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On a triaxial ellipsoid, there are only three simple closed geodesics, the three principal sections of the ellipsoid given by X = 0, Y = 0, and Z = 0. [7] To survey the other geodesics, it is convenient to consider geodesics that intersect the middle principal section, Y = 0 , at right angles.
The (non-trivial) intersection of a plane and ellipsoid is an ellipse. Therefore, the arc length, s 12 {\displaystyle s_{12}} , on the section path from P 1 {\displaystyle P_{1}} to P 2 {\displaystyle P_{2}} is an elliptic integral that may be computed to any desired accuracy using a truncated series or numerical integration.
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 ...
Geodesic on an oblate ellipsoid. An ellipsoid approximates the surface of the Earth much better than a sphere or a flat surface does. The shortest distance along the surface of an ellipsoid between two points on the surface is along the geodesic. Geodesics follow more complicated paths than great circles and in particular, they usually don't ...
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.
Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the program length (Vincenty 1975a). His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory. To obtain good accuracy for long lines, the solution uses the classical solution ...
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).
English: Closed geodesics on an ellipsoid of revolution. Vital statistics: f = 1/50, meridians λ = (0°, 10°, 20°, 30°, 40°, 50°), equator φ = 0°, orthographic projection from φ = 20°, λ = 60°. Geodesics computed with Matlab Central package 50605. See also