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A compass rose, showing absolute bearings in degrees. In nautical navigation the absolute bearing is the clockwise angle between north and an object observed from the vessel. If the north used as reference is the true geographical north then the bearing is a true bearing whereas if the reference used is magnetic north then the bearing is a ...
Traverse tables use three values for each of the crooked course segments – the Distance (Dist.), Difference of Latitude (D.Lat., movement along N–S axis) and the Departure (Dep., movement along E–W axis), the latter two calculated by the formulas: Difference of latitude = distance × cos θ Departure = distance × sin θ
View from the Swabian Jura to the Alps. 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.
For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north.
is the isometric latitude. [5] In the Rhumb line, as the latitude tends to the poles, φ → ± π / 2 , sin φ → ±1, the isometric latitude arsinh(tan φ) → ± ∞, and longitude λ increases without bound, circling the sphere ever so fast in a spiral towards the pole, while tending to a finite total arc length Δ s given by
If a navigator begins at P 1 = (φ 1,λ 1) and plans to travel the great circle to a point at point P 2 = (φ 2,λ 2) (see Fig. 1, φ is the latitude, positive northward, and λ is the longitude, positive eastward), the initial and final courses α 1 and α 2 are given by formulas for solving a spherical triangle
where φ (°) = φ / 1° is φ expressed in degrees (and similarly for β (°)). On the ellipsoid the exact distance between parallels at φ 1 and φ 2 is m(φ 1) − m(φ 2). For WGS84 an approximate expression for the distance Δm between the two parallels at ±0.5° from the circle at latitude φ is given by
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.