View source for Geodesy

{{Short description|Science of measuring the shape, orientation, and gravity of Earth}}
{{redirect|Geodetic|the mathematical concept|Geodesic}}
{{multiple|
{{more citations needed|date=February 2024}}
{{MOS|date=June 2024}}
{{Original research|date=October 2024}}
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[[File:Geodetic survey instruments 07.jpg|thumb|right|A modern instrument for geodetic [[measurements]] using [[GNSS|satellites]]]]
{{Geodesy}}

'''Geodesy''' or '''geodetics'''<ref>{{Cite book |title=[[Cambridge English Dictionary]] |chapter=geodetics |access-date=2024-06-08 |chapter-url=https://dictionary.cambridge.org/us/dictionary/english/geodetics}}</ref> is the [[science]] of measuring and representing the [[Figure of the Earth|geometry]], [[Gravity of Earth|gravity]], and [[Earth's rotation|spatial orientation]] of the [[Earth]] in [[Relative change|temporally varying]] [[Three-dimensional space|3D]]. It is called [[planetary geodesy]] when studying other [[astronomical body|astronomical bodies]], such as [[planet]]s or [[Natural satellite|circumplanetary system]]s.<ref name="VK">{{Cite book |url=https://shop.elsevier.com/books/geodesy/vanicek/978-0-444-87775-8 |title=Geodesy: The Concepts |date=November 1, 1986 |publisher=[[Elsevier]] |isbn=978-0-444-87775-8 |editor-last=Vaníček |editor-first=Petr |editor-link=Petr Vaníček |edition=Second |pages=45–51 |chapter=Structure of Geodesy |doi=10.1016/B978-0-444-87775-8.50009-5 |quote=...{{nbsp}}geodesy was thought to occupy the space delimited by the following definition ... "the science of measuring and portraying the earth's surface." ... the new definition of geodesy ... "the discipline that deals with the measurement and representation of the earth, including its gravity field, in a three-dimensional time varying space." ... a virtually identical definition ... the inclusion of other celestial bodies and their respective gravity fields. |editor2-last=Krakiwsky |editor2-first=Edward J.}}</ref> Geodesy is an [[earth science]] and many consider the study of Earth's shape and gravity to be central to that science.<ref>{{Cite book |url=https://www.iag-aig.org/doc/5cb5b3660b6c4.pdf |title=What is Geodesy? |publisher=[[International Association of Geodesy]]}}</ref><ref>{{Cite web |last=US Department of Commerce |first=National Oceanic and Atmospheric Administration |title=What is geodesy? |url=https://oceanservice.noaa.gov/facts/geodesy.html |access-date=2024-06-09 |website=oceanservice.noaa.gov |language=EN-US}}</ref> It is also a discipline of [[applied mathematics]].<ref>{{Cite web |title=Geodesy |url=https://c4g.lsu.edu/index.php/geodesy |access-date=2024-06-08 |website=LSU Center for GeoInformatics}}</ref><ref>{{Cite web |title=Geodesy Definition, Characteristics & Branches |url=https://study.com/academy/lesson/geodesy-definition-branches.html |access-date=2024-06-08 |website=Study.com |language=en |quote=The definition of geodesy can be explained as the academic field of earth science that is involved with measuring and comprehending the Earth's orientation in space, the Earth's gravity field, and the Earth's shape geometrically. ... Geodesy is an applied mathematics discipline used to understand various aspects of the Earth.}}</ref>

[[Geodynamics|Geodynamical]] phenomena, including [[crust (geology)|crustal]] motion, [[tide]]s, and [[polar motion]], can be studied by designing global and national [[Geodetic control network|control networks]], applying [[space geodesy]] and terrestrial geodetic techniques, and relying on [[Geodetic datum|datums]] and [[coordinate system]]s. Geodetic job titles include '''geodesist''' and '''geodetic surveyor'''.<ref>{{cite web | website=Occupational Information Network |title=Geodetic Surveyors | date=2020-11-26 | url=https://www.onetonline.org/link/summary/17-1022.01 | access-date=2022-01-28}}</ref>

== History ==
{{main|History of geodesy|templates=-Geodesy}}
Geodesy began in pre-scientific [[Classical antiquity|antiquity]], so the very word geodesy comes from the [[Ancient Greek]] word {{lang|grc|γεωδαισία}} or ''geodaisia'' (literally, "division of Earth").<ref name="routledge">{{cite book |last1=Kent |first1=Alexander |last2=Vujakovic |first2=Peter |title=The Routledge Handbook of Mapping and Cartography |date=4 October 2017 |publisher=Routledge |isbn=978-1-317-56822-3 |page=187 |url=https://books.google.com/books?id=dowEEAAAQBAJ&dq=translate+ancient+greek+%CE%B3%CE%B5%CF%89%CE%B4%CE%B1%CE%B9%CF%83%CE%AF%CE%B1&pg=PA187 |access-date=6 December 2024 |language=en}}</ref>

Early ideas about the figure of the Earth held the Earth to be [[flat Earth|flat]] and the heavens a [[Firmament|physical dome]] spanning over it.<ref name="Webb">{{cite book |last1=Webb |first1=Stephen H. |title=The Dome of Eden: A New Solution to the Problem of Creation and Evolution |date=1 January 2010 |publisher=Wipf and Stock Publishers |isbn=978-1-60608-741-1 |page=214 |url=https://books.google.com/books?id=wStMAwAAQBAJ&dq=flat+earth+dome+heavens&pg=PA214 |access-date=6 December 2024 |language=en}}</ref> Two early arguments for a spherical Earth were that lunar eclipses appear to an observer as circular shadows and that  [[Polaris]] appears lower and lower in the sky to a traveler headed South.<ref name="Posa">{{cite book |last1=Posamentier |first1=Alfred S. |last2=Maresch |first2=Guenter |last3=Thaller |first3=Bernd |last4=Spreitzer |first4=Christian |last5=Geretschlager |first5=Robert |last6=Stuhlpfarrer |first6=David |last7=Dorner |first7=Christian |title=Geometry In Our Three-dimensional World |date=24 November 2021 |publisher=World Scientific |isbn=978-981-12-3712-6 |pages=113–115 |url=https://books.google.com/books?id=DGxYEAAAQBAJ&dq=spherical+earth+lunar+eclipse+polaris&pg=PA114 |access-date=6 December 2024 |language=en}}</ref>

== Definition ==
In [[English language|English]], geodesy refers to the [[science]] of measuring and representing [[geospatial information]], while [[geomatics]] encompasses practical applications of geodesy on local and regional scales, including [[surveying]].

In [[German language|German]], geodesy can refer to either ''higher geodesy'' ({{lang|de|höhere Geodäsie}} or {{lang|de|Erdmessung}}, literally "geomensuration") — concerned with measuring Earth on the global scale, or ''engineering geodesy'' ({{lang|de|Ingenieurgeodäsie}}) that includes surveying — measuring parts or regions of Earth.

For the longest time, geodesy was the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field; however, geodetic science and operations are applied to other [[Astronomical object|astronomical bodies]] in our [[Solar System]] also.<ref name=VK/>

To a large extent, Earth's shape is the result of [[Earth's rotation|rotation]], which causes its [[equatorial bulge]], and the competition of geological processes such as the [[Continental collision|collision of plates]], as well as of [[Volcano|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 ==
{{main|Geoid|Reference ellipsoid}}
{{unsourced section|date=February 2024}}
[[File:Geoid undulation 10k scale.jpg|220px|thumb|right|[[Geoid]], an approximation for the shape of the [[Earth]]; shown here with [[vertical exaggeration]] (10000 vertical scaling factor).]]
[[File:Surface of latitude ellipsoid cone.gif|220px|thumb|right|[[Ellipsoid]] - a mathematical representation of the [[Earth]]. When mapping in geodetic coordinates, a latitude circle forms a truncated cone.]]
[[File:WGS84_mean_Earth_radius.svg|thumb|upright=1.0|Equatorial ({{mvar|a}}), polar ({{mvar|b}}) and mean Earth radii as defined in the 1984 [[World Geodetic System]]]]

The [[geoid]] essentially is the figure of Earth abstracted from its [[Topography|topographical]] features. It is an idealized equilibrium surface of [[seawater]], the [[mean sea level]] surface in the absence of [[Ocean current|currents]] and [[Atmospheric pressure|air pressure]] variations, and continued under the continental masses. Unlike a [[reference ellipsoid]], the geoid is irregular and too complicated to serve as the computational [[Surface (mathematics)|surface]] for solving geometrical problems like point positioning. The geometrical separation between the geoid and a reference ellipsoid is called ''geoidal [[wiktionary:undulate|undulation]]'', and it varies globally between ±110 m based on 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'' = {{sfrac|''a'' − ''b''|''a''}}, where ''b'' is the semi-minor axis (polar radius), is purely geometrical. The mechanical [[Flattening|ellipticity]] of Earth (dynamical flattening, symbol ''J''<sub>2</sub>) can be determined to high precision by observation of satellite [[Orbital perturbation analysis|orbit perturbations]]. Its relationship with geometrical flattening is indirect and depends on the internal density distribution or, in simplest terms, the degree of central concentration of mass.

The 1980 Geodetic Reference System ([[GRS80|GRS 80]]), adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics ([[IUGG]]), posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. GRS 80 essentially constitutes the basis for geodetic positioning by the [[Global Positioning System]] (GPS) and is thus also in widespread use outside the geodetic community. Numerous systems used for mapping and charting are becoming obsolete as countries increasingly move to global, geocentric reference systems utilizing the GRS 80 reference ellipsoid.

The geoid is a "realizable" surface, 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 physical ("real") surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, so it is an abstract surface. The third primary surface of geodetic interest — the [[Terrain|topographic surface]] of Earth — is also realizable.

== Coordinate systems in space ==
{{main|Geodetic system}}
{{further|World Geodetic System}}
{{unsourced section|date=February 2024}}
[[File:Datum Shift Between NAD27 and NAD83.png|220px|thumb|right|Datum shift between [[NAD27]] and [[NAD83]], in metres]]

The locations of points in 3D space most conveniently are described by three [[cartesian coordinate system|cartesian]] or rectangular coordinates, ''X'', ''Y'', and ''Z''. Since the advent of satellite positioning, such coordinate systems are typically [[geocentric]], with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis.

Before the era of [[satellite geodesy]], the coordinate systems associated with a geodetic [[datum (geodesy)|datum]] attempted to be [[geocentric]], but with the origin differing from the geocenter by hundreds of meters due to regional deviations in the direction of the [[plumbline]] (vertical). These regional geodetic datums, such as [[ED50|ED 50]] (European Datum 1950) or [[North American Datum#North American Datum of 1927|NAD 27]] (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to the [[geoid]]s within their areas of validity, minimizing the deflections of the vertical over these areas.

It is only because [[Global Positioning System|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 themselves get computed within such a system.

Geocentric coordinate systems used in geodesy can be divided naturally into two classes:
# The [[inertial]] reference systems, where the coordinate axes retain their orientation relative to the [[fixed star]]s or, equivalently, to the rotation axes of ideal [[gyroscopes]].  The ''X''-axis points to the [[Equinox (celestial coordinates)|vernal equinox]].
# The co-rotating reference systems (also [[ECEF]] or "Earth Centred, Earth Fixed"), in which the axes are "attached" to the solid body of Earth. The ''X''-axis lies within the [[Greenwich meridian|Greenwich]] observatory's [[Meridian (geography)|meridian]] plane.

The coordinate transformation between these two systems to good approximation is described by (apparent) [[sidereal time]], which accounts for variations in Earth's axial rotation ([[day|length-of-day]] variations). A more accurate description also accounts for [[polar motion]] as a phenomenon closely monitored by geodesists.

=== Coordinate systems in the plane ===
{{main|Horizontal position}}
[[File:Elliptical coordinates grid.svg|225px|thumb|2D grid for elliptical coordinates]]
[[File:Litography archive of the Bayerisches Vermessungsamt.jpg|225px|thumb|A [[Munich]] archive with [[lithography]] plates of maps of [[Bavaria]]]]

In geodetic applications like [[surveying]] and [[map]]ping, two general types of coordinate systems in the plane are in use:

# '''Plano-polar''', with points in the plane defined by their distance, ''s'', from a specified point along a ray having a direction ''α'' from a baseline or axis.
# '''Rectangular''', with points defined by distances from two mutually perpendicular axes, ''x'' and ''y''. Contrary to the mathematical convention, in geodetic practice, the ''x''-axis points [[Northing|North]] and the ''y''-axis [[Easting|East]].

One can intuitively use rectangular coordinates in the plane for one's current location, in which case the ''x''-axis will point to the local north. More formally, such coordinates can be obtained from 3D 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]] — preserves angles and length ratios so that small circles get mapped as small circles and small squares as squares.

An example of such a projection is UTM ([[Universal Transverse Mercator]]). Within the map plane, we have rectangular coordinates ''x'' and ''y''. In this case, the north direction used for reference is the ''map'' north, not the ''local'' north. The difference between the two is called [[Transverse Mercator projection#Convergence|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:

:<math>\begin{align}
x &= s \cos \alpha\\
y &= s \sin \alpha
\end{align}</math>

The reverse transformation is given by:

:<math>\begin{align}
s &= \sqrt{x^2 + y^2}\\
\alpha &= \arctan\frac{y}{x}.
\end{align}</math>

== Heights ==
{{further|Vertical position|Vertical datum}}
[[File:An-illustration-of-height-measurement-using-satellite-altimetry.jpg|285px|thumb|right|Height measurement using satellite altimetry]]

In geodesy, point or terrain ''[[height]]s'' are "[[above sea level]]" as an irregular, physically defined surface.
Height systems in use are:

# [[Orthometric height]]s
# [[Dynamic height]]s
# [[Geopotential height]]s
# [[Normal height]]s

Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in [[metre]]s above sea level, whereas geopotential numbers are measures of potential energy (unit: m<sup>2</sup> s<sup>−2</sup>) and not metric. The reference surface is the [[geoid]], an [[equigeopotential]] surface approximating the mean sea level as described above. For normal heights, the reference surface is the so-called ''[[quasi-geoid]]'', which has a few-metre separation from the geoid due to the density assumption in its continuation under the continental masses.<ref name="ForoughiTenzer2017">{{cite journal|last1=Foroughi|first1=Ismael|last2=Tenzer|first2=Robert|title=Comparison of different methods for estimating the geoid-to-quasi-geoid separation|journal=Geophysical Journal International|volume=210|issue=2|year=2017|pages=1001–1020|issn=0956-540X|doi=10.1093/gji/ggx221|doi-access=free |hdl=10397/75053|hdl-access=free}}</ref>

One can relate these heights through the [[geoid undulation]] concept to ''[[ellipsoidal height]]s'' (also known as ''geodetic heights''), representing the height of a point above the [[reference ellipsoid]]. [[Satellite positioning receiver]]s typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid.

== Geodetic datums ==
{{main|Geodetic datum}}
{{further|Datum transformation}}

Because coordinates and heights of geodetic points always get obtained within a system that itself was constructed based on real-world observations, geodesists introduced the concept of a "geodetic datum" (plural ''datums''): a physical (real-world) realization of a coordinate system used for describing point locations. This realization follows from ''choosing'' (therefore 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 datums, such as the NAVD 88 (North American Vertical Datum 1988), NAP ([[Normaal Amsterdams Peil]]), the Kronstadt datum, the Trieste datum, and numerous others.

In both mathematics and geodesy, a coordinate system is a "coordinate system" per [[International Organization for Standardization|ISO]] terminology, whereas the [[International Earth Rotation and Reference Systems Service]] (IERS) uses the term "reference system" for the same. When coordinates are realized by choosing datum points and fixing a geodetic datum, ISO speaks of a "coordinate reference system", whereas IERS uses a "reference frame" for the same. The ISO term for a datum transformation again is a "coordinate transformation".<ref>(ISO 19111: Spatial referencing by coordinates).</ref>

== Positioning ==
{{see also|Geodetic network#Measurement techniques}}
{{unsourced section|date=February 2024}}
[[File:GPS satellite approaching 23 years on orbit (1060259).jpeg|220px|thumb|right|[[GPS]] Block IIA satellite orbits over the [[Earth]].]]
[[File:Geodetic Control Mark.jpg|220px|thumb|Geodetic control mark]]
[[File:Apollo IMU at Draper Hack the Moon exhibit.agr.jpg|220px|thumb|right|[[Inertial navigation|Navigation]] device, [[Apollo program]]]]

General [[geopositioning]], or simply positioning, is the determination of the location of points on Earth, by myriad techniques. '''Geodetic positioning''' employs geodetic methods to determine a set of precise geodetic coordinates of a point on land, at sea, or in space. It may be done within a coordinate system ('''point positioning''' or '''absolute positioning''') or relative to another point ('''relative positioning'''). One computes the position of a point in space from measurements linking terrestrial or extraterrestrial points of known location ("known points") with terrestrial ones of unknown location ("unknown points"). The computation may involve transformations between or among astronomical and terrestrial coordinate systems. Known points used in point positioning can be [[Global Navigation Satellite Systems|GNSS]] [[continuously operating reference station]]s or [[Triangulation (surveying)|triangulation points]] of a higher-order network.

Traditionally, geodesists built a hierarchy of networks to allow point positioning within a country. The highest in this hierarchy were triangulation networks, densified into the networks of [[traverse (surveying)|traverse]]s ([[polygons]]) into which local mapping and surveying measurements, usually collected using a measuring tape, a [[Corner reflector|corner prism]], and the red-and-white poles, are tied.

Commonly used nowadays is GPS, except for specialized measurements (e.g., in underground or high-precision engineering). The higher-order networks are measured with [[Global Positioning System|static GPS]], using [[Differential GPS|differential measurement]] to determine vectors between terrestrial points. These vectors then get adjusted in a traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the [[IERS]] is the basis for defining a single global, geocentric reference frame that serves as the "zero-order" (global) reference to which national measurements are attached.

[[Real-time kinematic positioning]] (RTK GPS) is employed frequently in [[surveying|survey]] mapping. In that measurement technique, unknown points can get quickly tied into nearby terrestrial known points.

One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control. There can be thousands of those geodetically determined points in a country, usually documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements.

== Geodetic problems {{anchor|Problems}} ==
{{further|Geodesics on an ellipsoid#Solution of the direct and inverse problems}}
{{see also|Bearing (navigation)#Arcs}}
{{unsourced section|date=February 2024}}

In geometrical geodesy, there are two main problems:

* '''First geodetic problem''' (also known as ''direct'' or ''forward geodetic problem''): given the coordinates of a point and the directional ([[azimuth]]) and [[distance]] to a second point, determine the coordinates of that second point.
* '''Second geodetic problem''' (also known as ''inverse'' or ''reverse geodetic problem''): given the coordinates of two points, determine the azimuth and length of the (straight, curved, or [[geodesic]]) line connecting those points.

The solutions to both problems in plane geometry reduce to simple [[trigonometry]] and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in the inverse problem, the azimuths differ going between the two end points along the arc of the connecting [[great circle]].

The general solution is called the [[geodesic]] for the surface considered, and the [[differential equation]]s for the [[geodesic]] are solvable numerically. On the ellipsoid of revolution, geodesics are expressible in terms of elliptic integrals, which are usually evaluated in terms of a series expansion — see, for example, [[Vincenty's formulae]].

== Observational concepts ==
[[File:AxialTiltObliquity.png|285px|thumb|Axial tilt (or [[Obliquity]]), rotation axis, plane of [[orbit]], [[celestial equator]] and [[ecliptic]]. [[Earth]] is shown as viewed from the [[Sun]]; the orbit direction is counter-clockwise (to the left).]]
[[File:Global Gravity Anomaly Animation over OCEANS.gif|285px|thumb|right|Global [[gravity anomaly]] animation over oceans from the NASA's GRACE (Gravity Recovery and Climate Experiment)]]

As defined in geodesy (and also [[astronomy]]), some basic observational concepts like angles and coordinates include (most commonly from the viewpoint of a local observer):

* '''[[Plumbline]]''' or '''vertical''': (the line along) the direction of local gravity.
* '''[[Zenith]]''': the (direction to the) intersection of the upwards-extending gravity vector at a point and the [[celestial sphere]].
* '''[[Nadir]]''': the (direction to the) antipodal point where the downward-extending gravity vector intersects the (obscured) celestial sphere.
* '''Celestial horizon''': a plane perpendicular to the gravity vector at a point.
* '''[[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]] 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 ([[precession|precessing]] and [[nutation|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 (geography)|Meridian]] plane''': any plane perpendicular to the celestial equator and containing the celestial poles.
* '''Local meridian''': the plane which contains the direction to the zenith and the celestial pole.

== Measurements ==
{{further|Satellite geodesy|Geodetic astronomy|Surveying|Gravimetry|Levelling}}
{{unsourced section|date=February 2024}}
[[File:GRAIL's gravity map of the moon.jpg|285px|thumb|right|Variations in the gravity field of the [[Moon]], from [[NASA]]]][[File:Gravity measurement devices, pendulum (left) and absolute (right) - National Museum of Nature and Science, Tokyo - DSC07808.JPG|285px|thumb|right|Gravity measurement devices, pendulum (left) and absolute gravimeter (right)]]
[[File:Autograv CG5 P1150838.JPG|85px|thumb|right|A relative gravimeter]]

The reference surface (level) used to determine height differences and height reference systems is known as [[mean sea level]]. The traditional [[spirit level]] directly produces such (for practical purposes most useful) heights above [[sea level]]; 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 determination improves, one may expect that the use of GPS in height determination shall increase, too.

The [[theodolite]] is an instrument used to measure horizontal and vertical (relative to the local vertical) angles to target points. In addition, the [[Tachymeter (survey)|tachymeter]] determines, electronically or [[Electro-optics|electro-optically]], the distance to a target and is highly automated or even robotic in operations. Widely used for the same purpose is the method of free station position.

Commonly for local detail surveys, tachymeters are employed, although the old-fashioned rectangular technique using an angle prism and steel tape is still an inexpensive alternative. As mentioned, also there are quick and relatively accurate real-time kinematic (RTK) GPS techniques. Data collected are tagged and recorded digitally for entry into [[Geographic information system|Geographic Information System]] (GIS) databases.

Geodetic GNSS (most commonly [[Global Positioning System|GPS]]) receivers directly produce 3D coordinates in a [[geocentric]] coordinate frame. One such frame is [[WGS84]], as well as frames by the International Earth Rotation and Reference Systems Service ([[IERS]]). GNSS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys.

To monitor the Earth's rotation irregularities and plate tectonic motions and for planet-wide geodetic surveys, methods of [[very-long-baseline interferometry]] (VLBI) measuring distances to [[quasar]]s, [[lunar laser ranging]] (LLR) measuring distances to prisms on the Moon, and [[satellite laser ranging]] (SLR) measuring distances to prisms on [[artificial satellites]], are employed.

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

In the future, gravity and altitude might become measurable using the special-relativistic concept of [[time dilation]] as gauged by [[Atomic clock#Research|optical clocks]].

== Units and measures on the ellipsoid ==
{{further|Geodetic coordinates}}
{{unsourced section|date=February 2024}}
[[File:Latitude and longitude graticule on an ellipsoid.svg|225px|thumb|right|The definition of latitude (φ) and longitude (λ) on an ellipsoid of revolution (or spheroid). The graticule spacing is 10 degrees. The latitude is defined as the angle between the normal to the ellipsoid and the equatorial plane.]]

Geographical [[latitude]] and [[longitude]] are stated in the units degree, minute of arc, and second of arc. They are ''angles'', not metric
measures, and describe the ''direction'' of the local normal to the [[reference ellipsoid]] of revolution. This direction 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 reasonably well when one also uses an ellipsoidal model of the figure of the Earth.

One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One [[nautical mile]] is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator same as with the nautical mile.

A [[metre]] was originally defined as the 10-millionth part of the length from the equator to the North Pole along the meridian through Paris (the target was not quite reached in actual implementation, as it is off by 200 [[Parts-per notation#ppm|ppm]] in the current definitions). This situation means that one kilometre roughly equals (1/40,000) * 360 * 60 meridional minutes of arc, or 0.54 nautical miles. (This is not exactly so as the two units had been defined on different bases, so the international nautical mile is 1,852 m exactly, which corresponds to rounding the quotient from 1,000/0.54 m to four digits).

== Temporal changes ==
{{see also|Geoid#Temporal change}}
[[File:Global plate motion.jpg|280px|thumb|right|Global plate tectonic movement using GPS]]
[[File:How VLBI Works.gif|280px|thumb|right|How [[very-long-baseline interferometry]] (VLBI) works]]

Various techniques are used in geodesy to study temporally changing surfaces, bodies of mass, physical fields, and dynamical systems. Points on Earth's surface change their location due to a variety of mechanisms:

* Continental plate motion, [[plate tectonics]]<ref>{{cite journal |last1=Altamimi |first1=Zuheir |last2=Métivier |first2=Laurent |last3=Rebischung |first3=Paul |last4=Rouby |first4=Hélène |last5=Collilieux |first5=Xavier |title=ITRF2014 plate motion model |journal=Geophysical Journal International |date=June 2017 |volume=209 |issue=3 |pages=1906–1912 |doi=10.1093/gji/ggx136|doi-access=free }}</ref>
* The episodic motion of tectonic origin, especially close to [[fault line]]s
* Periodic effects due to tides and tidal loading<ref>{{cite journal |last1=Sośnica |first1=Krzysztof |last2=Thaller |first2=Daniela |last3=Dach |first3=Rolf |last4=Jäggi |first4=Adrian |last5=Beutler |first5=Gerhard |title=Impact of loading displacements on SLR-derived parameters and on the consistency between GNSS and SLR results |journal=[[Journal of Geodesy]] |date=August 2013 |volume=87 |issue=8 |pages=751–769 |doi=10.1007/s00190-013-0644-1|bibcode=2013JGeod..87..751S |s2cid=56017067 |url=https://boris.unibe.ch/45844/8/190_2013_Article_644.pdf |archive-url=https://web.archive.org/web/20220318082002/https://boris.unibe.ch/45844/8/190_2013_Article_644.pdf |archive-date=2022-03-18 |url-status=live }}</ref>
* [[glaciation|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<ref>{{cite journal |last1=Zajdel |first1=Radosław |last2=Sośnica |first2=Krzysztof |last3=Bury |first3=Grzegorz |last4=Dach |first4=Rolf |last5=Prange |first5=Lars |last6=Kazmierski |first6=Kamil |title=Sub-daily polar motion from GPS, GLONASS, and Galileo |journal=Journal of Geodesy |date=January 2021 |volume=95 |issue=1 |pages=3 |doi=10.1007/s00190-020-01453-w|bibcode=2021JGeod..95....3Z |doi-access=free }}</ref>
* Length-of-day variability<ref>{{cite journal |last1=Zajdel |first1=Radosław |last2=Sośnica |first2=Krzysztof |last3=Bury |first3=Grzegorz |last4=Dach |first4=Rolf |last5=Prange |first5=Lars |title=System-specific systematic errors in earth rotation parameters derived from GPS, GLONASS, and Galileo |journal=GPS Solutions |date=July 2020 |volume=24 |issue=3 |pages=74 |doi=10.1007/s10291-020-00989-w|doi-access=free |bibcode=2020GPSS...24...74Z }}</ref>
* Earth's center-of-mass (geocenter) variations<ref>{{cite journal |last1=Zajdel |first1=Radosław |last2=Sośnica |first2=Krzysztof |last3=Bury |first3=Grzegorz |title=Geocenter coordinates derived from multi-GNSS: a look into the role of solar radiation pressure modeling |journal=GPS Solutions |date=January 2021 |volume=25 |issue=1 |pages=1 |doi=10.1007/s10291-020-01037-3|doi-access=free |bibcode=2021GPSS...25....1Z }}</ref>
* Anthropogenic movements such as reservoir construction or [[petroleum]] or water extraction

[[File:Stephen Merkowitz NASA's Space Geodesy Project.ogv|thumb|upright=1.25|A NASA project manager talks about his work for the [[Space geodesy|Space Geodesy]] Project, including an overview of its four fundamental techniques: GPS, [[very-long-baseline interferometry|VLBI]], [[Lunar laser ranging|LLR]]/[[Satellite laser ranging|SLR]], and [[DORIS (geodesy)|DORIS]].]]

[[Geodynamics]] is the discipline that studies deformations and motions of Earth's crust and its solidity as a whole. Often the study of Earth's irregular rotation is included in the above definition. Geodynamical studies require terrestrial reference frames<ref>{{cite journal |last1=Zajdel |first1=R. |last2=Sośnica |first2=K. |last3=Drożdżewski |first3=M. |last4=Bury |first4=G. |last5=Strugarek |first5=D. |title=Impact of network constraining on the terrestrial reference frame realization based on SLR observations to LAGEOS |journal=Journal of Geodesy |date=November 2019 |volume=93 |issue=11 |pages=2293–2313 |doi=10.1007/s00190-019-01307-0|bibcode=2019JGeod..93.2293Z |doi-access=free }}</ref> realized by the stations belonging to the Global Geodetic Observing System (GGOS<ref>{{cite journal |last1=Sośnica |first1=Krzysztof |last2=Bosy |first2=Jarosław |title=Global Geodetic Observing System 2015–2018 |journal=Geodesy and Cartography |date=2019 |doi=10.24425/gac.2019.126090|doi-access=free }}</ref>).

Techniques for studying geodynamic phenomena on global scales include:

* Satellite positioning by [[Global Positioning System|GPS]], [[GLONASS]], [[Galileo_(satellite_navigation)|Galileo]], and [[BeiDou]]
* [[Very-long-baseline interferometry]] (VLBI)
* [[Satellite laser ranging]] (SLR)<ref>{{cite journal |last1=Pearlman |first1=M. |last2=Arnold |first2=D. |last3=Davis |first3=M. |last4=Barlier |first4=F. |last5=Biancale |first5=R. |last6=Vasiliev |first6=V. |last7=Ciufolini |first7=I. |last8=Paolozzi |first8=A. |last9=Pavlis |first9=E. C. |last10=Sośnica |first10=K. |last11=Bloßfeld |first11=M. |title=Laser geodetic satellites: a high-accuracy scientific tool |journal=Journal of Geodesy |date=November 2019 |volume=93 |issue=11 |pages=2181–2194 |doi=10.1007/s00190-019-01228-y|bibcode=2019JGeod..93.2181P |s2cid=127408940 }}</ref> and lunar [[laser ranging]] (LLR)
* [[DORIS_(satellite_system)|DORIS]]
* Regionally and locally precise leveling
* Precise tachymeters
* Monitoring of gravity change using land, airborne, shipborne, and spaceborne [[gravimetry]]
* Satellite [[altimetry]] 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 ==
{{Main|List of geodesists}}
{{see also|Surveying#Notable surveyors{{!}}Notable surveyors}}

== See also ==
{{Portal|Earth sciences|Geodesy|Physics}}
{{Main|Outline of metrology and measurement#Geodesy}}
{{main cat}}

*{{Annotated link|Earth system science}}
*{{Annotated link|List of geodesists}}
*{{Annotated link|Geomatics engineering}} 
*{{Annotated link|History of geophysics}}
*{{Annotated link|Geodynamics}}
*{{Annotated link|Planetary science}}

{{div col}}

'''Fundamentals'''
* [[Geodesy (book)|''Geodesy'' (book)]]
* ''[[Concepts and Techniques in Modern Geography]]''
*[[Geodesics on an ellipsoid]]
*[[History of geodesy]]
*[[Physical geodesy]]
*[[Earth's circumference]]
* [[Physics]]
* [[Geosciences]]

'''Governmental agencies'''
*[[National mapping agency|National mapping agencies]]
*[[U.S. National Geodetic Survey]]
*[[National Geospatial-Intelligence Agency]]
*[[Ordnance Survey]]
*[[United States Coast and Geodetic Survey]]
*[[United States Geological Survey]]

'''International organizations'''
*[[International Union of Geodesy and Geophysics]] (IUGG)
*[[International Association of Geodesy]] (IAG)
*[[International Federation of Surveyors]] (IFS)
*[[International Geodetic Student Organisation]] (IGSO)

'''Other'''
*{{ill|Council of European Geodetic Surveyors|fr|Comité de liaison des géomètres européens}}
*[[EPSG Geodetic Parameter Dataset]]
*[[Meridian arc]]
*[[Surveying]]

{{div col end}}

== References ==
{{reflist}}

== Further reading ==
* F. R. Helmert, [http://geographiclib.sf.net/geodesic-papers/helmert80-en.html ''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, [http://geographiclib.sf.net/geodesic-papers/helmert84-en.html ''Mathematical and Physical Theories of Higher Geodesy'', Part 2], ACIC (St. Louis, 1964). This is an English translation of ''Die mathematischen und physikalischen Theorieen der höheren Geodäsie'', Vol 2 (Teubner, Leipzig, 1884).
* B. Hofmann-Wellenhof and H. Moritz, ''Physical Geodesy'', Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).
* W. Kaula, ''Theory of Satellite Geodesy : Applications of Satellites to Geodesy'', Dover Publications, 2000. (This text is a reprint of the 1966 classic).
* Vaníček P. and E.J. Krakiwsky, ''Geodesy: the Concepts'', pp.&nbsp;714, Elsevier, 1986.
* Torge, W (2001), ''Geodesy'' (3rd edition), published by de Gruyter, {{ISBN|3-11-017072-8}}.
* Thomas H. Meyer, Daniel R. Roman, and David B. Zilkoski. "What does ''height'' really mean?" (This is a series of four articles published in ''Surveying and Land Information Science, SaLIS''.)
**[http://digitalcommons.uconn.edu/thmeyer_articles/2 "Part I: Introduction"] ''SaLIS'' Vol. 64, No. 4, pages 223–233, December 2004.
** [http://digitalcommons.uconn.edu/thmeyer_articles/3 "Part II: Physics and gravity"] ''SaLIS'' Vol. 65, No. 1, pages 5–15, March 2005.
** [http://digitalcommons.uconn.edu/nrme_articles/2 "Part III: Height systems"] ''SaLIS'' Vol. 66, No. 2, pages 149–160, June 2006.
** [http://digitalcommons.uconn.edu/nrme_articles/5 "Part IV: GPS heighting"] ''SaLIS'' Vol. 66, No. 3, pages 165–183, September 2006.

==External links==
{{Commonscat}}
{{Wikibooks-inline|Geodesy}}
{{commons category-inline|Geodesy}}
*[https://web.archive.org/web/20150924055300/http://www.ogp.org.uk/pubs/373-01.pdf Geodetic awareness guidance note, Geodesy Subcommittee, Geomatics Committee, International Association of Oil & Gas Producers]
*{{cite EB1911|wstitle=Geodesy|volume=11|pages=607–615|short=1}}

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