum Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crude ...
or water extraction The science of studying deformations and motions of Earth's crust and its solidity as a whole is called
geodynamics Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, ...
. Often, study of Earth's irregular rotation is also included in its definition. The
geodynamics Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, ...
studies require terrestrial reference frames that are realized by the stations belonging to the Global Geodedetic Observing System (GGOS). Techniques for studying geodynamic phenomena on the global scale include: * Satellite positioning by GPS,
GLONASS GLONASS (russian: ГЛОНАСС, label=none, ; rus, links=no, Глобальная навигационная спутниковая система, r=Global'naya Navigatsionnaya Sputnikovaya Sistema, t=Global Navigation Satellite System) is ...
, Galileo, and
BeiDou The BeiDou Navigation Satellite System (BDS; ) is a Chinese satellite navigation system. It consists of two separate satellite constellations. The first BeiDou system, officially called the BeiDou Satellite Navigation Experimental System and ...
* Very-long-baseline interferometry (VLBI) * Satellite laser ranging (SLR) and lunar
laser ranging A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...
(LLR) * DORIS * Regionally and locally precise levelling * Precise tacheometers * Monitoring of gravity change using land, airborne, shipborne, and spaceborne
gravimetry Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. Units of measurement Gr ...
* Satellite
altimetry An altimeter or an altitude meter is an instrument used to measure the altitude of an object above a fixed level. The measurement of altitude is called altimetry, which is related to the term bathymetry, the measurement of depth under water. The m ...
based on microwave and laser observations for studying the ocean surface, sea level rise, and ice cover monitoring * Interferometric synthetic aperture radar (InSAR) using satellite images


Notable geodesists


Geodesists before 1900 (arranged by date)

*
Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His politic ...
580–490 BC,
ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...
*
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexand ...
276–194 BC, ancient Greece *
Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equ ...
190–120 BC, ancient Greece *
Posidonius Posidonius (; grc-gre, wikt:Ποσειδώνιος, Ποσειδώνιος , "of Poseidon") "of Apamea (Syria), Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (), was a Greeks, Greek politician, astronomer, astrologer, geog ...
135–51 BC, ancient Greece *
Claudius Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importan ...
AD 83–168,
Roman Empire The Roman Empire ( la, Imperium Romanum ; grc-gre, Βασιλεία τῶν Ῥωμαίων, Basileía tôn Rhōmaíōn) was the post- Republican period of ancient Rome. As a polity, it included large territorial holdings around the Medite ...
( Roman Egypt) *
Al-Ma'mun Abu al-Abbas Abdallah ibn Harun al-Rashid ( ar, أبو العباس عبد الله بن هارون الرشيد, Abū al-ʿAbbās ʿAbd Allāh ibn Hārūn ar-Rashīd; 14 September 786 – 9 August 833), better known by his regnal name Al-Ma'm ...
786–833,
Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesipho ...
(Iraq/
Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the F ...
) *
Abu Rayhan Biruni Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 – after 1050) commonly known as al-Biruni, was a Khwarazmian Iranian in scholar and polymath during the Islamic Golden Age. He has been called variously the "founder of Indology", "Father of Co ...
973–1048, Khorasan (
Iran Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkm ...
/
Samanid Dynasty The Samanid Empire ( fa, سامانیان, Sāmāniyān) also known as the Samanian Empire, Samanid dynasty, Samanid amirate, or simply as the Samanids) was a Persianate Sunni Muslim empire, of Iranian dehqan origin. The empire was centred in K ...
) *
Muhammad al-Idrisi Abu Abdullah Muhammad al-Idrisi al-Qurtubi al-Hasani as-Sabti, or simply al-Idrisi ( ar, أبو عبد الله محمد الإدريسي القرطبي الحسني السبتي; la, Dreses; 1100 – 1165), was a Islamic geography, Muslim geo ...
1100–1166, (
Arabia The Arabian Peninsula, (; ar, شِبْهُ الْجَزِيرَةِ الْعَرَبِيَّة, , "Arabian Peninsula" or , , "Island of the Arabs") or Arabia, is a peninsula of Western Asia, situated northeast of Africa on the Arabian Plate. ...
& Sicily) *
Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental ...
1436–1476, (Germany/Austria) * Abel Foullon 1513–1563 or 1565, (France) *
Pedro Nunes Pedro Nunes (; Latin: ''Petrus Nonius''; 1502 – 11 August 1578) was a Portuguese mathematician, cosmographer, and professor, from a New Christian (of Jewish origin) family. Considered one of the greatest mathematicians of his time, Nu ...
1502–1578 (Portugal) * Gerhard Mercator 1512–1594 (Belgium & Germany) * Snellius (Willebrord Snel van Royen) 1580–1626,
Leiden Leiden (; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 119,713, but the city forms one densely connected agglomeration wit ...
(Netherlands) *
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists ...
1629–1695 (Netherlands) *
Pierre Bouguer Pierre Bouguer () (16 February 1698, Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture". Career Bouguer's father, Jean Bouguer, one ...
1698–1758, (France & Peru) * Pierre de Maupertuis 1698–1759 (France) *
Alexis Clairaut Alexis Claude Clairaut (; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had out ...
1713–1765 (France) *
Johann Heinrich Lambert Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made important contributions to the subjec ...
1728–1777 (France) * Roger Joseph Boscovich 1711–1787, (
Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus ( legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...
/
Berlin Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...
/
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...
) * Ino Tadataka 1745–1818, (
Tokyo Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and List of cities in Japan, largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, ...
) * Georg von Reichenbach 1771–1826,
Bavaria Bavaria ( ; ), officially the Free State of Bavaria (german: Freistaat Bayern, link=no ), is a state in the south-east of Germany. With an area of , Bavaria is the largest German state by land area, comprising roughly a fifth of the total l ...
(Germany) *
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
1749–1827,
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...
(France) *
Adrien Marie Legendre Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named ...
1752–1833,
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...
(France) * Johann Georg von Soldner 1776–1833,
Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and Ha ...
(Germany) *
George Everest Colonel Sir George Everest CB FRS FRAS FRGS (; 4 July 1790 – 1 December 1866) was a British surveyor and geographer who served as Surveyor General of India from 1830 to 1843. After receiving a military education in Marlow, Everest joined ...
1790–1866 (England and India) * Friedrich Wilhelm Bessel 1784–1846,
Königsberg Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was na ...
(Germany) * Heinrich Christian Schumacher 1780–1850 (Germany & Russian Empire) *
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refe ...
1777–1855, Göttingen (Germany) * Friedrich Georg Wilhelm Struve 1793–1864,
Dorpat Tartu is the second largest city in Estonia after the Northern European country's political and financial capital, Tallinn. Tartu has a population of 91,407 (as of 2021). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of ...
and Pulkovo (
Russian Empire The Russian Empire was an empire and the final period of the List of Russian monarchs, Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended th ...
) *
Johann Jacob Baeyer Johann Jacob Baeyer (born 5 November 1794 in Berlin, died 10 September 1885 in Berlin) was a German geodesist and a lieutenant-general Lieutenant general (Lt Gen, LTG and similar) is a three-star military rank (NATO code OF-8) used in many ...
1794–1885,
Berlin Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...
(Germany) *
George Biddell Airy Sir George Biddell Airy (; 27 July 18012 January 1892) was an English mathematician and astronomer, and the seventh Astronomer Royal from 1835 to 1881. His many achievements include work on planetary orbits, measuring the mean density of the ...
1801–1892,
Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge beca ...
&
London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
*
Carl Christopher Georg Andræ Carl may refer to: * Carl, Georgia, city in USA * Carl, West Virginia, an unincorporated community *Carl (name), includes info about the name, variations of the name, and a list of people with the name * Carl², a TV series * "Carl", an episode of ...
1812–1893,
Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...
(Denmark) * Karl Maximilian von Bauernfeind 1818–1894,
Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and Ha ...
(Germany) * Wilhelm Jordan 1842–1899, (Germany) * Hervé Faye 1814–1902 (France) *
George Gabriel Stokes Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Luc ...
1819–1903 (England) * Carlos Ibáñez e Ibáñez de Ibero 1825–1891,
Barcelona Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ...
(Spain) *
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
1854–1912,
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...
(France) *
Alexander Ross Clarke Col Alexander Ross Clarke FRS FRSE (1828–1914) was a British geodesist, primarily remembered for his calculation of the Principal Triangulation of Britain (1858), the calculation of the Figure of the Earth (1858, 1860, 1866, 1880) and on ...
1828–1914,
London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
(England) *
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for ...
1839–1914 (United States) *
Friedrich Robert Helmert Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and statistician with important contributions to the theory of errors. Career Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg an ...
1843–1917,
Potsdam Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of B ...
(Germany) * Heinrich Bruns 1848–1919,
Berlin Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...
(Germany) * Loránd Eötvös 1848–1919 (Hungary)


20th century geodesists (alphabetically arranged)

*
Tadeusz Banachiewicz Tadeusz Julian Banachiewicz (13 February 1882, Warsaw – 17 November 1954, Kraków) was a Polish astronomer, mathematician and geodesist. Scientific career He was educated at University of Warsaw and his thesis was on "reduction constan ...
, 1882–1954, (Poland) *
Arne Bjerhammar Arne Bjerhammar (September 15, 1917 – February 6, 2011) was a List of Swedish scientists, Swedish geodesy, geodesist. He was professor at Royal Institute of Technology (KTH) in Stockholm. He was born in Båstad, Scania in the south of Sweden. ...
, 1917–2011, (Sweden) *
Giovanni Boaga Giovanni Boaga (February 28, 1902 – November 17, 1961) was an Italian mathematician and geodesy professor. He was born in Trieste and died in Tripoli, Libya. His Gauss-Boaga Projection is the standard projection used in Italian topography by ...
, 1902–1961, (Italy) *
Guy Bomford Brigadier Guy Bomford (1899-1996) was a British geodesist. He worked at the Survey of India and the Corps of Royal Engineers. In 1947 he was appointed as reader in surveying and geodesy at the University of Oxford, holding this post until his retir ...
, 1899–1996, (England) * William Bowie, 1872–1940, (US) * Irene Kaminka Fischer, 1907–2009, (US) *
Buckminster Fuller Richard Buckminster Fuller (; July 12, 1895 – July 1, 1983) was an American architect, systems theorist, writer, designer, inventor, philosopher, and futurist. He styled his name as R. Buckminster Fuller in his writings, publishing m ...
, 1895–1983 (United States) * John Fillmore Hayford, 1868–1925, (US) * Veikko Aleksanteri Heiskanen, 1895–1971, (Finland and US) * Reino Antero Hirvonen, 1908–1989, (Finland) * Friedrich Hopfner, 1881–1949,
Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
, (Austria) * Martin Hotine, 1898–1968, (England) *
Harold Jeffreys Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was a British mathematician, statistician, geophysicist, and astronomer. His book, ''Theory of Probability'', which was first published in 1939, played an important role in the reviva ...
, 1891–1989,
London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
, (England) *
William M. Kaula William M. Kaula (May 19, 1926 – April 1, 2000) was an Australian-born American geophysicist and professor at the University of California, Los Angeles. Kaula was most notable for his contributions to geodesy, including using early satellites to ...
, 1926–2000,
Los Angeles Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the largest city in the state of California and the second most populous city in the United States after New York City, as well as one of the wor ...
, (US) *
Karl-Rudolf Koch Karl-Rudolf Koch (born 30 July 1935) is a German geodesist and professor at the University of Bonn (FRG). In the global geodetic community, he is well known for his research work in geodetic statistics, particularly robust parameter estimatio ...
1935,
Bonn The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ru ...
, (Germany) * Feodosy Nikolaevich Krasovsky, 1878–1948, (Russian Empire, USSR) * Mikhail Sergeevich Molodenskii, 1909–1991, (Russia) * John A. O'Keefe, 1916–2000, (US) *
Karl Ramsayer Karl Ramsayer (29 September 1911, Schwäbisch Gmünd''Große Kreisstadt Schwäbisch Gmünd. Personalia'' in ''ostalb einhorn. Vierteljahreshefte für Heimat und Kultur im Ostalbkreis'', Nr. 37/38, Arbeitsgemeinschaft Einhorn-Verlag E. Dietenberger ...
, 1911–1982, Stuttgart, (Germany) * Hellmut Schmid, 1914–1998, (Switzerland) * Yrjö Väisälä, 1889–1971, (Finland) * Petr Vaníček, 1935,
Fredericton Fredericton (; ) is the capital city of the Canadian province of New Brunswick. The city is situated in the west-central portion of the province along the Saint John River, which flows west to east as it bisects the city. The river is the do ...
, (Canada) * Felix Andries Vening-Meinesz, 1887–1966, (Netherlands) *
Thaddeus Vincenty Thaddeus Vincenty (born Tadeusz Szpila; 27 October 1920 – 6 March 2002) was a Polish American geodesist who worked with the U.S. Air Force and later the National Geodetic Survey to adapt three-dimensional adjustment techniques to NAD 83. He dev ...
, 1920–2002, (Poland) *
Alfred Wegener Alfred Lothar Wegener (; ; 1 November 1880 – November 1930) was a German climatologist, geologist, geophysicist, meteorologist, and polar researcher. During his lifetime he was primarily known for his achievements in meteorology and ...
, 1880–1930, (Germany and Greenland) * Hans-Georg Wenzel (1949–1999), (Germany)


See also

;Fundamentals * Concepts and Techniques in Modern Geography * Geodesics on an ellipsoid *
History of geodesy The history of geodesy deals with the historical development of measurements and representations of the Earth. The corresponding scientific discipline, ''geodesy'' ( /dʒiːˈɒdɪsi/), began in pre-scientific antiquity and blossomed during the ...
* Physical geodesy *
Earth's circumference Earth's circumference is the distance around Earth. Measured around the Equator, it is . Measured around the poles, the circumference is . Measurement of Earth's circumference has been important to navigation since ancient times. The first kn ...
;Governmental agencies * National mapping agency * U.S. National Geodetic Survey *
National Geospatial-Intelligence Agency The National Geospatial-Intelligence Agency (NGA) is a combat support agency within the United States Department of Defense whose primary mission is collecting, analyzing, and distributing geospatial intelligence (GEOINT) in support of natio ...
*
United States Coast and Geodetic Survey The United States Coast and Geodetic Survey (abbreviated USC&GS), known from 1807 to 1836 as the Survey of the Coast and from 1836 until 1878 as the United States Coast Survey, was the first scientific agency of the United States Government. It ...
*
United States Geological Survey The United States Geological Survey (USGS), formerly simply known as the Geological Survey, is a scientific agency of the United States government. The scientists of the USGS study the landscape of the United States, its natural resources, ...
;International organizations * International Association of Geodesy *
International Federation of Surveyors International Federation of Surveyors (abbreviated FIG, after the french: Fédération Internationale des Géomètres) is the UN-recognized global organization for the profession of surveying and related disciplines. It was established in 1878,
* International Geodetic Student Organisation ;Other * Éric Calais * EPSG Geodetic Parameter Dataset *
Meridian arc In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to ...
*
Surveying Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...


References


Further reading

* 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

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, . * 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


Geodetic awareness guidance note, Geodesy Subcommittee, Geomatics Committee, International Association of Oil & Gas Producers
* {{Authority control Articles containing video clips