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## Geodesy(geodesy)
Wolfgang Torge quotes in his 2001 textbook As Torge also remarks, the shape of the earth is to a large extent the result of its gravity field. This applies to the solid surface ( orogeny ; fewmountains are higher than 10 km, few deep sea trenches deeper than that). It affects similarly the liquid surface ( dynamic sea surface topography ) and the earth's atmosphere . For this reason, the study of the Earth's gravity field is seen as a partof geodesy, called physical geodesy .
## Geoid and reference ellipsoidThe geoid is essentially the shape of the earth abstracted from its topographicfeatures. It is an idealized equilibrium surface. The geoid, unlike the ellipsoid, is too complicated to serve as thecomputational surface on which to solve geometrical problems like point positioning.
A
reference ellipsoid
, customarily chosen to be the samesize (volume) as the geoid, is described by its semi-major axis (equatorial radius) The geoid is an irregular surface. The geometrical separation between it and the reference ellipsoid is called the geoidalundulation. It varies globally between 110 m. The 1967 Geodetic Reference System posited a 6,378,160 m semi-major axis and a 1:298.247 flattening. The 1980 GeodeticReference System ( GRS80 ) posited a 6,378,137 m semi-major axis and a 1:298.257flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG). Numerous other systems have been used by diverse countries for their maps and charts. The 1979 International Astronomic Union(IAU) values are 6,378,140 m and 1:298.257. ## Co-ordinate systems in space
The locations of points in three-dimensional space are most conveniently described by three cartesian or rectangularco-ordinates, Before the satellite geodesy era, the co-ordinate systems associated with geodetic datums attempted to be be geocentric, buttheir origins differed from the geocentre by hundreds of metres, due to regional deviations in the direction of the plumbline(vertical). 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. It is only because GPS satellites orbit about the geocentre, that this point becomesnaturally the origin of a co-ordinate system defined by satellite geodetic means, as the satellite positions in space arethemselves computed in such a system. ## Co-ordinate systems in the planeIn surveying and mapping, important aspects of geodesy, two general types of co-ordinate systems are used in the plane: - Plano-polar, in which points in a plane are defined by distance from a specified point along a ray having a specifieddirection with respect to a base line or axis;
- Rectangular, points are defined by distances from two perpendicular axes called
*x*and*y*. It is geodeticpractice -- contrary to the mathematical convention -- to let the*x*axis point to the Northand the*y*axis to the East.
Rectangular co-ordinates in the plane can be used intuitively with respect to one's current location, in which case the
An example of such a projection is
UTM
(Universal Transverse Mercator). Within the mapplane, we have rectangular co-ordinates
It is easy enough to "translate" between polar and rectangular co-ordinates in the plane: let direction and distance beα and The reverse translation is slightly more tricky.
Geodetic ## Geodetic datums
Because geodetic point co-ordinates (and heights) are always obtained in a system that has been constructed itself using realobservations, we have to introduce the concept of a
In the case of height datums, it suffices to choose
In case of plane or spatial co-ordinates, 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
Changing the co-ordinates of a point set referring to one datum, to make them refer to another datum, is calleda ## Point positioningPoint positioning is the determination of the coordinates of a point on land, at sea, or in space with respect to a coordinatesystem. Point position is solved by compution from measurements linking the known positions of terrestrial or extraterrestrialpoints with the unknown terrestrial position. This may involve transformations between or among astronomical and terrestrialcoordinate systems. The known points used for point positioning can be, e.g., triangulation points of a higher order network, or GPS satellites. Traditionally, a hierarchy of networks has been built to allow point positioning within a country. Highest in the hierarchywere triangulation networks. These were densified into networks of 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 . The higher order networks are measured with static GPS, using differential measurementto determine vectors between terrestrial points. These vectors are then adjusted in traditional network fashion. A globalpolyhedron of permanently operating GPS stations under the auspices of the IERS is used todefine a single global, geocentric reference frame which serves as the "zeroth order" global reference to which nationalmeasurements are attached. For surveying mappings, frequently Real Time Kinematic GPS is employed, tyingin 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 andvertical) control. In every country, thousands of such known points exist in the terrain and are documented by the nationalmapping agencies. Constructors and surveyors involved in real estate will use these to tie their local measurements to. ## Geodetic problemsIn geometric geodesy we formulate two standard problems: the geodetic principal problem and the geodetic inverse problem. - Geodetic principal problem
- Given a point (in terms of its co-ordinates) and the direction (azimut) and distance from that point to a second point,determine (the co-ordinates of) that second point.
- Geodetic inverse problem
- Given two points, determine the azimut and length of the line (straight line, great circle or geodesic) that connectsthem.
In the case of plane geometry (valid for small areas on the Earth's surface) the solutions to both problems reduce to simpletrigonometry. On the sphere, the solution is significantly more complex, e.g., in the inverse problem the azimuths will differbetween the two end points of the connecting great circle arc. On the ellipsoid of revolution, closed solutions do not exist; series expansions have been traditionally used that convergerapidly. Alternatively, the differential equations for the geodesic can be solved numerically, e.g., in MatLab(TM). ## Geodetic observational conceptsHere we define some basic observational concepts, like angles and co-ordinates, defined in geodesy (and astronomy as well)from the viewpoint of the local observer. - The
*plumbline*or*vertical*is the direction of local gravity. It is slightly curved.
- The
*zenith*is the point on the celestial sphere where the direction of the gravity vector in a point, extendedupwards, intersects it. 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 intersectsthe (invisible) celestial sphere.
- The celestial
*horizon*is a plane perpendicular to a point's gravity vector.
*Azimut*is the direction angle within the plane of the horizon, typically counted clockwise from the North (in geodesy)or South (in astronomy and France).
*Elevation*is the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90degrees minus elevation.
*Local topocentric co-ordinates*are azimut (direction angle within the plane of the horizon) and elevation angle (orzenith angle) as well as distance if known.
- The North
*celestial pole*is the extension of the Earth's (precessing and nutating) instantaneous spin axis extendedNorthward 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 celestialsphere.
- An
*astronomical meridian*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.
*Celestial co-ordinates*are rightascension (longitude along the celestial equator) and declination (latitude from thecelestial equator).
Zero right ascension is the position of the Sun at the instant of vernal equinox -- the beginning of spring, when the Suncrosses the equatorial plane from South to North. ## Units and measures on the ellipsoid
Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are A geographic mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. A nautical mile is one minute ofastronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and shortestat the equator as is the nautical mile. A metre was originally defined as the 40 millionth part of the length of a meridian. This means that a kilometre is equal to(1/40,000) * 360 * 60 meridional minutes of arc, which equals 0.54 nautical miles. Similarly a nautical mile is on average 1/0.54= 1.85185... km.
- See also
- History of Geodesy
- Geodesy forthe layman
- Important publications ingeodesy
## External Referencesegodesy, point, geodesi, plane, goedesy, earth, , points, geodsey, ordinate, geodes, surface, eodesy, axis, gedoesy, ellipsoid, geodeys, positioning, godesy, systems, geoedsy, known, gedesy, geoid, geoesy, space, geodey, gravity, geodsy, measurements This article is completely or partly from Wikipedia - The Free Online Encyclopedia. Original Article. The text on this site is made available under the terms of the GNU Free Documentation Licence. We take no responsibility for the content, accuracy and use of this article. Anoca.org Encyclopedia 0.01s |