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GEOIDE

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It is called geoide (of the Greek Hello gueia, 'land', y type eidos, 'shape', 'Appearance' -for which would mean 'form having the land’—) the body defined by the equipotential surface of the gravity field. As aforementioned, It is a fairly successful model of how the Earth, established in almost spherical but with a slight achatamiento at the poles (spheroid), but keeping their own differences of gravity in connection to differential mass profiles vertical composition of the planet.

Image land taken from the Apolo 17.

History of the concept

The name "geoid" originates from the following fact: planet Earth, like other stars, is not a sphere but for purposes of gravitation and of the centrifugal force produced by rotating on its axis the flattening polar and equatorial bulges is generated. Take into account that considering the bark, Earth is not exactly a geoid although it is if it represents the planet with the average level of the tides.

This notion of the Earth as geoid was predicted by Isaac Newton in their principles during the year 1687, Newton for that used a simple experiment: to rapidly rotate a viscous fluid in a liquid body, thus he stated that "the form of equilibrium that has a time under the influence of gravitation laws and turning around its axis is a spheroid flattened at its poles ».

This Newtonian hypothesis was studied by Domenico Y Jacques Cassini, and confirmed by the work geodetic expedition conducted in equatorial regions La Condamine, Godin Y bourger during the century XVIII, For this they made accurate measurement of the difference of a degree in the vicinity of the line of Ecuador and collated with differences latitudes European. Mathematical and geometric work in the XIX century by Gauss Y Helmert They ratified the above findings.

Geography and geoid

In geography and related disciplines or derived (geodesia, mapping, topography, etc.) now a geoide is the physical surface defined by gravitational potential, so that on it there at all points the same terrestrial attraction. phenomena are excluded orogenic, so the mountains are not included in the same. Graphically it can be defined as the surface of the seas in calm prolonged under the continents. Geometrically it is almost a spheroid of revolution (sphere flattened at the poles) with minor irregularities 100 meters.

Gravimetría y geoide

Technically and using tools gravimétricas It is called geoide physical surface defined by a particular gravitational potential (constant throughout the surface). To define the geoid, the potential value is arbitrarily adopted whose associated geoid is closer to the ocean surface (the average sea surface, regardless of the surf, the tides, currents and the earth's rotation, It coincides almost exactly with an equipotential surface). The shape of the geoid does not necessarily coincide with the Earth's topography, shaped by endogenous forces (Tectonic plates) and exogenous (geomorphological agents). Geometrically, the geoid is like a spheroid (sphere flattened at the poles).

The shape of the geoid can be determined by:

  1. Measures of gravitational anomalies measuring the magnitude of the intensity of gravity in many parts of the earth's surface. Since it is similar to a spheroid (sphere flattened at the poles) the acceleration of gravity increases from the ecuador to the poles. These measurements of the earth's gravity have to be corrected to remove abnormalities due to local density variations.
  2. astronomical measurements: They are based on measuring the vertical of the place and see your changes. This variation is related to its shape.
  3. Measuring deformations in orbit of the satellites caused because land It is not homogeneous. This has given a geoid tens bulges or depressions of from the reference spheroid. These irregularities are under 100 meters.

Spheroid

It is important to remember that the surfaces of revolution are those generated by rotating a curve around an axis. Some geophysicists consider the spheroid as a geometric model of the earth and not only this but also the sphere, therefore the spheroid has principal meridian and Ecuador. Ellipse: closed oval shaped curve.

Achatamiento

It is the dimensionless quantity:

f = a − b a = 1 298 , 2 {\displaystyle f={\frac {a-b}{a}}={\frac {1}{298,2}}}

It is the inverse flattening Flattening.

A) Yes, the equatorial diameter is 43 km greater than the polar diameter. That is why the points furthest from the center of the Earth and, thus, points having less serious) are being Chimborazo volcano 6.384,4 m Ecuador-South America and other high points of the American continent in the equatorial zone (and to a lesser extent, the Kilimanjaro and other mountains in Africa).

Latitude and geocentric latitude

Latitude Phi {\displaystyle Phi } Y geocentric latitude Phi ′ {\displaystyle Phi ‘}

As the Earth approximately spheroid, the latitude or forming an angle with the place Earth Ecuador and the geocentric latitude angle between the place seen from the center of the Earth with respect to Ecuador, do not match.

To relate the auxiliary variable is introduced in:

tan ⁡ ( in ) = b a × tan ⁡ ( Phi ) {\displaystyle tan(in)={\frac {b}{a}}\times tan(\Phi )}

If H is the height above sea level in meters of the observer and p {\displaystyle rho } the distance to the center of the Earth, is fulfilled:

p × its ⁡ ( Phi ′ ) = b a s ( in ) + H 6378140 × cos ⁡ ( Phi ) {\displaystyle rho times operatorname {its} (\Phi ‘)={\frac {b}{as(in)+{\frac {H}{6378140}}\times cos(\Phi )}}}

Geoide y geodesia

The geoide is a reference surface used to determine the geodetic altimetric profiles, this is often the determining height above mean sea level of all points in the area that is mensurada.

Since the geoide It is a surface normal at every point in the vertical direction, this is in the common direction force of gravity, this is the way that best describes the average surface ocean tide variations discounting, sea ​​currents or meteorological events, and therefore the planet; This is the geoide It is regarded as an equipotential surface (where gravity is comparable values) about him mean sea level.

However from the standpoint cartographic the geoid can not be used for determinations planimétricas accurate because a portion of ground even if it were possible to relate the correspondence of points on the surface of the Earth could not be put in correspondence with the points of the geoid system Cartesian plano. That is why in practice it is not feasible to use the geoid for creating a architectural plant because the data derived from the projection on the geoid of the earth surface can not be described on a plano. Therefore the geoid is mainly used to reference level dimensions.

All of the above is because it is virtually impossible to describe the geoid with a mathematical formula resolvable in a plane: to know and represent the relief of the geoid would need to know at any point of the earth's surface the direction of the force of gravity, which in turn depends on the density that the Earth has at each point. Such knowledge is still impossible without some approach which leaves significant room for error, thus resulting in little operational from the mathematical point of view the definition of the geoid.

It is then necessary to pay attention to the differences between the geoid itself and the spheroid (another reference surface used in topographic maps): while the former already has a rigorous physical definition however is not well described in mathematics. Instead the second (spheroid) has a well defined equation mathematics. For others there is a certain deviation from vertical between both surfaces.

See also


D. ANGEL ALARCON MARTI

PRESIDENT / PROFESSOR Founder of the E.O.I.T International School of Survival.

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