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Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (,,) that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces , the ellipsoidal coordinate system is based on confocal quadrics .
The set (u,β,λ) define the ellipsoidal-harmonic coordinates [19] or simply ellipsoidal coordinates [5]: §4.2.2 (although that term is also used to refer to geodetic coordinate). These coordinates are the natural choice in models of the gravity field for a rotating ellipsoidal body.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} are generally taken to be fixed at − a {\displaystyle -a} and + a {\displaystyle +a} , respectively, on the x ...
There are two types of ellipsoid: mean and reference. A data set which describes the global average of the Earth's surface curvature is called the mean Earth Ellipsoid.It refers to a theoretical coherence between the geographic latitude and the meridional curvature of the geoid.
Longitude (/ ˈ l ɒ n dʒ ɪ tj uː d /, AU and UK also / ˈ l ɒ ŋ ɡ ɪ-/) [1] [2] is a geographic coordinate that specifies the east-west position of a point on the surface of the Earth, or another celestial body.
In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a reference ellipsoid closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid.
Ellipsoidal dome; Ellipsoidal coordinates; Elliptical distribution, in statistics; Flattening, also called ellipticity and oblateness, is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid), respectively. Focaloid, a shell bounded by two concentric, confocal ellipsoids