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The oblate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. (See ellipse.) [2] A prolate spheroid with c > a has surface area
If the third axis is shorter, the ellipsoid is a sphere that has been flattened (called an oblate spheroid). If the third axis is longer, it is a sphere that has been lengthened (called a prolate spheroid). If the three axes have the same length, the ellipsoid is a sphere.
As before, the oblate spheroid corresponding to σ is shown in red, and φ measures the azimuthal angle between the green and yellow half-planes. However, the surface of constant τ is a full one-sheet hyperboloid, shown in blue. This produces a two-fold degeneracy, shown by the two black spheres located at (x, y, ±z).
Better approximations can be made by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoid. For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature.
The WGS 84 datum surface is an oblate spheroid with equatorial radius a = 6 378 137 m at the equator and flattening f = 1 ⁄ 298.257 223 563. The refined value of the WGS 84 gravitational constant (mass of Earth's atmosphere included) is GM = 3.986 004 418 × 10 14 m 3 /s 2. The angular velocity of the Earth is defined to be ω = 72.921 15 × ...
In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of a flattened ("oblate") ellipsoid of revolution, generated by an ellipse rotated around its minor diameter; a shape which he termed an oblate spheroid. [2] [3]
A geodesic on an oblate ellipsoid. ... (the term spheroid is also used) ... where dT is an element of surface area and K is the Gaussian curvature.
A sphere of radius a compressed to an oblate ellipsoid of revolution. Flattening 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.