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Then calculate the central angle in radians between two points (,) and (,) on a sphere using the Great-circle distance method (haversine formula), with longitudes and being the same on the sphere as on the spheroid.
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
U. S. Census Bureau Geographic Information Systems FAQ, (content has been moved to What is the best way to calculate the distance between 2 points?) R. W. Sinnott, "Virtues of the Haversine", Sky and Telescope 68 (2), 159 (1984). "Deriving the haversine formula". Ask Dr. Math. April 20–21, 1999. Archived from the original on 20 January 2020.
The length of a degree of longitude (east–west distance) depends only on the radius of a circle of latitude. For a sphere of radius a that radius at latitude φ is a cos φ, and the length of a one-degree (or π / 180 radian) arc along a circle of latitude is
The precise standard meanings of latitude, longitude and altitude are currently defined by the World Geodetic System (WGS), and take into account the flattening of the Earth at the poles (about 21 km or 13 miles) and many other details. Planetary coordinate systems use formulations analogous to the geographic coordinate system.
Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
Informally, specifying a geographic location usually means giving the location's latitude and longitude.The numerical values for latitude and longitude can occur in a number of different units or formats: [2]
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 ...