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  2. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...

  3. Haversine formula - Wikipedia

    en.wikipedia.org/wiki/Haversine_formula

    The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.

  4. Vincenty's formulae - Wikipedia

    en.wikipedia.org/wiki/Vincenty's_formulae

    They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such as great-circle distance. The first (direct) method computes the location of a point that is a given distance and azimuth (direction) from another point. The second (inverse) method ...

  5. Spherical trigonometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_trigonometry

    Consider the great circle that contains the side BC. This great circle is defined by the intersection of a diametral plane with the surface. Draw the normal to that plane at the centre: it intersects the surface at two points and the point that is on the same side of the plane as A is (conventionally) termed the pole of A and it is denoted by A'.

  6. Great circle - Wikipedia

    en.wikipedia.org/wiki/Great_circle

    The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1. Half of a great circle may be called a great ...

  7. Geodesics on an ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid

    For a sphere the solutions to these problems are simple exercises in spherical trigonometry, whose solution is given by formulas for solving a spherical triangle. (See the article on great-circle navigation.) For an ellipsoid of revolution, the characteristic constant defining the geodesic was found by Clairaut (1735).

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  9. Geographical distance - Wikipedia

    en.wikipedia.org/wiki/Geographical_distance

    The shortest distance along the surface of a sphere between two points on the surface is along the great-circle which contains the two points. The great-circle distance article gives the formula for calculating the shortest arch length on a sphere about the size of the Earth. That article includes an example of the calculation.

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