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Vincenty Inverse (distance between points) Calculators from the U.S. National Geodetic Survey: Online and downloadable PC-executable calculation utilities, including forward (direct) and inverse problems, in both two and three dimensions (accessed 2011-08-01).
The geodesic distance between opposite umbilical points is the same regardless of the initial direction of the geodesic. Whereas the closed geodesics on the ellipses X = 0 and Z = 0 are stable (a geodesic initially close to and nearly parallel to the ellipse remains close to the ellipse), the closed geodesic on the ellipse Y = 0 , which goes ...
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". The noun geodesic and the adjective geodetic come from geodesy, the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry.
The inverse problem for earth sections is: given two points, and on the surface of the reference ellipsoid, find the length, , of the short arc of a spheroid section from to and also find the departure and arrival azimuths (angle from true north) of that curve, and . The figure to the right illustrates the notation used here.
Equatorial (a), polar (b) and mean Earth radii as defined in the 1984 World Geodetic System revision (not to scale) The reference ellipsoid models listed below have had utility in geodetic work and many are still in use. The older ellipsoids are named for the individual who derived them and the year of development is given.
Adrien-Marie Legendre showed that the distance along a geodesic on a spheroid is the same as the distance along the perimeter of an ellipse. [29] For this reason, the expression for m in terms of β and its inverse given above play a key role in the solution of the geodesic problem with m replaced by s , the distance along the geodesic, and β ...
Geodesy or geodetics [1] is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D.It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. [2]