Geodesy
From Wikinfo
[[de:Geod�sie]] [[fr:G�od�sie]]
Geodesy is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional time varying space. Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations.
Some would also include the study of the Earth's magnetic field.
Wolfgang Torge quotes in his 2001 textbook Geodesy (3rd edition) Friedrich Robert Helmert as defining geodesy as "the science of the measurement and mapping of the earth's surface."
As Torge also remarks, the shape of the earth is to a large extent shaped by its gravity field. This applies to the solid surface (orogeny; few mountains are higher than 10 km, few deep sea trenches deeper than that) as it does to 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 part of geodesy, called physical geodesy.
The geoid is esentially the real shape of the earth, without accounting for the topographic features. It is an idealized equilibrium surface. The geoid, unlike the ellipsoid, is too complicated to serve as the computational surface on which to solve geometrical problems like point position.
A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its the semi-major axis (equatorial radius) $a$ and flattening $f$. The quantity $f = (a-b)/a$, where $b$ is the semi-minor axis (polar radius) is a purely geometrical one. The mechanical ellipticity of the earth (dynamical flattening) is determined by observation and differs from the geometrical because the earth is not of uniform density.
The geoid is an irregular surface. The geometrical separation between it and the reference ellipsoid is called the geoidal undulation. It varies globally between $pm$110 m.
The 1967 Geodetic Reference System posited a 6,378,160 m semi-major axis and 1:298.247 flattening. The 1980 Geodetic Reference System posited a 6,378,137 m semi-major axis and 1:298.257 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG).
The Geodetic Reference System 1980 system is used for the Figure of the Earth data following below. 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.
Defining Constant:
Semi-major axis = Equatorial Radius = 6,378,137.0 m
Derived Geometrical Constants:
Semi-minor axis = Polar Radius = 6,356,752.3141 m
mean radius = ( 2a + b ) / 3 = 6,371,008.7714 m
radius of a sphere with the same surface = 6,371,007.1810 m
radius of a sphere of the same volume = 6,371,000.7900 m
linear eccentricity = 521,854.0097 m
Polar Radius of Curvature = 6,399,593.6259 m
meridian quadrant = 10,001,965.7293 m
reciprocal of flattening = 298.257222101
flattening = 0.00335281068118
Additional derived physical constants and geodetic formulas are found in the following reference: Geodetic Reference System 1980, Bulletin Geodesique, Vol 54:3, 1980.
Coordinate systems are used as reference systems for defining points in space or on planes and surfaces with relation to designated axis, planes or surfaces. In surveying and mapping, important aspects of geodesy, three general types are used: (1.) Plano-polar, in which points in a plane are defined by distance from a specified point along a ray having a specified direction with respect to a base line; (2.) Rectangular, points are defined by distance from two perpendicular axis or three mutually perpendicular planes; (3.) Spherical, points on a surface are defined by the angles between a normal or radius through a point and two perpendicular diametrical planes.
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 compution from measurements linking the known positions of extraterrestrial objects with the terrestrial position. This typically involves transformations of astronomical and terrestrial coordinate systems.
Here follow other important concepts defined by geodesy. Zenith is the gravity vector of a point extended upwards to intersect the celestial sphere, with the opposite point called the nadir. Astronomical meridian is any plane perpendicular to the celestial equator and containing the poles. The North celestial pole is the extension of the earth's (precessing and nutating) instantaneous spin axis to intersect the celestial sphere. The celestial horizon is a plane perpendicular to a point's gravity vector. Zero right ascension is the position of the Sun at the instant of Spring equinox.
A geographic mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. A 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 shortest at the equator as is the nautical mile.
See also:
External References
References
- Adapted from the Wikipedia article, "Geodesy" http://en.wikipedia.org/wiki/Geodesy, used under the GNU Free Documentation License
