Map projection of the triaxial ellipsoid information
In geodesy, a map projection of the triaxial ellipsoid maps Earth or some other astronomical body modeled as a triaxial ellipsoid to the plane. Such a model is called the reference ellipsoid. In most cases, reference ellipsoids are spheroids, and sometimes spheres. Massive objects have sufficient gravity to overcome their own rigidity and usually have an oblate ellipsoid shape. However, minor moons or small solar system bodies are not under hydrostatic equilibrium. Usually such bodies have irregular shapes. Furthermore, some of gravitationally rounded objects may have a tri-axial ellipsoid shape due to rapid rotation (such as Haumea) or unidirectional strong tidal forces (such as Io).
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mapprojectionofthetriaxialellipsoid for further information. One way to classify mapprojections is based on the type of surface onto which the globe...
d\theta \,d\phi .} Ellipsoidal latitude Focaloid (shell given by two coordinate surfaces) Mapprojectionofthetriaxialellipsoid "Ellipsoid Quadrupole Moment"...
by theellipsoid are called the principal axes, or simply axes oftheellipsoid. If the three axes have different lengths, the figure is a triaxial ellipsoid...
by triaxialellipsoids; however, triaxialellipsoids would render many computations more complicated, especially those related to mapprojections. Many...
ellipsoidof revolution a triaxial (or scalene) ellipsoid is used. The shape of an ellipsoidof revolution is determined by the shape parameters of that...
(1983). Geodesy for the Layman (Report). United States Air Force. Heiskanen, W. A. (1962). "Is the Earth a triaxialellipsoid?". Journal of Geophysical Research...
have an axis of symmetry are termed triaxial.) Many different reference ellipsoids have been used in the history of geodesy. In pre-satellite days they...
mapprojection or a geodesic polygon. Earth's volume, or that ofthe reference ellipsoid, is V = 4/3πa2b. Using the parameters from WGS84 ellipsoid of...
are usually dropped. An ellipsoid that is not an ellipsoidof revolution is called a triaxialellipsoid. Spheroid and ellipsoid are used interchangeably...
large amount of rotational symmetry around their spin axis (see triaxialellipsoidal longitude for a generalization). The conversion for the latitude and...
Earth, though many ofthe underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between...
topographic maps are still based on Clarke's 1866 ellipsoid. Moreover, many US legal documents include boundary definitions in terms of latitude and...
the "Theoria attractionis..." (1813), Gauss provided a closed-form expression to the gravitational attraction of an homogeneous triaxialellipsoid at...
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