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The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface.
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).
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: 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
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 His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory.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 ...
English: Non-standard closed geodesics on an ellipsoid of revolution 2. Vital statistics: b/a = 2/7, green curve α 0 = 53.174764534°, blue curve α 0 = 75.192358015°, orthographic projection from φ = 90°. Geodesics computed with GeodSolve with the -E option. See also