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The difference between a sphere and a reference ellipsoid for Earth is small, only about one part in 300. Historically, flattening was computed from grade measurements. Nowadays, geodetic networks and satellite geodesy are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys.
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).
The shape of an ellipsoid of revolution is determined by the shape parameters of that ellipse. The semi-major axis of the ellipse, a, becomes the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, becomes the distance from the centre to either pole. These two lengths completely specify the shape of the ellipsoid.
VDs are used in astrogeodetic levelling: as a vertical deflection describes the difference between the geoidal vertical direction and ellipsoidal normal direction, it represents the horizontal spatial gradient of the geoid undulations of the geoid (i.e., the inclination between geoid and reference ellipsoid).
The geoid undulation (also known as geoid height or geoid anomaly), N, is the height of the geoid relative to a given ellipsoid of reference. N = h − H {\displaystyle N=h-H} The undulation is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 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
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid , respectively, in iso-density plots.
The geometrical separation between the geoid and a reference ellipsoid is called geoidal undulation, and it varies globally between ±110 m based on the GRS 80 ellipsoid. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f.