Radius For Spherical Earth
See also: Earth radiusThe shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial radius of 6,378.137 km; distance from the center of the spheroid to each pole is 6356.752 km. When calculating the length of a short north-south line at the equator, the sphere that best approximates that part of the spheroid has a radius of, or 6,335.439 km, while the spheroid at the poles is best approximated by a sphere of radius, or 6,399.594 km, a 1% difference. So as long as we're assuming a spherical Earth, any single formula for distance on the Earth is only guaranteed correct within 0.5% (though we can do better if our formula is only intended to apply to a limited area). McCaw recommends using the mean radius for a spherical approximation of the figure of the Earth, i.e., approximately 6371.01 km.
Read more about this topic: Great-circle Distance
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—Henry Vaughan (1622–1695)