Geodesy

Geodesy

Overview


Geodesy also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, including its gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

, in a three-dimensional time-varying space. Geodesists also study geodynamic
Geodynamics
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and...

al phenomena such as crustal
Crust (geology)
In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle...

 motion, tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s, and polar motion
Polar motion
Polar motion of the earth is the movement of Earth's rotational axis across its surface. This is measured with respect to a reference frame in which the solid Earth is fixed...

. For this they design global and national control network
Control network
In geodesy and surveying a control network or simply control, is a set of reference-points of known geospatial coordinates. The higher-order control points are normally defined in both space and time using global or space techniques, and are used for "lower-order" points to be tied into...

s, using space
Space techniques
In geodesy, the term Space techniques includes modern measuring methods which make use of artificial satellites, interplanetary space probes and of quasars....

 and terrestrial techniques while relying on datums and coordinate system
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...

s.

Geodesy (from Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

 γεωδαισίαgeodaisia, lit.
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Encyclopedia


Geodesy also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, including its gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

, in a three-dimensional time-varying space. Geodesists also study geodynamic
Geodynamics
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and...

al phenomena such as crustal
Crust (geology)
In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle...

 motion, tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s, and polar motion
Polar motion
Polar motion of the earth is the movement of Earth's rotational axis across its surface. This is measured with respect to a reference frame in which the solid Earth is fixed...

. For this they design global and national control network
Control network
In geodesy and surveying a control network or simply control, is a set of reference-points of known geospatial coordinates. The higher-order control points are normally defined in both space and time using global or space techniques, and are used for "lower-order" points to be tied into...

s, using space
Space techniques
In geodesy, the term Space techniques includes modern measuring methods which make use of artificial satellites, interplanetary space probes and of quasars....

 and terrestrial techniques while relying on datums and coordinate system
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...

s.

Definition


Geodesy (from Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

 γεωδαισίαgeodaisia, lit. "division of the Earth") is primarily concerned with positioning within the temporally
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

 varying gravity field. Somewhat obsolete nowadays, geodesy in the German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....

 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
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

.

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 volcanism
Volcano
2. Bedrock3. Conduit 4. Base5. Sill6. Dike7. Layers of ash emitted by the volcano8. Flank| 9. Layers of lava emitted by the volcano10. Throat11. Parasitic cone12. Lava flow13. Vent14. Crater15...

, resisted by the Earth's gravity field. This applies to the solid surface, the liquid surface (dynamic sea surface topography) and the Earth's atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. For this reason, the study of the Earth's gravity field is called physical geodesy
Physical geodesy
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.-Measurement procedure:...

 by some.

Geoid and reference ellipsoid


The geoid
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 the continents . According to C.F...

 is essentially the figure of the 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, air pressure variations etc. 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. The geometrical separation between the geoid and the reference ellipsoid is called the geoidal undulation. It varies globally between ±110 m.

A reference ellipsoid
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....

, 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 = (ab)/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 1:298.257 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 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


The locations of points in three-dimensional space are most conveniently described by three cartesian
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

 or rectangular coordinates, and . Since the advent of satellite positioning, such coordinate systems are typically geocentric: the axis is aligned with the Earth's (conventional or instantaneous) rotation axis.

Prior to satellite geodesy
Satellite geodesy
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 artificial satellite techniques—geodesy by means of artificial satellites...

 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
Plumbline
A plumbline is a string with a lead weight or plumb-bob, used to provide a vertical reference line.It may also refer to:*The Plumbline, a joke newspaper produced by the McMaster Engineering Society...

 (vertical). These regional geodetic datums, such as ED50
ED50
ED 50 is a geodetic datum which was defined after World War II for the international connection of geodetic networks....

 (European Datum 1950) or NAD83 (North American Datum 1983) have ellipsoids associated with them that are regional 'best fits' to the geoid
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 the continents . According to C.F...

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

It is only because GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

 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.

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 star
    Fixed star
    The fixed stars are celestial objects that do not seem to move in relation to the other stars of the night sky. Hence, a fixed star is any star except for the Sun. A nebula or other starlike object may also be called a fixed star. People in many cultures have imagined that the stars form pictures...

    s, or equivalently, to the rotation axes of ideal gyroscopes; the 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. The axis lies within the Greenwich observatory's meridian
    Meridian (geography)
    A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...

     plane.


The coordinate transformation between these two systems is described to good approximation by (apparent) sidereal time
Sidereal time
Sidereal time is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky...

, which takes into account variations in the Earth's axial rotation (length-of-day
Day
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...

 variations). A more accurate description also takes polar motion
Polar motion
Polar motion of the earth is the movement of Earth's rotational axis across its surface. This is measured with respect to a reference frame in which the solid Earth is fixed...

 into account, a phenomenon closely monitored by geodesists.

Coordinate systems in the plane


In surveying
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

 and map
Map
A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes....

ping, 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 from a specified point along a ray having a specified direction with respect to a base line or axis;
  2. Rectangular, points are defined by distances from two perpendicular axes called and . It is geodetic practice—contrary to the mathematical convention—to let the axis point to the North and the axis to the East.


Rectangular coordinates in the plane can be used intuitively with respect to one's current location, in which case the 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
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...

. 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.

An example of such a projection is UTM (Universal Transverse Mercator). Within the map plane, we have rectangular coordinates and . 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 and respectively, then we have


The reverse transformation is given by:

Heights


In geodesy, point or terrain height
Height
Height is the measurement of vertical distance, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is. For example "The height of the building is 50 m" or "The height of the airplane is 10,000 m"...

s
are "above sea level
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...

", an irregular, physically defined 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 , in addition to the horizontal coordinates and , 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 height
    Orthometric height
    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.Orthometric heights are what are usually used in the US for ordinary engineering work. Values for measured points can be obtained from the National Geodetic Survey...

    s
  2. Normal height
    Normal height
    Normal heights are heights above sea level, one of several types of height which are all computed slightly differently. Alternatives are: orthometric heights and dynamic heights....

    s
  3. Geopotential height
    Geopotential height
    Geopotential height is a vertical coordinate referenced to Earth's mean sea level — an adjustment to geometric height using the variation of gravity with latitude and elevation. Thus it can be considered a "gravity-adjusted height"...

    s


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: 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
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 the continents . According to C.F...

, an equipotential surface approximating mean sea level.

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
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
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 the continents . According to C.F...

.

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
Normaal Amsterdams Peil
Normaal Amsterdams Peil or Amsterdam Ordnance Datum is a vertical datum in use in large parts of Western Europe. Originally created for use in the Netherlands, it was adopted by Prussia in 1879 under the name Normalnull, and in 1955 by other European countries.Mayor Johannes Hudde of Amsterdam in...

), the North American Vertical Datum 1988 (NAVD88), 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 ED50
ED50
ED 50 is a geodetic datum which was defined after World War II for the international connection of geodetic networks....

 can be fixed by prescribing the undulation of the geoid
Undulation of the geoid
Undulation of the geoid is the mathematical process of determining the height in meters above the geoid from the height provided by the GPS system which uses the ellipsoid as reference...

 and the deflection of the vertical in one datum point, in this case the Helmert Tower in Potsdam
Potsdam
Potsdam is the capital city of the German federal state of Brandenburg and part of the Berlin/Brandenburg Metropolitan Region. It is situated on the River Havel, southwest of Berlin city centre....

. 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
Helmert transformation
The Helmert transformation is a transformation method within a three-dimensional space...

 has four parameters; in space, seven.

A note on terminology


In the abstract, a coordinate system as used in mathematics and geodesy is, e.g., in ISO
International Organization for Standardization
The International Organization for Standardization , widely known as ISO, is an international standard-setting body composed of representatives from various national standards organizations. Founded on February 23, 1947, the organization promulgates worldwide proprietary, industrial and commercial...

 terminology, referred to as a coordinate system. International geodetic organizations like the IERS
IERS
IERS may refer to:* International Earth Rotation and Reference Systems Service* Independent Electricity Retail Solutions Pty Ltd* Information Exchange Requirements - used within MODAF and DODAF as the OV-3 view - called Information Exchange Matrix....

 (International Earth Rotation and Reference Systems Service) speak of a reference system.

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
Triangulation
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 end of a fixed baseline, rather than measuring distances to the point directly...

 points of a higher order network, or GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

 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 traverse
Traverse (surveying)
Traverse is a method in the field of surveying to establish control networks. It is also used in geodesy. Traverse networks involve placing survey stations along a line or path of travel, and then using the previously surveyed points as a base for observing the next point...

s (polygons), into which local mapping surveying measurements, usually with measuring tape, corner prism and the familiar red and white poles, are tied.

Nowadays all but special measurements (e.g., underground or high precision engineering measurements) are performed with GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

. The higher order networks are measured with static GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

, 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
IERS
IERS may refer to:* International Earth Rotation and Reference Systems Service* Independent Electricity Retail Solutions Pty Ltd* Information Exchange Requirements - used within MODAF and DODAF as the OV-3 view - called Information Exchange Matrix....

 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
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

 mappings, frequently Real Time Kinematic
Real Time Kinematic
Real Time Kinematic satellite navigation is a technique used in land survey and in hydrographic survey based on the use of carrier phase measurements of the GPS, GLONASS and/or Galileo signals where a single reference station provides the real-time corrections, providing up to centimetre-level...

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

First geodetic problem

Given a point (in terms of its coordinates) and the direction (azimuth) and distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

 from that point to a second point, determine (the coordinates of) that second point.

Second (inverse) geodetic problem

Given two points, determine the azimuth and length of the line (straight line, arc or geodesic
Geodesic
In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

) 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
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

.
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
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

, arc, i.e. the geodesic.

On the ellipsoid of revolution, geodesics may be written in terms of elliptic integrals, which are usually evaluated in terms of a series expansion; for example, see Vincenty's formulae
Vincenty's formulae
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than...

.

In the general case, the solution is called the geodesic
Geodesic
In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

 for the surface considered. The differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s for the geodesic
Geodesic
In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

 can be solved numerically.

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
    Plumbline
    A plumbline is a string with a lead weight or plumb-bob, used to provide a vertical reference line.It may also refer to:*The Plumbline, a joke newspaper produced by the McMaster Engineering Society...

    or vertical is the direction of local gravity, or the line that results by following it. It is slightly curved.
  • The zenith
    Zenith
    The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

    is the point on the celestial sphere
    Celestial sphere
    In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

     where the direction of the gravity vector in a point, extended upwards, intersects it. More correct is to call it a rather than a point.
  • The nadir
    Nadir
    The nadir is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous...

    is the opposite point (or rather, direction), where the direction of gravity extended downward intersects the (invisible) celestial sphere.
  • 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).
  • Elevation
    Elevation
    The elevation of a geographic location is its height above a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface ....

    is the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90 degrees minus elevation.
  • 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
    Celestial pole
    The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere...

    is the extension of the Earth's (precessing
    Precession
    Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

     and nutating
    Nutation
    Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

    ) instantaneous spin axis extended Northward to intersect the celestial sphere. (Similarly for the South celestial pole.)
  • The celestial equator is the intersection of the (instantaneous) Earth equatorial plane with the celestial sphere.
  • A meridian
    Meridian (geography)
    A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...

     plane
    is any plane perpendicular to the celestial equator and containing the celestial poles.
  • 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. The traditional spirit level
Spirit level
A spirit level or bubble level is an instrument designed to indicate whether a surface ishorizontal or vertical . Different types of spirit levels may be used by carpenters, stonemasons, bricklayers, other building trades workers, surveyors, millwrights and other metalworkers, and in some...

 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
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 the continents . According to C.F...

, as GPS only gives heights above the GRS80 reference ellipsoid. As geoid knowledge accumulates, one may expect use of GPS heighting to spread.

The theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...

 is used to measure horizontal and vertical angles to target points. 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. 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
Geographic Information System
A geographic information system, geographical information science, or geospatial information studies is a system designed to capture, store, manipulate, analyze, manage, and present all types of geographically referenced data...

 (GIS) database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...

.

Geodetic GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

 receivers produce directly three-dimensional coordinates in a geocentric coordinate frame. 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
IERS
IERS may refer to:* International Earth Rotation and Reference Systems Service* Independent Electricity Retail Solutions Pty Ltd* Information Exchange Requirements - used within MODAF and DODAF as the OV-3 view - called Information Exchange Matrix....

).

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
Satellite laser ranging
In satellite laser ranging a global network of observation stations measure the round trip time of flight of ultrashort pulses of light to satellites equipped with retroreflectors...

 (SLR) and Lunar Laser Ranging (LLR) and Very Long Baseline Interferometry
Very Long Baseline Interferometry
Very Long Baseline Interferometry is a type of astronomical interferometry used in radio astronomy. It allows observations of an object that are made simultaneously by many telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.Data...

 (VLBI) techniques. All these techniques also serve to monitor Earth rotation irregularities as well as plate tectonic motions.

Gravity is measured using gravimeters. 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 tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s, rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

, interior, and ocean
Ocean
An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...

 and atmospheric loading, as well as for verifying the Newtonian constant of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

.

Units and measures on the ellipsoid


Geographical latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

 and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

 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
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....

 of revolution. 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
    Plate tectonics
    Plate tectonics is a scientific theory that describes the large scale motions of Earth's lithosphere...

  • Episodic motion of tectonic origin, esp. 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
    Petroleum
    Petroleum or crude oil is a naturally occurring, flammable liquid consisting of a complex mixture of hydrocarbons of various molecular weights and other liquid organic compounds, that are found in geologic formations beneath the Earth's surface. Petroleum is recovered mostly through oil drilling...

     or water extraction or reservoir construction.


The science of studying deformations and motions of the Earth's crust and the solid Earth as a whole is called geodynamics
Geodynamics
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and...

. 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
    Global Positioning System
    The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

     and other such systems,
  • Very Long Baseline Interferometry
    Very Long Baseline Interferometry
    Very Long Baseline Interferometry is a type of astronomical interferometry used in radio astronomy. It allows observations of an object that are made simultaneously by many telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.Data...

     (VLBI)
  • satellite and lunar laser ranging
  • Regionally and locally, precise levelling,
  • precise tacheometers,
  • monitoring of gravity change,
  • Interferometric synthetic aperture radar
    Interferometric synthetic aperture radar
    Interferometric synthetic aperture radar, also abbreviated InSAR or IfSAR, is a radar technique used in geodesy and remote sensing. This geodetic method uses two or more synthetic aperture radar images to generate maps of surface deformation or digital elevation, using differences in the phase of...

     (InSAR) using satellite images, etc.

International organizations


Governmental agencies



Note: This list is still largely incomplete.

See also


Fundamentals: Geodynamics
Geodynamics
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and...

Geomatics
Geomatics
Geomatics is the discipline of gathering, storing, processing, and delivering geographic information, or spatially referenced information.-Overview and etymology:...

Cartography
Cartography
Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...

Geodesic (in mathematics)
Geodesic
In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

Physical geodesy
Physical geodesy
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.-Measurement procedure:...



Concepts: DatumDistance
Geographical distance
Geographical distance is the distance measured along the surface of the earth. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude.-An abstraction:...

Figure of the Earth
Figure of the Earth
The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earth's size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and water areas. This is, in fact, the surface...

Geoid
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 the continents . According to C.F...

Geodetic system
Geodetic system
Geodetic systems or geodetic data are used in geodesy, navigation, surveying by cartographers and satellite navigation systems to translate positions indicated on their products to their real position on earth....

Geog. coord. system
Geographic coordinate system
A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...

Horizontal position representation
Horizontal position representation
A position representation is the parameters used to express a position relative to a reference. Representing position in three dimensions is often done by a Euclidean vector. However, when representing position relative to the Earth it is often more convenient to represent vertical position as...

Map projection
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...

Reference ellipsoid
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 geodesy
Satellite geodesy
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 artificial satellite techniques—geodesy by means of artificial satellites...

Spatial reference system 

Geodesy community: Important publications in geodesyInternational Association of Geodesy (IAG)
International Association of Geodesy
International Association of Geodesy is an international organization of geodesists, founded in 1940. There are 4 commissions to IAG:*Reference Frames*Gravity Field*Geodynamics and Earth Rotation*Positioning & Applications...



Technologies: GNSSGPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

Space techniques
Space techniques
In geodesy, the term Space techniques includes modern measuring methods which make use of artificial satellites, interplanetary space probes and of quasars....

...

Standards: ED50
ED50
ED 50 is a geodetic datum which was defined after World War II for the international connection of geodetic networks....

ETRS89
European Terrestrial Reference System 1989
The European Terrestrial Reference System 1989 is a ECEF geodetic Cartesian reference frame, in which the Eurasian Plate as a whole is static...

NAD83NAVD88
North American Vertical Datum of 1988
The North American Vertical Datum of 1988 is the vertical control datum of orthometric height established for vertical control surveying in the United States of America based upon the General Adjustment of the North American Datum of 1988....

SAD69SRID
SRID
A Spatial Reference System Identifier is a unique value used to unambiguously identify projected, unprojected, and local spatial coordinate system definitions...

UTM
Universal Transverse Mercator coordinate system
The Universal Transverse Mercator geographic coordinate system uses a 2-dimensional Cartesian coordinate system to give locations on the surface of the Earth. It is a horizontal position representation, i.e...

WGS84
World Geodetic System
The World Geodetic System is a standard for use in cartography, geodesy, and navigation. It comprises a standard coordinate frame for the Earth, a standard spheroidal reference surface for raw altitude data, and a gravitational equipotential surface that defines the nominal sea level.The latest...

...

History: History of geodesy
History of geodesy
Geodesy ,[1] also named geodetics, is the scientific discipline that deals with the measurement and representation of the Earth.Humanity has always been interested in the Earth...

NAVD29
Sea Level Datum of 1929
The Sea Level Datum of 1929 was the vertical control datum established for vertical control surveying in the United States of America by the General Adjustment of 1929. The datum was used to measure elevation above, and depression below, mean sea level .Mean sea level was measured at 26 tide...

...

Other: Geodesic (general relativity)
Geodesic (general relativity)
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational, force is a particular type of geodesic...

Surveying
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

Meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...


External links