Geodesy (pronounced /dʒiːˈɒdɪsi/^[1]), also called geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. ||-||-||} Ostend  (  Oostende, French and German Ostende) is a Belgian City and municipality located in the Flemish The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those Munich (München; Minga is the capital city of Bavaria, Germany. Lithography is a method for Printing using a plate or stone with a completely smooth surface Bavaria ( German:, with an area of 70553 Km² (27241 square miles and almost 12 Earth science (also known as geoscience, the geosciences or the Earth Sciences) is an all-embracing term for the Sciences related to the planet EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 A gravitational field is a model used within Physics to explain how gravity exists in the universe Besides the Earth's gravitational field, geodesists also study geodynamical phenomena such as crustal motion, tides, and polar motion. Geodynamics is a subfield of Geophysics dealing with dynamics of the Earth masses In Geology, a crust is the outermost solid shell of a planet or moon Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood Polar motion is the movement of Earth 's rotation axis across its surface For this they design global and national Control networks, using Space and terrestrial techniques while relying on datums and coordinate systems. A Control network or simply Control, is a set of reference-points of known Geospatial Coordinates. In Geodesy, the term Space techniques includes modern measuring methods which make use of artificial Satellites interplanetary Space probes and of Quasars This article describes a concept from Surveying and Geodesy. For other meanings see Datum (disambiguation. In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point

Contents 1 Definition 2 History 3 Geoid and reference ellipsoid 4 Coordinate systems in space 4.1 Coordinate systems in the plane 5 Heights 6 Geodetic data 6.1 A note on terminology 7 Point positioning 8 Geodetic problems 8.1 First geodetic problem 8.2 Second (inverse) geodetic problem 9 Geodetic observational concepts 10 Geodetic measurements 11 Units and measures on the ellipsoid 12 Temporal change 13 Famous geodesists 13.1 Mathematical Geodesists before 1900 13.2 20th century 14 International organizations 15 Governmental agencies 16 See also 17 Notes 18 References 19 External links

Definition

Geodesy (from Greek Γεωδαισία lit. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly division of the Earth) is primarily concerned with positioning within the temporally varying gravity field. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Somewhat obsolete nowadays, geodesy in the German speaking world is divided into "Higher Geodesy" ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the Earth on the global scale, and "Practical Geodesy" or "Engineering Geodesy" ("Ingenieurgeodäsie"), which is concerned with measuring specific parts or regions of the Earth, and which includes surveying. The German language (de ''Deutsch'') is a West Germanic language and one of the world's major languages. Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between

The shape of the Earth is to a large extent the result of its rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates and of vulcanism, resisted by the Earth's gravity field. Plate tectonics and hotspots Divergent plate boundaries At the Gravitation is a natural Phenomenon by which objects with Mass attract one another This applies to the solid surface, the liquid surface (dynamic sea surface topography) and the Earth's atmosphere. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five For this reason, the study of the Earth's gravity field is called physical geodesy by some. A gravitational field is a model used within Physics to explain how gravity exists in the universe Physical geodesy is the study of the physical properties of the Gravity field of the Earth the Geopotential, with a view to their application in Geodesy

History

Main article: History of geodesy

Geoid and reference ellipsoid

The geoid is essentially the figure of the Earth abstracted from its topographical features. See also the main article on Geodesy. Humanity has always been interested in the Earth. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface and continued under the continental masses. The geoid, unlike ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. The geometrical separation between it and the reference ellipsoid is called the geoidal undulation. It varies globally between ±110 m.

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. In Geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the Geoid, the truer Figure of the Earth, or other planetary body The quantity f = (a−b)/a, where b is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the Earth (dynamical flattening, symbol J₂) 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 (GRS80) posited a 6,378,137 m semi-major axis and a 1:298. GRS 80, or Geodetic Reference System 1980, is a Geodetic reference system consisting of a global Reference ellipsoid and a Gravity field model 257 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG). The International Union of Geodesy and Geophysics, or IUGG, is a Non-governmental organisation dedicated to the scientific study of the Earth using It is essentially the basis for geodetic positioning by the Global Positioning System and is thus also in extremely widespread use outside the geodetic community.

The numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid.

Coordinate systems in space

See also: Geodetic system

The locations of points in three-dimensional space are most conveniently described by three cartesian or rectangular coordinates, X,Y and Z. Geodetic systems or geodetic data are used in Geodesy, Navigation, Surveying by Cartographers and Satellite navigation systems In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane Since the advent of satellite positioning, such coordinate systems are typically geocentric: the Z axis is aligned with the Earth's (conventional or instantaneous) rotation axis. In Astronomy, the geocentric model of the Universe is the superseded theory that the Earth is the center of the universe and other

Prior to satellite geodesy era, the coordinate systems associated with a geodetic datum attempted to be geocentric, but their origins differed from the geocentre by hundreds of metres, due to regional deviations in the direction of the plumbline (vertical). Satellite geodesy is the measurement of the form and dimensions of the Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of satellite This article describes a concept from Surveying and Geodesy. For other meanings see Datum (disambiguation. In Astronomy, the geocentric model of the Universe is the superseded theory that the Earth is the center of the universe and other A plumb-bob or a plummet is a weight with a pointed tip on the bottom that is suspended from a string and used as a vertical reference line These regional geodetic datums, such as ED50 (European Datum 1950) or NAD83 (North American Datum 1983) have ellipsoids associated with them that are regional 'best fits' to the geoids within their areas of validity, minimising the deflections of the vertical over these areas. ED 50 ( European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of Geodetic networks The North American Datum is the official datum used for the primary Geodetic network in North America The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through

It is only because GPS satellites orbit about the geocentre, 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. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth

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

1. 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
2. Co-rotating, also ECEF ("Earth Centred, Earth Fixed"), where the axes are attached to the solid body of the Earth. In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest The fixed stars (from the Latin stellae fixae) are celestial objects that do not seem to move in relation to the other stars of the night sky A gyroscope is a device for measuring or maintaining orientation, based on the principles of Angular momentum. An equinox is the event of the Sun passing over the Earth's equator in its annual cycle The X axis lies within the Greenwich observatory's meridian plane. The Prime Meridian is the meridian (line of Longitude) at which longitude is defined to be 0° This article is about the geographical concept For other uses of the word see Meridian.

The coordinate transformation between these two systems is described to good approximation by (apparent) sidereal time, which takes into account variations in the Earth's axial rotation (length-of-day variations). Sidereal time is a measure of the position of the Earth in its rotation around its axis or time measured by the apparent Diurnal motion of the Vernal equinox A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the A more accurate description also takes polar motion into account, a phenomenon closely monitored by geodesists. Polar motion is the movement of Earth 's rotation axis across its surface

Coordinate systems in the plane

In surveying and mapping, important fields of application of geodesy, two general types of coordinate systems are used in the plane:

1. 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;
2. Rectangular, points are defined by distances from two perpendicular axes called x and y. Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between 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. A map projection is any method of representing the Surface of a sphere or other shape on a plane. It is not possible to map the curved surface of the 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. In Mathematics, a conformal map is a function which preserves Angles In the most common case the function is between domains in the Complex plane

An example of such a projection is UTM (Universal Transverse Mercator). The Universal Transverse Mercator ( UTM) Coordinate system is a grid-based method of specifying locations on the surface of the Earth 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 is given by:

Heights

In geodesy, point or terrain heights are "above sea level", an irregular, physically defined surface. Height is the measurement of vertical Distance, but has two meanings in common use Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface Therefore a height should ideally not be referred to as a coordinate. It is more like a physical quantity, and though it can be tempting to treat height as the vertical coordinate z, in addition to the horizontal coordinates x and y, and though this actually is a good approximation of physical reality in small areas, it quickly becomes invalid for regional considerations.

Heights come in the following variants:

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

Each has its advantages and disadvantages. The orthometric height is the distance H along a line of force from a given point P at the physical surface of an object to the Geoid. Normal heights are heights above Sea level, one of several types of heightwhich are all computed slightly differently Geopotential height is a vertical coordinate referenced to Earth's Mean sea level — an adjustment to geometric height ( Elevation above mean sea level using the Both orthometric and normal heights are heights in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m² s⁻²) and not metric. Orthometric and normal heights differ in the precise way in which mean sea level is conceptually continued under the continental masses. The reference surface for orthometric heights is the geoid, an equipotential surface approximating mean sea level. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through

None of these heights is in any way related to geodetic or ellipsoidial heights, which express the height of a point above the reference ellipsoid. In Geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the Geoid, the truer Figure of the Earth, or other planetary body Satellite positioning receivers typically provide ellipsoidal heights, unless they are fitted with special conversion software based on a model of the geoid. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through

Geodetic data

Because geodetic point coordinates (and heights) are always obtained in a system that has been constructed itself using real observations, geodesists introduce the concept of a geodetic datum: a physical realization of a coordinate system used for describing point locations. The realization is the result of choosing conventional coordinate values for one or more datum points.

In the case of height datums, it suffices to choose one datum point: the reference bench mark, typically a tide gauge at the shore. Thus we have vertical datums like the NAP (Normaal Amsterdams Peil), the North American Vertical Datum 1988 (NAVD88), the Kronstadt datum, the Trieste datum, and so on. Normaal Amsterdams Peil (NAP or Amsterdam Ordnance Datum is a vertical datum in use in large parts of Western Europe

In case of plane or spatial coordinates, we typically need several datum points. A regional, ellipsoidal datum like ED50 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. ED 50 ( European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of Geodetic networks The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through Also see Potsdam New York (in the USA For the Potsdam Conference see Potsdam Conference. 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 datums, 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. The Helmert transformation (named after Friedrich Robert Helmert, 1843&ndash1917 also called a seven-parameter transformation) is a transformation method within

A note on terminology

In the abstract, a coordinate system as used in mathematics and geodesy is, e. g. , in ISO terminology, referred to as a coordinate system. International geodetic organizations like the IERS (International Earth Rotation and Reference Systems Service) speak of a reference system. "IERS" redirects here for other uses see IERS (disambiguation The International Earth Rotation and Reference Systems Service is

When these coordinates are realized by choosing datum points and fixing a geodetic datum, ISO uses the terminology coordinate reference system, while IERS speaks of a reference frame. A datum transformation again is referred to by ISO as a coordinate transformation. (ISO 19111: Spatial referencing by coordinates).

Point positioning

Point positioning is the determination of the coordinates of a point on land, at sea, or in space with respect to a coordinate system. Point position is solved by computation from measurements linking the known positions of terrestrial or extraterrestrial points with the unknown terrestrial position. This may involve transformations between or among astronomical and terrestrial coordinate systems.

The known points used for point positioning can be triangulation points of a higher order network, or GPS satellites. In Trigonometry and Geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth

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 red and white poles, are tied. In Geometry a polygon (ˈpɒlɨɡɒn ˈpɒliɡɒn is traditionally a plane figure that is bounded by a closed path or circuit

Nowadays all but special measurements (e. g. , underground or high precision engineering measurements) are performed with GPS. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth 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. "IERS" redirects here for other uses see IERS (disambiguation The International Earth Rotation and Reference Systems Service is

For surveying mappings, frequently Real Time Kinematic GPS is employed, tying in the unknown points with known terrestrial points close by in real time. Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between Real Time Kinematic (RTK Satellite navigation is a technique used in Land survey and in Hydrographic survey based on the use of carrier phase measurements

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 the national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements to.

Geodetic problems

In geometric geodesy, two standard problems exist:

First 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. Azimuth ( is a mathematical concept defined as the angle usually measured in degrees (° between a reference plane and a point.

Second (inverse) geodetic problem

Given two points, determine the azimuth and length of the line (straight line, arc or geodesic) that connects them.

In the case of plane geometry (valid for small areas on the Earth's surface) the solutions to both problems reduce to simple trigonometry. Circle-trig6svg|300px|thumb|right|All of the Trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. On the sphere, the solution is significantly more complex, e. g. , in the inverse problem the azimuths will differ between the two end points of the connecting great circle, arc, i. A great circle is a Circle on the surface of a Sphere that has the same circumference as the sphere dividing the sphere into two equal Hemispheres. e. the geodesic.

On the ellipsoid of revolution, solutions in closed form do not exist, so rapidly converging series expansions have traditionally been used, such as Vincenty's formulae.

In the general case, the solution is called the geodesic for the surface considered. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces It may be nonexistent or non-unique. The differential equations for the geodesic can be solved numerically, e. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces g. , in MATLAB. MATLAB is a numerical computing environment and Programming language.

Geodetic observational concepts

Here we define some basic observational concepts, like angles and coordinates, defined in geodesy (and astronomy as well), mostly from the viewpoint of the local observer.

• The plumbline or vertical is the direction of local gravity, or the line that results by following it. A plumb-bob or a plummet is a weight with a pointed tip on the bottom that is suspended from a string and used as a vertical reference line It is slightly curved.

• The zenith is the point on the celestial sphere where the direction of the gravity vector in a point, extended upwards, intersects it. In broad terms the zenith is the direction pointing directly above a particular location ( Perpendicular, Orthogonal) In Astronomy and Navigation, the celestial sphere is an imaginary rotating Sphere of "gigantic Radius " More correct is to call it a <direction> rather than a point.

• The nadir is the opposite point (or rather, direction), where the direction of gravity extended downward intersects the (invisible) celestial sphere. The nadir (from Arabic ندير nadeer نظير nathir, "opposite" is the astronomical term for the point directly

• The celestial horizon is a plane perpendicular to a point's gravity vector.

• Azimuth is the direction angle within the plane of the horizon, typically counted clockwise from the North (in geodesy and astronomy) or South (in France). Azimuth ( is a mathematical concept defined as the angle usually measured in degrees (° between a reference plane and a point.

• Elevation is the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90 degrees minus elevation. The elevation of a Geographic location is its height above a fixed reference point often the mean sea level.

• Local topocentric coordinates are azimuth (direction angle within the plane of the horizon) and elevation angle (or zenith angle) and distance.

• The North celestial pole is the extension of the Earth's (precessing and nutating) instantaneous spin axis extended Northward to intersect the celestial sphere. The north and south celestial poles are the two imaginary points in the sky where the Earth's Axis of rotation, "infinitely extended" intersects the Precession refers to a change in the direction of the axis of a rotating object Nutation is a slight irregular motion (etymologically a "nodding" in the Axis of rotation of a largely axially symmetric object such as a Gyroscope (Similarly for the South celestial pole. )

• The celestial equator is the intersection of the (instantaneous) Earth equatorial plane with the celestial sphere.

• A meridian plane is any plane perpendicular to the celestial equator and containing the celestial poles. This article is about the geographical concept For other uses of the word see Meridian.

• The local meridian is the plane containing the direction to the zenith and the direction to the celestial pole.

Geodetic measurements

The level is used for determining height differences and height reference systems, commonly referred to mean sea level. LEVEL is a Computer and video games Magazine originating in the Czech Republic with branches in Romania and Turkey Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface The traditional spirit level produces these practically most useful heights above sea level directly; the more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid, as GPS only gives heights above the GRS80 reference ellipsoid. A spirit level or bubble level is an instrument designed to indicate whether a surface is Level or Plumb. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through GRS 80, or Geodetic Reference System 1980, is a Geodetic reference system consisting of a global Reference ellipsoid and a Gravity field model As geoid knowledge accumulates, one may expect use of GPS heighting to spread.

The theodolite is used to measure horizontal and vertical angles to target points. A theodolite ( is an instrument for measuring both horizontal and vertical Angles as used in Triangulation networks These angles are referred to the local vertical. The tacheometer additionally determines, electronically or electro-optically, the distance to target, and is highly automated to even robotic in its operations. A tachymeter or tacheometer is a kind of Theodolite used for rapid Measurements and determines electronically or electro-optically the distance to target The method of free station position is widely used.

For local detail surveys, tacheometers are commonly employed although the old-fashioned rectangular technique using angle prism and steel tape is still an inexpensive alternative. Real-time kinematic (RTK) GPS techniques are used as well. Data collected are tagged and recorded digitally for entry into a Geographic Information System (GIS) database. A Computer Database is a structured collection of records or data that is stored in a computer system

Geodetic GPS receivers produce directly three-dimensional coordinates in a geocentric coordinate frame. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth In Astronomy, the geocentric model of the Universe is the superseded theory that the Earth is the center of the universe and other Such a frame is, e. g. , WGS84, or the frames that are regularly produced and published by the International Earth Rotation and Reference Systems Service (IERS). The World Geodetic System defines a reference frame for the earth for use in Geodesy and Navigation. "IERS" redirects here for other uses see IERS (disambiguation The International Earth Rotation and Reference Systems Service is

GPS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. For Planet-wide geodetic surveys, previously impossible, we can still mention Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR) and Very Long Baseline Interferometry (VLBI) techniques. In satellite laser ranging ( SLR) a global network of observation stations measure the round trip time of flight of ultrashort pulses of Light to Satellites The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Very Long Baseline Interferometry (VLBI is a type of astronomical interferometry used in Radio astronomy. All these techniques also serve to monitor Earth rotation irregularities as well as plate tectonic motions.

Gravity is measured using gravimeters. Gravitation is a natural Phenomenon by which objects with Mass attract one another Gravimetry#How_gravity_is_measured A gravimeter or Gravitometer, is an instrument used in Gravimetry for measuring the local Gravitational field. Basically, there are two kinds of gravimeters. Absolute gravimeters, which nowadays can also be used in the field, are based directly on measuring the acceleration of free fall (for example, of a reflecting prism in a vacuum tube). They are used for establishing the vertical geospatial control. Most common relative gravimeters are spring based. They are used in gravity surveys over large areas for establishing the figure of the geoid over these areas. Most accurate relative gravimeters are superconducting gravimeters, and these are sensitive to one thousandth of one billionth of the Earth surface gravity. Twenty-some superconducting gravimeters are used worldwide for studying Earth tides, rotation, interior, and ocean and atmospheric loading, as well as for verifying the Newtonian constant of gravitation. Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. Gravitation is a natural Phenomenon by which objects with Mass attract one another

Units and measures on the ellipsoid

Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement They are angles, not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. In Geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the Geoid, the truer Figure of the Earth, or other planetary body This is approximately the same as the direction of the plumbline, i. e. , local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination - measuring the direction of the plumbline by astronomical means - works fairly well provided an ellipsoidal model of the figure of the Earth is used.

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 as is the nautical mile.

A metre was originally defined as the 40-millionth part of the length of a meridian (the target wasn't quite reached in actual implementation, so that is off by 0. 02% in the current definitions). This means that one kilometre is roughly equal to (1/40,000) * 360 * 60 meridional minutes of arc, which equals 0. 54 nautical mile, though this is not exact because the two units are defined on different bases (the international nautical mile is defined as exactly 1,852 m, corresponding to a rounding of 1000/0. 54 m to four digits).

Temporal change

In geodesy, temporal change can be studied by a variety of techniques. Points on the Earth's surface change their location due to a variety of mechanisms:

• Continental plate motion, plate tectonics
• Episodic motion of tectonic origin, esp. Plate tectonics (from Greek τέκτων tektōn "builder" or "mason" describes the large scale motions of Earth 's Lithosphere close to fault lines
• Periodic effects due to Earth tides
• Postglacial land uplift due to isostatic adjustment
• Various anthropogenic movements due to, for instance, petroleum or water extraction or reservoir construction. "Glacial" and "Glaciation" redirect here For the geological periods see Glacial period. Petroleum ( L petroleum, from Greek πετρέλαιον, lit

The science of studying deformations and motions of the Earth's crust and the solid Earth as a whole is called geodynamics. Geodynamics is a subfield of Geophysics dealing with dynamics of the Earth masses Often, study of the Earth's irregular rotation is also included in its definition.

Techniques for studying geodynamic phenomena on the global scale include:

• satellite positioning by GPS and other such systems,
• Very Long Baseline Interferometry (VLBI)
• satellite and lunar laser ranging
• Regionally and locally, precise levelling,
• precise tacheometers,
• monitoring of gravity change,
• Interferometric synthetic aperture radar (InSAR) using satellite images, etc. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth Very Long Baseline Interferometry (VLBI is a type of astronomical interferometry used in Radio astronomy. LIDAR ( Li ght D etection a nd R anging is an optical remote sensing technology that measures properties of scattered light to find range and/or Interferometric synthetic aperture radar, also abbreviated InSAR or IfSAR, is a Radar technique used in Geodesy and Remote sensing

Famous geodesists

Mathematical Geodesists before 1900

• Abu Rayhan Biruni 973-1048, Khwarezm (Iran/Persia)^[2][3]
• Sir George Biddell Airy 1801-1892, Cambridge & London
• Muhammad al-Idrisi 1100-1166, (Arabia & Sicily)
• Al-Ma'mun 786-833, Baghdad (Iraq/Mesopotamia)
• Johann Jacob Baeyer 1794-1885, Berlin (Germany)
• Karl Maximilian von Bauernfeind, Munich (Germany)
• Friedrich Wilhelm Bessel, Königsberg (Germany)
• Roger Joseph Boscovich, Rome/ Berlin/ Paris
• Pierre Bouguer 1698-1758, (France & Peru)
• Heinrich Bruns 1848-1919, Berlin (Germany)
• Alexis Claude Clairaut 1713-1765 (France)
• Alexander Ross Clarke, London (England)
• Loránd Eötvös 1848-1919 (Hungary)
• Eratosthenes, Alexandria (Greece & Egypt)
• Sir George Everest 1830-1843 (England & India)
• Hervé Faye 1814-1902 (France)
• Abel Foullon (France)
• Carl Friedrich Gauß 1777-1855, Göttingen (Germany)
• Friedrich Robert Helmert, Potsdam (Germany)
• Hipparchos, Nicosia (Greece)
• Christiaan Huygens 1629-1695 (Netherlands)
• Jean Henri Lambert 1728-1777 (France)
• Pierre-Simon Laplace 1749-1827, Paris (France)
• Adrien Marie Legendre 1752-1833, Paris (France)
• Johann Benedikt Listing 1808-1882 (Germany)
• Pierre de Maupertuis 1698-1759 (France)
• Gerhard Mercator 1512-1594 (Belgium & Germany)
• Friedrich H. Khwarezm were a series of States centered on the Amu Darya River delta of the Sir George Biddell Airy FRS (27 July 1801&ndash2 January 1892 was an English Mathematician and Astronomer, Astronomer Royal Abu Abd Allah Muhammad al-Idrisi al-Qurtubi al-Hasani al-Sabti or simply El Idrisi ( Arabic أبو عبد الله محمد الإدريسي Latin: The Arabian Peninsula (in Arabic: شبه الجزيرة العربية šibh al-jazīra al-ʻarabīya or جزيرة العرب jazīrat al-ʻarab) Abu Jafar al-Ma'mun ibn Harun (also spelled Almamon and el-Mâmoûn) ( September 14, 786 &ndash August 9, 833) (المأمون Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous Mesopotamia (from the Greek meaning "land between the rivers" is an area geographically located between the Tigris and Euphrates rivers largely corresponding Friedrich Wilhelm Bessel (22 July 1784 &ndash 17 March 1846 was a German Mathematician, Astronomer, and systematizer of the Bessel functions Pierre Bouguer ( February 16, 1698 &ndash August 15, 1758) was a French Mathematician and astronomer Alexis Claude de Clairault (or Clairaut) ( May 3, 1713 – May 17, 1765) was a French Mathematician and Alexander Ross Clarke (1828-1914 was a British geodesist primarily remembered for his work defining different Reference ellipsoids approximating the shape of the Geoid Baron Loránd von Eötvös, more commonly called Baron Roland von Eötvös in the English literature (in Hungarian Vásárosnaményi Báró Eötvös Loránd, or Eratosthenes of Cyrene ( Greek; 276 BC - 194 BC was a Greek Mathematician, Poet, athlete, Geographer and Colonel Sir George Everest ( 4 July, 1790 &ndash 1 December, 1866) was a Welsh surveyor, Geographer and Hervé Auguste Étienne Albans Faye ( October 3, 1814 &ndash July 4, 1902) was a French Astronomer, born at Saint-Benoît-du-Sault Abel Foullon; France ( 1513 - 1563 or 1565) was an author director of the Mint for Henry II of France and also an engineer to the king of France Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German Friedrich Robert Helmert ( July 31 1843 &ndash June 15 1917) was a German Geodesist and an important writer on the theory Christiaan Huygens (ˈhaɪgənz in English ˈhœyɣəns in Dutch) ( April 14, 1629 &ndash July 8, 1695) was a Dutch Adrien-Marie Legendre ( September 18 1752 – January 10 1833) was a French Mathematician. Pierre-Louis Moreau de Maupertuis ( July 17, 1698 &ndash July 27, 1759) was a French Mathematician, Philosopher A separate article is about the mathematician Nicholas Mercator. C. Paschen, Schwerin (Germany)
• Charles S. Peirce 1839-1914 (United States)
• Henri Poincaré, Paris (France)
• J. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher Jules Henri Poincaré ( 29 April 1854 &ndash 17 July 1912) (ˈʒyl ɑ̃ˈʁi pwɛ̃kaˈʁe was a French Mathematician H. Pratt 1809-1871, London (England)
• Posidonius, Alexandria (Greece & Egypt)
• Ptolemäus, Alexandria (Greece & Egypt)
• Regiomontanus (Germany/Austria)
• Georg von Reichenbach 1771-1826, Bavaria (Germany)
• Heinrich Christian Schumacher 1780-1850 (Germany & Estonia)
• Snellius (Willebrord Snel van Royen) 1580-1626, Leiden (Netherlands)
• Johann Georg von Soldner 1776-1833, Munich (Germany)
• George Gabriel Stokes (England)
• Friedrich Georg Wilhelm Struve 1793-1864, Dorpat and Pulkowa/St. Posidonius ( Greek: Ποσειδώνιος / Poseidonios "of Apameia " (ὁ Απαμεύς or "of Rhodes " (ὁ Ρόδιος (ca Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca Johannes Müller von Königsberg ( June 6, 1436 &ndash July 6, 1476) known by his Latin Pseudonym Regiomontanus Georg Friedrich von Reichenbach ( 1771-08-21 - 1826-05-21) German Scientific instrument maker was born at Durlach in Baden Heinrich Christian Schumacher ( September 3, 1780 &ndash December 28, 1850) was a German Astronomer. “Snellius” redirects here For the lunar crater named Snellius see Snellius (crater. Johann Georg von Soldner ( 16 July 1776 - 13 May 1833) was a German Physicist, Mathematician and Astronomer Sir George Gabriel Stokes 1st Baronet FRS ( 13 August 1819 &ndash 1 February 1903) was a mathematician and physicist Friedrich Georg Wilhelm von Struve (Vasily Yakovlevich Struve ( April 15, 1793 &ndash November 23, 1864 ( Julian calendar -Petersburg (Russia)

20th century

• Arne Bjerhammar,KTH, Stockholm (Sweden)
• W. Bowie 1872-1940 (USA)
• John Fillmore Hayford (USA)
• Friedrich Hopfner, Vienna (Austria)
• Harold Jeffreys, London (England)
• John A. O'Keefe 1916-2000 (USA)
• Karl-Rudolf Koch, Bonn (Germany)
• Mikhail Sergeevich Molodenskii 1909-1991 (Russia)
• Hellmut Schmid, (Switzerland)
• Petr Vaníček, Fredericton (Canada)
• Yrjö Väisälä 1889-1971, (Finland)
• Felix Andries Vening-Meinesz 1887-1966 (Netherlands)
• Thaddeus Vincenty, (Poland)
• Alfred Wegener 1880-1930, (Germany & Greenland)

International organizations

• International Association of Geodesy (IAG)
• International Union of Geodesy and Geophysics (IUGG)
• Fédération Internationale des Géomètres (FIG)
• European Petroleum Survey Group (EPSG) (which despite being officially disbanded in 2005 continues to refine a well tested set of Geodetic Parameters)

Governmental agencies

• National Geodetic Survey (NGS), Silver Spring MD, USA
• National Geospatial-Intelligence Agency (NGA), Bethesda MD, USA (Previously National Imagery and Mapping Agency NIMA, previously Defense Mapping Agency DMA)
• U.S. Geological Survey (USGS), Reston VA, USA
• Institut Géographique National (IGN), Saint-Mandé, France
• Bundesamt für Kartographie und Geodäsie (BKG), Frankfurt a. Arne Bjerhammar (born 1917 is a Swedish geodesist. He is doctor at Kungliga Tekniska Högskolan (KTH in Stockholm. The Royal Institute of Technology or Kungliga Tekniska högskolan ( KTH) is a University in Stockholm, Sweden. ('stɔkhɔlm is Sweden 's Capital and its largest City. It is the site of the national Swedish government, the parliament, and the William Bowie BS CE MA ( May 6, 1872 &ndash August 25, 1940) was an American geodetic engineer John Fillmore Hayford ( May 19, 1868 – March 10, 1925) was an eminent United States Geodesist. Friedrich Hopfner ( 28 October 1881 &mdash 5 September 1949) was an Austrian Geodesist, Geophysicist and Planetary Vienna ( in Wien; see also other names) is the Capital of Austria, and is also one of the nine States of Austria. Sir Harold Jeffreys ( 22 April 1891 &ndash 18 March 1989) was a mathematician statistician geophysicist and astronomer London ( ˈlʌndən is the capital and largest urban area in the United Kingdom. John Aloysius O'Keefe (1916 – 2000 was a planetary scientist with the National Aeronautics and Space Administration (NASA from 1958 to 1995 Karl-Rudolf Koch (* 1935) is a German Geodesist and professor at the University of Bonn (FRG Bonn is the 19th largest city in Germany. Located about 20 kilometres south of Cologne on the river Rhine in the Federal State of North Rhine-Westphalia Mikhail Sergeevich Molodenskii (Михаил Сергеевич Молоденский - November 12 1991) was a famous Soviet physical geodesist Hellmut H Schmid (1914-1998 was Professor of Geodesy and Photogrammetry on the ETH Zürich (Switzerland where he emerited in 1985 Petr Vaníček (born 1935 in Sušice, Czechoslovakia, today in Czech Republic) is a Czech Fredericton (pronounced ˈfrɛdrɨktɨn is the capital of the Canadian province of New Brunswick, by virtue of the provincial Yrjö Väisälä ( ( September 6, 1891 – July 21, 1971) was a Finnish Astronomer and Physicist. Felix Andries Vening Meinesz ( The Hague July 30 1887 - Amersfoort August 10 1966) was a Dutch geophysicist and Thaddeus Vincenty (born Tadeusz Szpila 27 October 1920 in Grodzisko, Lwów Voivodship, Poland; died 6 March 2002 Alfred Lothar Wegener ( November 1, 1880 – November 2 or 3 1930 was a German Scientist and Meteorologist. European Petroleum Survey Group or EPSG ( 1986 – 2005) was a scientific organization with ties to the European Petroleum industry consisting Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals The National Geospatial-Intelligence Agency ( NGA) is an agency of the United States Government with the primary mission of collection analysis and The United States Geological Survey ( USGS) is a scientific agency of the United States government. M. , Germany (Previously Institut für Angewandte Geodäsie, IfAG)
• Central Research Institute for Geodesy, Remote Sensing and Cartography (CNIIGAIK), Moscow, Russia
• Geodetic Survey Division, Natural Resources Canada, Ottawa, Canada
• Geoscience Australia, Australian Federal Agency
• Finnish Geodetic Institute (FGI), Masala, Finland
• Portuguese Geographic Institute (IGEO), Lisbon, Portugal
• Brazilian Institute for Geography and Statistics - IBGE
• Spanish National Geographic Institute (IGN), Madrid, Spain
• Land Information New Zealand.

Note: This list is still largely incomplete.

See also

Notes

References

• 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).
• Vaníček P. and E. J. Krakiwsky, Geodesy: the Concepts, pp. 714, Elsevier, 1986.
• 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

• International Association of Geodesy (IAG).
• The Geodesy Page.
• Geodesy and Geomatics Home Page
• Welcome to Geodesy
• MapRef.org: The Collection of Map Projections and Reference Systems for Europe
• Geodesy on the World Wide Web
• Pennsylvania Geospatial Data Sharing Standard - Geodesy and Geodetic Monumentation
• References on Absolute Gravimeters
• Geodesy tutorial at University of New Brunswick
• Vincenty's Direct and Inverse Solutions of Geodesics on the Ellipsoid, in JavaScript
• Vincenty's Solution of Geodesics on the Ellipsoid, in C#
• Vincenty's Solution of Geodesics on the Ellipsoid, in Java
• EarthScope Project
• UNAVCO - EarthScope - Plate Boundary Observatory
• Polish Internet Informant of Geodesy

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