Geodesy

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Geodesy" – news · newspapers · books · scholar · JSTOR (February 2024) (Learn how and when to remove this message) This article needs editing to comply with Wikipedia's Manual of Style. Please help improve the content. (June 2024) (Learn how and when to remove this message) This article possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (October 2024) (Learn how and when to remove this message) (Learn how and when to remove this message)

satellites

Geodesy
Fundamentals Geodesy Geodynamics Geomatics History
Concepts Geographical distance Geoid Figure of the Earth (radius and circumference) Geodetic coordinates Geodetic datum Geodesic Horizontal position representation Latitude / Longitude Map projection Reference ellipsoid Satellite geodesy Spatial reference system Spatial relations Vertical positions
Technologies Global Nav. Sat. Systems (GNSSs) Global Pos. System (GPS) GLONASS (Russia) BeiDou (BDS) (China) Galileo (Europe) NAVIC (India) Quasi-Zenith Sat. Sys. (QZSS) (Japan) Discrete Global Grid and Geocoding
Standards (history) GRS 80 Geodetic Reference System 1980 ISO 6709 Geographic point coord. 1983 NAD 83 North American Datum 1983 WGS 84 World Geodetic System 1984 NAVD 88 N. American Vertical Datum 1988 ETRS89 European Terrestrial Ref. Sys. 1989 GCJ-02 Chinese obfuscated datum 2002 Geo URI Internet link to a point 2010 International Terrestrial Reference System Spatial Reference System Identifier (SRID) Universal Transverse Mercator (UTM)
v t e

Geodesy or geodetics

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 systems. Geodetic job titles include geodesist and geodetic surveyor.^[7]

Geodesy began in pre-scientific antiquity, so the very word geodesy comes from the Ancient Greek word γεωδαισία or geodaisia (literally, "division of Earth").^[8]

Early ideas about the figure of the Earth held the Earth to be flat and the heavens a physical dome spanning over it.^[9] 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.^[10]

In

.

In German, geodesy can refer to either higher geodesy (höhere Geodäsie or Erdmessung, literally "geomensuration") — concerned with measuring Earth on the global scale, or engineering geodesy (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 bodies in our Solar System also.^[2]

To a large extent, Earth's shape is the result of

.

Geoid and reference ellipsoid

Main articles:

Reference ellipsoid

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2024) (Learn how and when to remove this message)

The

, 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 = ⁠a − b/a⁠, where b is the semi-minor axis (polar radius), is purely geometrical. The mechanical

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 (

(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 topographic surface of Earth — is also realizable.

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2024) (Learn how and when to remove this message)

NAD83

, in metres

The locations of points in 3D space most conveniently are described by three

, with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis.

Before the era of

within their areas of validity, minimizing the deflections of the vertical over these areas.

It is only because GPS satellites orbit about the geocenter that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system.

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

1. The
   gyroscopes. The X-axis points to the vernal equinox
   .
2. The co-rotating reference systems (also
   Greenwich observatory's 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 (length-of-day variations). A more accurate description also accounts for polar motion as a phenomenon closely monitored by geodesists.

In geodetic applications like surveying and mapping, two general types of coordinate systems in the plane are in use:

1. 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.
2. 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
   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

— 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 (

.

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:

${\displaystyle {\begin{aligned}x&=s\cos \alpha \\y&=s\sin \alpha \end{aligned}}}$

The reverse transformation is given by:

${\displaystyle {\begin{aligned}s&={\sqrt {x^{2}+y^{2}}}\\\alpha &=\arctan {\frac {y}{x}}.\end{aligned}}}$

Heights

In geodesy, point or terrain

" as an irregular, physically defined surface. Height systems in use are:

1. Orthometric heights
2. Dynamic heights
3. Geopotential heights
4. Normal heights

Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in

One can relate these heights through the

Satellite positioning receivers

typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid.

Geodetic datums

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 (

), the Kronstadt datum, the Trieste datum, and numerous others.

In both mathematics and geodesy, a coordinate system is a "coordinate system" per 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".^[12]

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2024) (Learn how and when to remove this message)

GPS Block IIA satellite orbits over the Earth

.

Navigation device, Apollo program

General

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

, 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

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 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.

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2024) (Learn how and when to remove this message)

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 equations 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.

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).

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).
• 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 (precessing and nutating) instantaneous spin axis extended northward to intersect the celestial sphere. (Similarly for the south celestial pole.)
• Celestial equator: the (instantaneous) intersection of Earth's equatorial plane with the celestial sphere.
• Meridian plane: any plane perpendicular to the celestial equator and containing the celestial poles.
• Local meridian: the plane which contains the direction to the zenith and the celestial pole.

Measurements

Further information: Satellite geodesy, Geodetic astronomy, Surveying, Gravimetry, and Levelling

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2024) (Learn how and when to remove this message)

The reference surface (level) used to determine height differences and height reference systems is known as

GRS80

reference ellipsoid. As geoid determination improves, one may expect that the use of GPS in height determination shall increase, too.

The

tachymeter determines, electronically or 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 (GIS) databases.

Geodetic GNSS (most commonly

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

artificial satellites

, are employed.

Newtonian constant of gravitation

.

In the future, gravity and altitude might become measurable using the special-relativistic concept of time dilation as gauged by optical clocks.

Units and measures on the ellipsoid

Further information: Geodetic coordinates

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2024) (Learn how and when to remove this message)

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 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

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^[13]
• The episodic motion of tectonic origin, especially close to
  fault lines
• Periodic effects due to tides and tidal loading^[14]
• 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^[15]
• Length-of-day variability^[16]
• Earth's center-of-mass (geocenter) variations^[17]
• Anthropogenic movements such as reservoir construction or petroleum or water extraction

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^[18] realized by the stations belonging to the Global Geodetic Observing System (GGOS^[19]).

Techniques for studying geodynamic phenomena on global scales include:

• Satellite positioning by GPS, GLONASS, Galileo, and BeiDou
• Very-long-baseline interferometry (VLBI)
• laser ranging
  (LLR)
• 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 article: List of geodesists

See also: Notable surveyors

See also

Main article: Outline of metrology and measurement § Geodesy

Main category: Geodesy

• Earth system science – Scientific study of the Earth's spheres and their natural integrated systems
• List of geodesists – Notable geodesists
• Geomatics engineering
   – Geographic data disciplinePages displaying short descriptions of redirect targets
• History of geophysics
• Geodynamics – Study of dynamics of the Earth
• Planetary science – Science of planets and planetary systems

Fundamentals

• 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 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

• Council of European Geodetic Surveyors [fr]
• EPSG Geodetic Parameter Dataset
• Meridian arc
• Surveying

References

1. Cambridge English Dictionary
   . Retrieved 2024-06-08.
2. ^
   ISBN 978-0-444-87775-8
   . ... 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.
3. ^ What is Geodesy? (PDF). International Association of Geodesy.
4. ^ US Department of Commerce, National Oceanic and Atmospheric Administration. "What is geodesy?". oceanservice.noaa.gov. Retrieved 2024-06-09.
5. ^ "Geodesy". LSU Center for GeoInformatics. Retrieved 2024-06-08.
6. ^ "Geodesy Definition, Characteristics & Branches". Study.com. Retrieved 2024-06-08. 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.
7. ^ "Geodetic Surveyors". Occupational Information Network. 2020-11-26. Retrieved 2022-01-28.
8. ISBN 978-1-317-56822-3
   . Retrieved 6 December 2024.
9. ISBN 978-1-60608-741-1
   . Retrieved 6 December 2024.
10. ISBN 978-981-12-3712-6
    . Retrieved 6 December 2024.
11. ISSN 0956-540X
    .
12. ^ (ISO 19111: Spatial referencing by coordinates).
13. doi:10.1093/gji/ggx136
    .
14. S2CID 56017067. Archived
    (PDF) from the original on 2022-03-18.
15. doi:10.1007/s00190-020-01453-w
    .
16. doi:10.1007/s10291-020-00989-w
    .
17. doi:10.1007/s10291-020-01037-3
    .
18. doi:10.1007/s00190-019-01307-0
    .
19. doi:10.24425/gac.2019.126090
    .
20. S2CID 127408940
    .

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

External links

Wikimedia Commons has media related to Geodesy.

Geodesy at Wikibooks Media related to Geodesy at Wikimedia Commons

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