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If the starting point is β 1 = 90°, ω 1 ∈ (0°, 180°), and α 1 = 180°, then γ < 0 and the geodesic encircles the ellipsoid in a "transpolar" sense. The geodesic oscillates east and west of the ellipse X = 0 ; on each oscillation it completes slightly more than a full circuit around the ellipsoid.
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.
English: Non-standard closed geodesics on an ellipsoid of revolution 1. Vital statistics: b/a = 2/7, green curve α 0 = 53.174764534°, blue curve α 0 = 75.192358015°, orthographic projection from φ = 10°. Geodesics computed with GeodSolve with the -E option. See also
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).
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 ...
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 His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory.
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 ...
English: Four geodesics connecting two points on an oblate ellipsoid. Vital statistics: f = 1/10, φ 1 = −30°, λ 1 = 0°, α 1 = [165.126870°, 25.907443°, 71.515418°, −84.636539°], φ 2 = 26°, λ 2 = 175°, orthographic projection from φ = 15°, λ = 130°. Geodesics computed with Matlab Central package 50605. See also