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l geodetic techniques and relying on datums and coordinate systems the job title is geodesist or geodetic surveyor 3 contents 1 history 2 definition 3 geoid and reference ellipsoid 4 coordinate systems in space 4 1 coordinate systems in the plane 5 heights 6 geodetic data 7 point positioning 8 geodetic problems 9 observational concepts 10 measurements 11 units and measures on the ellipsoid 12 temporal change 13 notable geodesists 13 1 geodesists before 1900 arranged by date 13 2 20th century geodesists alphabetically arranged 14 see also 15 references 16 further reading 17 external links history edit definition edit the word geodesy comes from the ancient greek word γεωδαισία geodaisia literally division of earth it is primarily concerned with positioning within the temporally varying gravitational field geodesy in the german speaking world is divided into higher geodesy erdmessung or höhere geodäsie which is concerned with measuring earth on the global scale and practical geodesy or engineering geodesy ingenieurgeodäsie which is concerned with measuring specific parts or regions of earth and which includes surveying such geodetic operations are also applied to other astronomical bodies 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 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 edit main articles 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 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 is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning the geometrical separation between the geoid and the reference ellipsoid is called the geoidal undulation it varies globally between 110 m when referred to the grs 80 ellipsoid a reference ellipsoid customarily chosen to be the same size volume as the geoid is described by its semi major axis equatorial radius a and flattening f the quantity f a b a where b is the semi minor axis polar radius is a purely geometrical one the mechanical ellipticity of earth dynamical flattening symbol j 2 can be determined to high precision by observation of satellite orbit perturbations its relationship with the geometrical flattening is indirect the relationship depends on the internal density distribution or in simplest terms the degree of central concentration of mass the 1980 geodetic reference system grs 80 posited a 6 378 137 m semi major axis and a 1 298 257 flattening this system was adopted at the xvii general assembly of the international union of geodesy and geophysics iugg it is essentially the basis for geodetic positioning by the global positioning system gps and is thus also in widespread use outside the geodetic community the numerous systems that countries have used to create maps and charts are becoming obsolete as countries increasingly move to global geocentric reference systems using the grs 80 reference ellipsoid the geoid is realizable meaning it can be consistently located on earth by suitable simple measurements from physical objects like a tide gauge 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 edit main article geodetic system the locations of points in three dimensional space are most conveniently described by three cartesian or rectangular coordinates x y and z since the advent of satellite positioning such coordinate systems are typically geocentric 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 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 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 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 stars or equivalently to the rotation axes of ideal gyroscopes the x axis points to the vernal equinox co rotating also ecef earth centred earth fixed where the axes are attached to the solid body of earth the x axis lies within the greenwich observatory s meridian plane the coordinate transformation between these two systems is described to good approximation by apparent sidereal time 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 edit main article horizontal position a munich archive with lithography plates of maps of bavaria in surveying 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 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 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 x s cos α y s sin α displaystyle begin aligned x s cos alpha y s sin alpha end aligned the reverse transformation is given by s x 2 y 2 α arctan y x displaystyle begin aligned s sqrt x 2 y 2 alpha arctan frac y x end aligned heights edit further information vertical position and vertical datum in geodesy point or terrain heights are above sea level 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 m 2 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 4 these heights can be related to ellipsoidal height also known as geodetic height which express the height of a point above the reference ellipsoid by means of the geoid undulation satellite positioning receivers typically provide ellipsoidal heights unless they are fitted with special conversion software based on a model of the geoid geodetic data edit main article datum transformation 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 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 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 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 5 point positioning edit geodetic control mark example of a deep benchmark 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 points of a higher order network or gps satellites traditionally a hierarchy of networks has been built to allow point positioning within a country highest in the hierarchy were triangulation networks these were densified into networks of traverses polygons into which local mapping surveying measurements usually with measuring tape corner prism and the familiar where red and white poles are tied nowadays all but special measurements e g underground or high precision engineering measurements are performed with gps the higher order networks are measured with static gps using differential measurement to determine vectors between terrestrial points these vectors are then adjusted in traditional network fashion a global polyhedron of permanently operating gps stations under the auspices of the iers 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 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 edit main article geodesics on an ellipsoid solution of the direct and inverse 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 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 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 in the general case the solution is called the geodesic for the surface considered the differential equations for the geodesic can be solved numerically observational concepts edit 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 or vertical the direction of local gravity or the line that results by following it zenith the point on 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...
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