Shortest paths on a bounded deformed sphere-like quadric surface
Geodesy
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A geodesic on an oblate ellipsoid
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. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry (Euler 1755).
If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, Newton (1687) showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed to become a triaxial ellipsoid (with three distinct semi-axes), only three geodesics are closed.
and 26 Related for: Geodesics on an ellipsoid information
The study of geodesicsonanellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth...
axes of anellipsoid are distinct, but sufficiently close to each other, then the ellipsoid has only three simple closed geodesics. A geodesic, on a Riemannian...
an ellipse or anellipsoid of revolution (spheroid), respectively. Focaloid, a shell bounded by two concentric, confocal ellipsoidsGeodesicsonan ellipsoid...
methods are available. Local geodetic coordinates Geodetic datum Geodesicsonanellipsoid Planetary coordinate system National Geodetic Survey (U.S.).;...
Geodesicsonanellipsoid behave in a more complicated way than on a sphere; in particular, they are not closed in general (see figure). A geodesic triangle...
(geometry), a vector Cardinal directions 180-degree apart Inverse geodesicsonanellipsoid A 180-degree rotation A point reflection This disambiguation page...
parametric angle on the ellipse. (A similar mapping to an auxiliary sphere is carried out in the solution of geodesicsonanellipsoid. The differences...
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...
French Geodesic Mission Struve Geodetic Arc Rectifying latitude Geodesicsonanellipsoid Russo, Lucio (2004). The Forgotten Revolution. Berlin: Springer...
Bessel who solved problems for geodesicson the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude...
scale based onGeodesic grid. The colored strip indicate the simulated ocean vorticity strength based on MPAS model. Geodesicsonanellipsoid Geographic...
solving for geodesicsonanellipsoid. The method of least squares had been introduced into geodesy by Gauss and Helmert wrote a fine book on least squares...
found by multiplying the ellipsoidal meridian arc length by the secant of the azimuth. Great circle Geodesicsonanellipsoid Great ellipse Isoazimuthal...
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy...
equation Elliptical distribution, in statistics Elliptical dome Geodesicsonanellipsoid Great ellipse Kepler's laws of planetary motion n-ellipse, a generalization...
Fundamentals Geodesy (book) Concepts and Techniques in Modern Geography Geodesicsonanellipsoid History of geodesy Physical geodesy Earth's circumference Physics...
models to calculate the qibla, replacing the great circle by the geodesicsonanellipsoid. This results in more complicated calculations, while the improvement...
ellipsoid were developed by Maxim Nyrtsov. Jacobi conformal projections were described by Carl Gustav Jacob Jacobi. Geodesicson a triaxial ellipsoid...
such as a reference ellipsoid or a geoid; an origin at which the ellipsoid/geoid is tied to a known (often monumented) location on or inside Earth (not...
spheroid; geodetic azimuth (or geodesic azimuth) is the angle between north and the ellipsoidalgeodesic (the shortest path on the surface of the spheroid...
uk, retrieved 29 December 2006 Direct and Inverse Solutions of Geodesicson the Ellipsoid with application of nested equations (pdf), Survey Review, April...
celestial body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid. Anellipsoid of revolution is uniquely defined...
shortest paths or geodesics in X {\displaystyle X} from S {\displaystyle S} to p {\displaystyle p} . For example, the cut locus of every point on the regular...
19111 standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude...
Erdmessung (Central Bureau of International Geodesy), and a series of global ellipsoids of the Earth were derived (e.g., Helmert 1906, Hayford 1910/ 1924). A...
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