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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).
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.
Satellite geodesy is geodesy by means of artificial satellites—the measurement of the form and dimensions of Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques.
A brief history of geodesy from NASA. [1]The history of geodesy (/dʒiːˈɒdɪsi/) began during antiquity and ultimately blossomed during the Age of Enlightenment.. Many early conceptions of the Earth held it to be flat, with the heavens being a physical dome spanning over it.
Fig. 14. Definition of reduced length and geodesic scale. where K(s) is the Gaussian curvature at s. As a second order, linear, homogeneous differential equation, its solution may be expressed as the sum of two independent solutions = (,) + (,) where
Given a (pseudo-)Riemannian manifold M, a geodesic may be defined as the curve that results from the application of the principle of least action.A differential equation describing their shape may be derived, using variational principles, by minimizing (or finding the extremum) of the energy of a curve.