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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 spheres ...
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 on ...
and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as '' planetary geodesy''). Geodynamical phenomena, including crustal motion, tides and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques and relying on datums and
coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
s. The job title is geodesist or geodetic surveyor.


History


Definition

The word geodesy comes from the Ancient Greek word ''geodaisia'' (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying
gravitational field In physics, a gravitational field is a model used to explain the influences 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 phenome ...
. 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 ca ...
. Such geodetic operations are also applied to other
astronomical bodies An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
in the Solar System. 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, and the competition of geological processes such as the collision of plates and of volcanism, resisted by Earth's gravitational 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 gravitational field is called physical geodesy.


Geoid and reference ellipsoid

The geoid is essentially the figure of Earth abstracted from its topographical 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 approx ...
, 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 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 approximations ...
, 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 Undulation may refer to: * Lateral undulation, the most primitive of vertebrate locomotor patterns * Undulation of the geoid, the separation between the geoid and the reference ellipsoid of the Earth * Undulation point, a point on a curve where th ...
. 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 The Geodetic Reference System 1980 (GRS 80) is a geodetic reference system consisting of a global reference ellipsoid and a normal gravity model. Background Geodesy is the scientific discipline that deals with the measurement and representation ...
) 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 The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
(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.


Coordinate systems in space

The locations of points in three-dimensional space are most conveniently described by three
cartesian Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory *Cartesian coordinate system, modern ...
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 In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted. ...
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 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 vertic ...
(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 The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
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 star In astronomy, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points, astronomical objects actually and mainly stars, that appear not to move relative to one another against the darkness of the night sky in the backg ...
s, 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 The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, ...
("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 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 coord ...
, 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.


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 ca ...
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 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 means i ...
). 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 '' heights'' 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 comb ...
", an irregular, physically defined surface. Heights come in the following variants: # Orthometric heights # Dynamic heights # Geopotential heights # Normal heights Each has its advantages and disadvantages. Both orthometric and normal heights are heights in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m2 s−2) and not metric. The reference surface is the geoid, 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 approximations ...
, by means of the geoid undulation.
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 ...
), 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 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 ...
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 Pa ...
(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 me ...
points of a higher-order network or
GPS The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
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 In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...
), 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 Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
. 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 ca ...
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) 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 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. 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 geomet ...
, 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 ...
. 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 equations 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 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 vertic ...
or vertical: the direction of local gravity, or the line that results by following it. * Zenith: 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 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 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. 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 Tacheometry (; from Greek for "quick measure") is a system of rapid surveying, by which the horizontal and vertical positions of points on the earth's surface relative to one another are determined without using a chain or tape, or a separate le ...
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 and information, geographic data (that is, descriptions of phenomena for which location is relevant), combined with Geographic information system software, sof ...
(GIS) database. Geodetic
GPS The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
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 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 Very-long-baseline interferometry (VLBI) is a type of astronomical interferometer, astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telesco ...
(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 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 G ...
, 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 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 and atmospheric loading, as well as for verifying the Newtonian constant of
gravitation 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 stron ...
. In the future, gravity and altitude will be measured by relativistic time dilation measured by optical clocks.


Units and measures on the ellipsoid

Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are ''angles'', not metric measures, and describe the ''direction'' of the local normal to the
reference ellipsoid 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 approximations ...
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 ...
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 * Episodic motion of tectonic origin, especially close to fault lines * Periodic effects due to tides and tidal loading * Postglacial 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 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. The geodynamics 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 The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
, GLONASS,
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
, and BeiDou *
Very-long-baseline interferometry Very-long-baseline interferometry (VLBI) is a type of astronomical interferometer, astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telesco ...
(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 * 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 580–490 BC, ancient Greece *
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 Alexandria ...
276–194 BC, ancient Greece * Hipparchus 190–120 BC, ancient Greece * Posidonius 135–51 BC, ancient Greece * Claudius Ptolemy AD 83–168, Roman Empire (
Roman Egypt , conventional_long_name = Roman Egypt , common_name = Egypt , subdivision = Province , nation = the Roman Empire , era = Late antiquity , capital = Alexandria , title_leader = Praefectus Augustalis , image_map = Roman E ...
) *
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'mu ...
786–833, Baghdad (Iraq/ Mesopotamia) * Abu Rayhan Biruni 973–1048,
Khorasan Khorasan may refer to: * Greater Khorasan, a historical region which lies mostly in modern-day northern/northwestern Afghanistan, northeastern Iran, southern Turkmenistan, Tajikistan, and Uzbekistan * Khorasan Province, a pre-2004 province of Ira ...
( Iran/ Samanid Dynasty) * Muhammad al-Idrisi 1100–1166, ( Arabia & Sicily) * Regiomontanus 1436–1476, (Germany/Austria) *
Abel Foullon Abel Foullon (1513–1563 or 1565, in France) was an author, director of the Mint (coin), Mint for Henry II of France and also an engineer to the king of France after Leonardo da Vinci. His Holometer is an instrument for making of angular mea ...
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, Nunes ...
1502–1578 (Portugal) *
Gerhard Mercator Gerardus Mercator (; 5 March 1512 – 2 December 1594) was a 16th-century geographer, cosmographer and cartographer from the County of Flanders. He is most renowned for creating the 1569 world map based on a new projection which represented sa ...
1512–1594 (Belgium & Germany) * Snellius (Willebrord Snel van Royen) 1580–1626, Leiden (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 of ...
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 1713–1765 (France) * Johann Heinrich Lambert 1728–1777 (France) * Roger Joseph Boscovich 1711–1787, ( Rome/ Berlin/ Paris) *
Ino Tadataka Ino or INO may refer to: Arts and music *I-No, a character in the ''Guilty Gear'' series of video games *Ino (Greek mythology), a queen of Thebes in Greek mythology *INO Records, an American Christian music label * Ino Yamanaka, a character in t ...
1745–1818, ( Tokyo) *
Georg von Reichenbach Georg Friedrich von Reichenbach (24 August 1772 – 21 May 1826), German scientific instrument maker, was born at Durlach in Baden on 24 August 1772. Early life Reichenbach's father was a master mechanic, and a master cannon-borer, who moved to M ...
1771–1826, Bavaria (Germany) * Pierre-Simon Laplace 1749–1827, Paris (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 (France) *
Johann Georg von Soldner Johann Georg von Soldner (16 July 1776 in Feuchtwangen, Ansbach – 13 May 1833 in Bogenhausen, Munich) was a German physicist, mathematician and astronomer, first in Berlin and later in 1808 in Munich. Life He was born in Feuchtwangen in Ans ...
1776–1833, Munich (Germany) * George Everest 1790–1866 (England and India) * Friedrich Wilhelm Bessel 1784–1846, Königsberg (Germany) * Heinrich Christian Schumacher 1780–1850 (Germany & Russian Empire) * Carl Friedrich Gauss 1777–1855, Göttingen (Germany) * Friedrich Georg Wilhelm Struve 1793–1864, Dorpat and Pulkovo ( Russian Empire) *
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 in the Royal Prussian Army. He was the first director of the Royal Prussian Geodetic Institute and is regarded ...
1794–1885, Berlin (Germany) * George Biddell Airy 1801–1892, Cambridge & London *
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 (Denmark) *
Karl Maximilian von Bauernfeind Karl Maximilian von Bauernfeind (28 November 1818 – 3 August 1894) was a German geodesist and civil engineer. Education At the age of 18, Bauernfeind studied under Georg Ohm at the Polytechnic School in Nuremberg. Two years later, he studi ...
1818–1894, Munich (Germany) *
Wilhelm Jordan Wilhelm Jordan may refer to: * Carl Friedrich Wilhelm Jordan (1819–1904), known as Wilhelm Jordan, German writer and politician * Wilhelm Jordan (geodesist) (1842–1899), German scientist, noted for the Gauss–Jordan elimination algorithm {{hn ...
1842–1899, (Germany) * Hervé Faye 1814–1902 (France) * George Gabriel Stokes 1819–1903 (England) *
Carlos Ibáñez e Ibáñez de Ibero Carlos Ibáñez e Ibáñez de Ibero, 1st Marquis of Mulhacén, (14 April 1825 – 28 or 29 January 1891) was a Spanish divisional general and geodesist. He represented Spain at the 1875 Conference of the Metre Convention and was the first presid ...
1825–1891, Barcelona (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 (France) * Alexander Ross Clarke 1828–1914, London (England) * Charles Sanders Peirce 1839–1914 (United States) * Friedrich Robert Helmert 1843–1917, Potsdam (Germany) *
Heinrich Bruns Ernst Heinrich Bruns (4 September 1848 – 23 September 1919) was a German mathematician and astronomer, who also contributed to the development of the field of theoretical geodesy. Early life Heinrich Bruns was born on 4 September 1848 in Ber ...
1848–1919, Berlin (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, 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, (Austria) * Martin Hotine, 1898–1968, (England) * Harold Jeffreys, 1891–1989, London, (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, (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 estimation a ...
1935, Bonn, (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 Stuttgart (; Swabian: ; ) is the capital and largest city of the German state of Baden-Württemberg. It is located on the Neckar river in a fertile valley known as the ''Stuttgarter Kessel'' (Stuttgart Cauldron) and lies an hour from the ...
, (Germany) * Hellmut Schmid, 1914–1998, (Switzerland) * Yrjö Väisälä, 1889–1971, (Finland) *
Petr Vaníček Petr Vaníček (born 18 July 1935) is a Czech Canadian geodesist and theoretical List of geophysicists, geophysicist who has made important breakthroughs in theory of frequency spectrum#Spectrum analysis, spectral analysis and geoid computation. ...
, 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, 1880–1930, (Germany and Greenland) *
Hans-Georg Wenzel Hans-Georg Wenzel (3 February, 1945 – 11 November, 1999), also known as George Wenzel, was a German geodesist, geophysicist and university lecturer. His most important field of work was physical geodesy, where he worked after his dissertation on ...
(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 th ...
* 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 know ...
;Governmental agencies *
National mapping agency A national mapping agency is an organisation, usually publicly owned, that produces topographic maps and geographic information of a country. Some national mapping agencies also deal with cadastral matters. According to 2007/2/EC European directi ...
* U.S. National Geodetic Survey * National Geospatial-Intelligence Agency * United States Coast and Geodetic Survey * United States Geological Survey ;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 Éric Calais is a French geologist-geophysicist, born in 1964, internationally recognized practitioner of high-precision space geodesy (GPS and InSAR radar interferometry) and a pioneer in its applications to measure seismic deformations at the bou ...
*
EPSG Geodetic Parameter Dataset EPSG Geodetic Parameter Dataset (also EPSG registry) is a public registry of geodetic datums, spatial reference systems, Earth ellipsoids, coordinate transformations and related units of measurement. Originally created by European Petroleum Survey ...
*
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 de ...
*
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 ca ...


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