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WGS-84 ellipsoid model defines an ellipsis with
Major Axis (the Equator), radius = 6378137
Minor axis (Polar), radius = 6356752.3
FAI Sphere radius: 6371000
Mean radius defined by IUGG: 6371009.
The "mean radius" is equal to (2*a + b)/3, a is ecuatorial radius, b is polar radius on the ellipsis model, and apparently minimizes the "ellipsoidal mean square error", so it's a good "mean radius".