Bad value of EARTH_RADIUS

[cffk]

EARTH_RADIUS is earth's radius for use in great circle calculations where the earth is treated as a sphere. The recommended value for such a quantity is the mean radius = (2a + b)/3 = 6371 km. The value defined in coordinate_calculation.hpp and haversine.hpp is about (3a + b)/4 = 6372.8 km. There's no justification for this value.

[danpat]

@cffk Ultimately, the 6372.8km value comes from http://math.wikia.com/wiki/Ellipsoidal_quadratic_mean_radius. I believe it was copied from libosmium

Whether it's the right thing to use or not is another question. We have a PR open at the moment here #5041 that will likely deprecate this constant.

[cffk]

Yes, I know about this source. Unfortunately, I can't make head or tail of it. There's a long discussion between me and Kaimbridge, the proponent of the quadratic mean radius here. Click on the "show" for the "extended discussion".

[github-actions]

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[1ec5]

The constant is still there:

osrm-backend/include/util/coordinate_calculation.hpp

Lines 22 to 24 in 4930d2e

	// earth radius varies between 6,356.750-6,378.135 km (3,949.901-3,963.189mi)
	// The IUGG value for the equatorial radius is 6378.137 km (3963.19 miles)
	const constexpr long double EARTH_RADIUS = 6372797.560856;

But nothing uses it anymore as of #6315.