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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).
= 6,371.009 kilometers = 3,958.761 statute miles = 3,440.069 nautical miles. D {\displaystyle D_{\,}\!} = Distance between the two points, as measured along the surface of the Earth and in the same units as the value used for radius unless specified otherwise.
More importantly, the radius of curvature of a north-south line on the earth's surface is 1% greater at the poles (≈6399.594 km) than at the equator (≈6335.439 km)—so the haversine formula and law of cosines cannot be guaranteed correct to better than 0.5%.
If the initial point is at the North or South pole, then the first equation is indeterminate. If the initial azimuth is due East or West, then the second equation is indeterminate. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly. [clarification needed]
using SI units of meters for , hertz (s −1) for , and meters per second (m⋅s −1) for , (where c=299 792 458 m/s in vacuum, ≈ 300 000 km/s) For typical radio applications, it is common to find d {\displaystyle d} measured in kilometers and f {\displaystyle f} in gigahertz , in which case the FSPL equation becomes
When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius , or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed ...
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 ...
kilometre (km) or kilometer is a metric unit used, outside the US, to measure the length of a journey; the international statute mile (mi) is used in the US; 1 mi = 1.609344 km; nautical mile is rarely used to derive units of transportation quantity.