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The geoid, unlike ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning.
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geoid and unlike
The geoid surface is irregular, unlike the reference ellipsoid which is a mathematical idealized representation of the physical Earth, but considerably smoother than Earth's physical surface.
The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning.
geoid and ellipsoid
The geometrical separation between the geoid and the reference ellipsoid is called the geoidal undulation.
A reference ellipsoid, customarily chosen to be the same size ( volume ) as the geoid, is described by its semi-major axis ( equatorial
The traditional spirit level 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, as GPS only gives heights above the GRS80 reference ellipsoid.
The simplest choice for the reference surface is a sphere, but the geoid is more accurately modelled by an ellipsoid.
This difference is the geoid height, positive above or outside the ellipsoid, negative below or inside.
Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).
Map of the undulation of the geoid, in meters ( based on the EGM96 gravity model and the WGS84 reference ellipsoid ).
Modern GPS receivers have a grid implemented inside where they obtain the geoid ( e. g. EGM-96 ) height over the WGS ellipsoid from the current position.
Then they are able to correct the height above WGS ellipsoid to the height above WGS84 geoid.
In some places, like west of Ireland, the geoid — mathematical mean sea level — sticks out as much as 100 m above the regular, rotationally symmetric reference ellipsoid of GRS80 ; in other places, like close to Ceylon, it dives under the ellipsoid by nearly the same amount.
As the science of geodesy measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid, a specific type of ellipsoid.
It comprises a standard coordinate frame for the Earth, a standard spheroidal reference surface ( the datum or reference ellipsoid ) for raw altitude data, and a gravitational equipotential surface ( the geoid ) that defines the nominal sea level.
The deviations of the EGM96 geoid from the WGS 84 reference ellipsoid range from about − 105 m to about + 85 m. EGM96 differs from the original WGS 84 geoid, referred to as EGM84.
Therefore, a motivation, and a substantial problem in the WGS and similar work is to patch together data that were not only made separately, for different regions, but to re-reference the elevations to an ellipsoid model rather than to the geoid.
As this vertical is everywhere perpendicular to the idealized surface of mean sea level, or the geoid, this means that the figure of the Earth is even more irregular than an ellipsoid of revolution.
In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.
A reference ellipsoid, customarily chosen to be the same size ( volume ) as the geoid, is described by its semi-major axis ( equatorial
Undulation of the geoid is the mathematical process of determining the height in meters above the geoid ( relative to the mean sea level ) from the height provided by the GPS system which uses the ( WGS84 ) ellipsoid as reference.
Earth's ellipsoid, geoid, and two types of vertical deflection
geoid and is
International Atomic Time ( TAI, from the French name Temps atomique international ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid.
Thus for clocks on or near the geoid, T < sub > eph </ sub > ( within 2 milliseconds ), but not so closely TCB, can be used as approximations to Terrestrial Time, and via the standard ephemerides T < sub > eph </ sub > is in widespread use.
The geoid is essentially the figure of the Earth abstracted from its topographical features.
The reference surface for orthometric heights is the geoid, an equipotential surface approximating mean sea level.
This is approximately the same as the direction of the plumbline, i. e., local gravity, which is also the normal to the geoid surface.
In the first step the physical surface is modelled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses.
The second step is to approximate the geoid by a mathematically simpler reference surface.
In relativistic terms, the SI second is defined as the proper time on the rotating geoid.
This terminology is also used for astronomical bodies such as the planet Earth, even though it is not spherical and only approximately spheroidal ( see geoid ).
TT was defined to be a linear scaling of TCG, such that the unit of TT is the SI second on the geoid ( Earth surface at mean sea level ).
Experimental determination of the gravitational potential at the geoid surface is a task in physical geodesy.
( As measured on the geoid surface, the rate of TCG is very slightly faster than that of TT, see below, Relativistic relationships of TT.
In relativistic terms, TT is described as the proper time of a clock located on the geoid ( essentially mean sea level ).
The geopotential surface called the geoid is one definition of the shape of the Earth.
In the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called " a radius of the Earth " or " the radius of the Earth at that point ".
The geoid height variation is under 110 m on Earth.
A sphere being a gross approximation of the spheroid, which itself is an approximation of the geoid, units are given here in kilometers rather than the millimeter resolution appropriate for geodesy.
geoid and irregular
Due to the irregularity of the Earth's true gravity field, the equilibrium figure of sea water, or the geoid, will also be of irregular form.
The geoid, being irregular, is impossible to precisely model mathematically.
geoid and surface
Maps that depict the surface of the Earth also use a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture.
The TAI service, running since 1958, attempts to match the rate of proper time on the geoid, using an ensemble of atomic clocks spread over the surface and low orbital space of the Earth.
When Greenwich was an active observatory, geographical coordinates were referred to a local oblate spheroid called a datum, whose surface closely matched local mean sea level, called the geoid.
Ellipsoid-based datums such as WGS84, GRS80 or NAD83 use a theoretical surface that may differ significantly from the geoid.
* The geoid, defined by mean sea level at each point on the real surface ;
The geoid is that equipotential surface which would coincide with the mean ocean surface of the Earth, if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth, and extended through the continents ( such as with very narrow canals ).
If the ocean surface were isopycnic ( of constant density ) and undisturbed by tides, currents, or weather, it would closely approximate the geoid.
In reality the geoid does not have a physical meaning under the continents, but geodesists are able to derive the heights of continental points above this imaginary, yet physically defined, surface by a technique called spirit leveling.
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