The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes.
The vertical deflection are the angular components between the true zenith–nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface). VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10″ in flat areas or 20–50″ in mountainous terrain).[ citation needed ]
The deflection of the vertical has a north–south component ξ (xi) and an east–west component η (eta). The value of ξ is the difference between the astronomic latitude and the geodetic latitude (taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network coordinates. The value of η is the product of cosine of latitude and the difference between the astronomic longitude and the longitude (taking east longitudes to be positive and west longitudes to be negative). When a new mapping datum replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will also change.
The deflections reflect the undulation of the geoid and gravity anomalies, for they depend on the gravity field and its inhomogeneities.
Vertical deflections are usually determined astronomically. The true zenith is observed astronomically with respect to the stars, and the ellipsoidal zenith (theoretical vertical) by geodetic network computation, which always takes place on a reference ellipsoid. Additionally, the very local variations of the vertical deflection can be computed from gravimetric survey data and by means of digital terrain models (DTM), using a theory originally developed by Vening-Meinesz.
VDs are used in astrogeodetic levelling: as a vertical deflection describes the difference between the geoidal and ellipsoidal normal direction, it represents the horizontal spatial gradient of the geoid undulations of the geoid (i.e., the separation between geoid and reference ellipsoid).
In practice, the deflections are observed at special points with spacings of 20 or 50 kilometers. The densification is done by a combination of DTM models and areal gravimetry. Precise vertical deflection observations have accuracies of ±0.2″ (on high mountains ±0.5″), calculated values of about 1–2″.
The maximal vertical deflection of Central Europe seems to be a point near the Großglockner (3,798 m), the highest peak of the Austrian Alps. The approx. values are ξ = +50″ and η = −30″. In the Himalaya region, very asymmetric peaks may have vertical deflections up to 100″ (0.03°). In the rather flat area between Vienna and Hungary the values are less than 15", but scatter by ±10″ for irregular rock densities in the subsurface.
More recently, a combination of digital camera and tiltmeter have also been used, see zenith camera. [1]
Vertical deflections are principally used in four matters:
Vertical deflections were used to measure Earth's density in the Schiehallion experiment.
Vertical deflection is the reason why modern prime meridian passes more than 100 m to the east of the historical astronomic prime meridian in Greenwich. [2]
The meridian arc measurement made by Nicolas-Louis de Lacaille north of Cape Town in 1752 (de Lacaille's arc measurement) was affected by vertical deflection. [3] The resulting discrepancy with Northern Hemisphere measurements was not explained until a visit to the area by George Everest in 1820; Maclear's arc measurement resurvey ultimately confirmed Everest's conjecture. [4]
Errors in the meridian arc of Delambre and Méchain determination, which affected the original definition of the metre, [5] were long known to be mainly caused by an uncertain determination of Barcelona's latitude later explained by vertical deflection. [6] [7] [8] When these errors where acknowledged in 1866, [9] it became urgent to proceed to a new measurement of the French arc between Dunkirk and Perpignan. The operations concerning the revision of the French arc linked to Spanish triangulation were completed only in 1896. Meanwhile the French geodesists had accomplished in 1879 the junction of Algeria to Spain, with the help of the geodesists of the Madrid Institute headed by the late Carlos Ibañez Ibáñez de Ibero (1825-1891), who had been president of the International Geodetic Association (now called International Association of Geodesy), first president of the International Committee for Weights and Measures and one of the 81 initial members of the International Statistical Institute. [10] Until Hayford ellipsoid was calculated in 1910, vertical deflections were considered as random errors. [11] Plumb line deviations were identified by Jean Le Rond d'Alembert as an important source of error in geodetic surveys as early as 1756, a few years later, in 1828, Carl Friedrich Gauss proposed the concept of geoid. [12] [13]
Geodesy is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems.
In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).
The geoid is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents. According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.
Physical geodesy is the study of the physical properties of Earth's gravity and its potential field, with a view to their application in geodesy.
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency.
Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approximation of the figure of the Earth that is satisfactory for many purposes. Several models with greater accuracy have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.
The National Geodetic Survey (NGS) is a United States federal agency based in Washington, D.C. that defines and manages a national coordinate system, providing the foundation for transportation and communication, mapping and charting, and a large number of science and engineering applications. Since its founding in 1970, it has been part of the National Oceanic and Atmospheric Administration (NOAA), a division within the United States Department of Commerce.
A geodetic datum or geodetic system is a global datum reference or reference frame for precisely representing the position of locations on Earth or other planetary bodies by means of geodetic coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a location across the Earth's surface, in latitude and longitude or another coordinate system; a vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS 84 is intended for global use, unlike most earlier datums.
Arc measurement, sometimes degree measurement, is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the latitude difference and the geographic distance surveyed between two locations on Earth's surface. The most common variant involves only astronomical latitudes and the meridian arc length and is called meridian arc measurement; other variants may involve only astronomical longitude or both geographic coordinates . Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG).
Geodetic astronomy or astronomical geodesy (astro-geodesy) is the application of astronomical methods into geodetic networks and other technical projects of geodesy.
A zenith camera is an astrogeodetic telescope used today primarily for the local surveys of Earth's gravity field. Zenith cameras are designed as transportable field instruments for the direct observation of the plumb line and vertical deflections.
The orthometric height is the vertical distance H along the plumb line from a point of interest to a reference surface known as the geoid, the vertical datum that approximates mean sea level. Orthometric height is one of the scientific formalizations of a laypersons' "height above sea level", along with other types of heights in Geodesy.
Mikhail Sergeevich Molodenskii was a Soviet physical geodesist. He was once said to be "probably the only geodesist who would have deserved a Nobel prize".
The North American Datum (NAD) is the horizontal datum now used to define the geodetic network in North America. A datum is a formal description of the shape of the Earth along with an "anchor" point for the coordinate system. In surveying, cartography, and land-use planning, two North American Datums are in use for making lateral or "horizontal" measurements: the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83). Both are geodetic reference systems based on slightly different assumptions and measurements.
The Bessel ellipsoid is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
Irene Kaminka Fischer was an Austrian-American mathematician and geodesist. She was a member of the National Academy of Engineering, a Fellow of the American Geophysical Union, and inductee of the National Imagery and Mapping Agency Hall of Fame. Fischer became one of two internationally known women scientists in the field of geodesy during the golden age of the Project Mercury and the Apollo program. Her Mercury datum, as well as her work on the lunar parallax, were instrumental in conducting these missions. "In his preface to the ACSM publication, Fischer's former colleague, Bernard Chovitz, referred to her as one of the most renowned geodesists of the third quarter of the twentieth century. Yet this fact alone makes her one of the most renowned geodesists of all times, because, according to Chovitz, the third quarter of the twentieth century witnessed "the transition of geodesy from a regional to a global enterprise."
Carlos Ibáñez e Ibáñez de Ibero, 1st Marquis of Mulhacén, was a Spanish divisional general and geodesist. He represented Spain at the 1875 Conference of the Metre Convention and was the first president of the International Committee for Weights and Measures. As a forerunner geodesist and president of the International Geodetic Association, he played a leading role in the worldwide dissemination of the metric system. His activities resulted in the distribution of a platinum and iridium prototype of the metre to all States parties to the Metre Convention during the first meeting of the General Conference on Weights and Measures in 1889. These prototypes defined the metre right up until 1960.
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