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54-442: This facility was closed in spring 2003 43°28′39″N 141°59′36″E  /  43.477593°N 141.993278°E  / 43.477593; 141.993278 https://www.jstage.jst.go.jp/article/bss/23/2/23_2_85/_pdf This Hokkaidō location article is a stub . You can help Misplaced Pages by expanding it . This geodesy -related article is a stub . You can help Misplaced Pages by expanding it . Geodesy Geodesy or geodetics

108-660: 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 quasars , lunar laser ranging (LLR) measuring distances to prisms on

162-406: A "reference frame" for the same. The ISO term for a datum transformation again is a "coordinate transformation". 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

216-566: 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 GNSS continuously operating reference stations or triangulation points of

270-420: A country, usually documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements. In geometrical geodesy, there are two main problems: 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

324-421: A discipline of applied mathematics . 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 . Geodesy began in pre-scientific antiquity , so

378-418: 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 traverses ( polygons ) into which local mapping and surveying measurements, usually collected using a measuring tape, a corner prism , and the red-and-white poles, are tied. Commonly used nowadays

432-416: A large extent, Earth's shape is the result of rotation , which causes its equatorial bulge , and the competition of geological processes such as the collision of plates , as well as 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

486-513: 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 ),

540-482: A projection is UTM ( Universal Transverse Mercator ). Within the map plane, we have rectangular coordinates x and y . In this case, the north direction used for reference is the map north, not the local north. The difference between the two is called meridian convergence . It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be α and s respectively, then we have The reverse transformation

594-481: A series expansion — see, for example, Vincenty's formulae . 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): 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 ;

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648-543: 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

702-681: A variety of mechanisms: 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 realized by the stations belonging to the Global Geodetic Observing System (GGOS ). Techniques for studying geodynamic phenomena on global scales include: [REDACTED] Geodesy at Wikibooks [REDACTED] Media related to Geodesy at Wikimedia Commons Physical geodesy Physical geodesy

756-454: 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

810-412: Is 9.80665 m/s (32.1740 ft/s ) by definition. This quantity is denoted variously as g n , g e (though this sometimes means the normal gravity at the equator, 9.7803267715 m/s (32.087686258 ft/s )), g 0 , or simply g (which is also used for the variable local value). Due to the irregularity of the Earth's true gravity field, the equilibrium figure of sea water, or

864-470: Is GPS, except for specialized measurements (e.g., in underground or high-precision engineering). The higher-order networks are measured with static GPS , using 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

918-453: Is an oversimplification; in practice the location in space at which γ is evaluated will differ slightly from that where g has been measured.) We thus get These anomalies are called free-air anomalies , and are the ones to be used in the above Stokes equation. In geophysics , these anomalies are often further reduced by removing from them the attraction of the topography , which for a flat, horizontal plate ( Bouguer plate ) of thickness H

972-518: Is called physical geodesy . The geoid essentially is the figure of Earth abstracted from its topographical features. It is an idealized equilibrium surface of seawater , the mean sea level surface in the absence of currents and 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 for solving geometrical problems like point positioning. The geometrical separation between

1026-416: 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: One can intuitively use rectangular coordinates in

1080-467: Is expressed as gravity times distance, m ·s . Travelling one metre in the direction of a gravity vector of strength 1 m·s will increase your potential by 1 m ·s . Again employing G as a multiplier, the units can be changed to joules per kilogram of attracted mass. A more convenient unit is the GPU, or geopotential unit: it equals 10 m ·s . This means that travelling one metre in the vertical direction, i.e.,

1134-411: Is given by The Bouguer reduction to be applied as follows: so-called Bouguer anomalies . Here, Δ g F A {\displaystyle \Delta g_{FA}} is our earlier Δ g {\displaystyle \Delta g} , the free-air anomaly. In case the terrain is not a flat plate (the usual case!) we use for H the local terrain height value but apply

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1188-399: Is given by: In geodesy, point or terrain heights are " above sea level " as an irregular, physically defined surface. Height systems in use are: Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m s ) and not metric. The reference surface is

1242-578: 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). 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

1296-463: 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

1350-447: Is physically realized by tide gauge bench marks on the coasts of different countries and continents, a number of slightly incompatible "near-geoids" will result, with differences of several decimetres to over one metre between them, due to the dynamic sea surface topography . These are referred to as vertical datums or height datums . For every point on Earth, the local direction of gravity or vertical direction , materialized with

1404-421: Is purely geometrical. 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 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 ( GRS 80 ), adopted at

1458-451: Is the science of measuring and representing the geometry , gravity , and spatial orientation of the Earth in temporally varying 3D . It is called planetary geodesy when studying other astronomical bodies , such as planets or circumplanetary systems . Geodesy is an earth science and many consider the study of Earth's shape and gravity to be central to that science. It is also

1512-524: Is the study of the physical properties of Earth's gravity and its potential field (the geopotential ), with a view to their application in geodesy . Traditional geodetic instruments such as theodolites rely on the gravity field for orienting their vertical axis along the local plumb line or local vertical direction with the aid of a spirit level . After that, vertical angles ( zenith angles or, alternatively, elevation angles) are obtained with respect to this local vertical, and horizontal angles in

1566-494: The centrifugal force (from the Earth's rotation ). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm g = ‖ g ‖ {\displaystyle g=\|{\mathit {\mathbf {g} }}\|} . In SI units , this acceleration is expressed in metres per second squared (in symbols, m / s or m·s ) or equivalently in newtons per kilogram (N/kg or N·kg ). Near Earth's surface,

1620-446: 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. One can relate these heights through the geoid undulation concept to ellipsoidal heights (also known as geodetic heights ), representing

1674-414: The geoid , will also be of irregular form. In some places, like west of Ireland , the geoid—mathematical mean sea level—sticks out as much as 100 m above the regular, rotationally symmetric reference ellipsoid of GRS80; in other places, like close to Sri Lanka , it dives under the ellipsoid by nearly the same amount. The separation between the geoid and the reference ellipsoid is called the undulation of

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1728-527: The geoids within their areas of validity, minimizing the deflections of the vertical over these areas. It is only because GPS satellites orbit about the geocenter that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system. Geocentric coordinate systems used in geodesy can be divided naturally into two classes: The coordinate transformation between these two systems to good approximation

1782-643: The plumb line , is perpendicular to the geoid (see astrogeodetic leveling ). Above we already made use of gravity anomalies Δ g {\displaystyle \Delta g} . These are computed as the differences between true (observed) gravity g = ‖ g → ‖ {\displaystyle g=\|{\vec {g}}\|} , and calculated (normal) gravity γ = ‖ γ → ‖ = ‖ ∇ U ‖ {\displaystyle \gamma =\|{\vec {\gamma }}\|=\|\nabla U\|} . (This

1836-702: 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 GPS ) receivers directly produce 3D coordinates in

1890-465: The topographic surface of Earth — is also realizable. The locations of points in 3D space most conveniently are described by three 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 ,

1944-488: 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 —

1998-633: 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

2052-584: 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

2106-700: 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

2160-530: The acceleration due to gravity, accurate to 2 significant figures , is 9.8 m/s (32 ft/s ). This means that, ignoring the effects of air resistance , the speed of an object falling freely will increase by about 9.8 metres per second (32 ft/s) every second. This quantity is sometimes referred to informally as little g (in contrast, the gravitational constant G is referred to as big G ). The precise strength of Earth's gravity varies with location. The agreed-upon value for standard gravity

2214-414: The coordinate systems associated with a geodetic 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 ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to

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2268-454: The direction of the 9.8 m·s ambient gravity, will approximately change your potential by 1 GPU. Which again means that the difference in geopotential, in GPU, of a point with that of sea level can be used as a rough measure of height "above sea level" in metres. The gravity of Earth , denoted by g , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth ) and

2322-476: 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 tides , rotation , interior, oceanic and atmospheric loading, as well as in verifying the Newtonian constant of gravitation . In

2376-401: The future, gravity and altitude might become measurable using the special-relativistic concept of time dilation as gauged by optical clocks . Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles , not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. This direction

2430-443: The geoid , symbol N {\displaystyle N} . The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land. Technically, an equipotential surface of the true geopotential, chosen to coincide (on average) with mean sea level. As mean sea level

2484-412: The geoid and a reference ellipsoid is called geoidal 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 = ⁠ a − b / a ⁠ , where b is the semi-minor axis (polar radius),

2538-399: 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. To

2592-430: The height of a point above the reference ellipsoid . Satellite positioning receivers typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid. 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 ):

2646-405: 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

2700-500: 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,

2754-507: 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

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2808-504: The plane of the local horizon, perpendicular to the vertical. Levelling instruments again are used to obtain geopotential differences between points on the Earth's surface. These can then be expressed as "height" differences by conversion to metric units. Gravity is commonly measured in units of m·s ( metres per second squared). This also can be expressed (multiplying by the gravitational constant G in order to change units) as newtons per kilogram of attracted mass. Potential

2862-422: The sky to a traveler headed South. In 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 , geodesy can refer to either higher geodesy ( höhere Geodäsie or Erdmessung , literally "geomensuration") — concerned with measuring Earth on

2916-462: The very word geodesy comes from the Ancient Greek word γεωδαισία or geodaisia (literally, "division of Earth"). Early ideas about the figure of the Earth held the Earth to be flat and the heavens a physical dome spanning over it. 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

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