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The azimuth is the angle formed between a reference direction (in this example north) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith. An azimuth (/ ˈ æ z ə m ə θ / ⓘ; from Arabic: اَلسُّمُوت, romanized: as-sumūt, lit.
The azimuth (or azimuthal angle) is the signed angle measured from the azimuth reference direction to the orthogonal projection of the radial line segment OP on the reference plane. The sign of the azimuth is determined by designating the rotation that is the positive sense of turning about the zenith. This choice is arbitrary, and is part of ...
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 ...
It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the azimuth line. This name was shortened to intercept method and the intercept distance was shortened to 'intercept'. The method yields a line of position (LOP) on which the observer is situated. The intersection of two or more ...
The angle p is given by splitting this direction along two orthogonal directions in the plane tangential to the sphere at the point s. The two directions are given by the partial derivatives of s with respect to φ and with respect to λ, normalized to unit length:
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). 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 ...
The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically: Absolute bearing refers to the clockwise angle between the magnetic north (magnetic bearing) or true north (true bearing) and an object. For example, an object to due east would have an absolute bearing of 90 degrees.
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.