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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. The term also has meaning in any differentiable manifold with a connection.
The definition of latitude (φ) and longitude (λ) on an ellipsoid of revolution (or spheroid). The graticule spacing is 10 degrees. The latitude is defined as the angle between the normal to the ellipsoid and the equatorial plane. Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc.
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 ...
There are several ways of defining geodesics (Hilbert & Cohn-Vossen 1952, pp. 220–221).A simple definition is as the shortest path between two points on a surface. However, it is frequently more useful to define them as paths with zero geodesic curvature—i.e., the analogue of straight lines on a curved su
The geodesic equations are second-order differential equations; they can be re-expressed as first-order equations by introducing additional independent variables, as shown below. Note that a coordinate neighborhood U with coordinates x a induces a local trivialization of
The Toise of Peru had been constructed in 1735 for Bouguer and De La Condamine as their standard of reference in the French Geodesic Mission, conducted in actual Ecuador from 1735 to 1744 in collaboration with the Spanish officers Jorge Juan and Antonio de Ulloa. [130] [122] Gravimeter with variant of Repsold pendulum
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic.