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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 ...
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 distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
A Cartesian coordinate system is defined in terms of several oriented reference lines, called coordinate axes; any arbitrary direction can be represented numerically by finding the direction cosines (a list of cosines of the angles) between the given direction and the directions of the axes; the direction cosines are the coordinates of the ...
On an ellipsoid of revolution, for short meridian arcs, their length can be approximated using the Earth's meridional radius of curvature and the circular arc formulation. For longer arcs, the length follows from the subtraction of two meridian distances, the distance from the equator to a point at a latitude φ.
True distance = rhumb distance ≅ ruler distance × cos φ / RF. (short lines) (short lines) With radius and great circle circumference equal to 6,371 km and 40,030 km respectively an RF of 1 / 300M , for which R = 2.12 cm and W = 13.34 cm, implies that a ruler measurement of 3 mm. in any direction from a point on the equator ...
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:
A standard Brunton compass, used commonly by geologists and surveyors to obtain a bearing in the field. In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:
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