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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.) [3] A prolate spheroid with c > a has surface area
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 surface area of this general ellipsoid can also be expressed in terms of ... (oblate spheroid) or Jacobi ellipsoid (scalene ellipsoid) ...
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 geophysics, geodesy, and related areas, the word 'ellipsoid' is understood to mean 'oblate ellipsoid of revolution', and the older term 'oblate spheroid' is hardly used. [ 4 ] [ 5 ] For bodies that cannot be well approximated by an ellipsoid of revolution a triaxial (or scalene) ellipsoid is used.
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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.