Because d is then large approaching π R, half the circumference a small error is often not a major concern in this unusual case although there are other great-circle distance formulas that avoid this problem.
The haversine of the central angle (which is d/r) is calculated by the following formula: where r is the radius of the earth (6371 km), d is the distance between two points, is the latitude of the two points, and is the longitude of the two points respectively.
The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical triangles. Task
haversine (θ) = sin² (θ/2) The following equation where φ is latitude, λ is longitude, R is earth’s radius (mean radius = 6,371km) is how we translate the above formula to include latitude and longitude coordinates. Note that angles need to be in radians to pass to trig functions: a = sin² (φB - φA/2) + cos φA * cos φB * sin² (λB - λA /2)
Definition of the Haversine Formula We can now define the formula of haversine for calculating the distance between two points in the spherical coordinate system. The formula itself is simple, and it works for any pair of points that are defined according to their radial coordinates for a given radius:
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