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The distance along the great circle will then be s 12 = Rσ 12, where R is the assumed radius of the Earth and σ 12 is expressed in radians. Using the mean Earth radius, R = R 1 ≈ 6,371 km (3,959 mi) yields results for the distance s 12 which are within 1% of the geodesic length for the WGS84 ellipsoid; see Geodesics on an ellipsoid for details.
Radius = zenith distance: zd [nm] = 60 ⋅ (90 - Ho) (aka co-altitude of Ho) As the circles used for navigation generally have a radius of thousands of miles, a segment a few tens of miles long closely approximates a straight line, as described in Sumner's original use of the method.
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 ...
For example, the reference GJQJ0207S6X8 designates a rectangle centered on Deal Island (GJQJ0207), running 6 nautical miles (11 km) east–west and 8 nautical miles (15 km) north–south. Designation GJPJ4103R5 means a circle around Point Lookout (GJPJ4103) with a radius of 5 nautical miles (9 km).
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 ...
d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula allows the haversine of θ to be computed directly from the latitude (represented by φ) and longitude (represented by λ) of the two points:
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Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.