Earth Mean Radius

Eratosthenes got here first, around 240 BC: knowing the Sun stood directly over a well in Syene at midsummer noon while casting a 7.2° shadow in Alexandria, he scaled the distance between the cities up by 360/7.2 and obtained a circumference within a few per cent of the truth. His method needed no instrument more exotic than a stick.

The modern mean radius is a convenience rather than a physical boundary: it is the IUGG arithmetic mean of the ellipsoid's three semi-axes, and the real solid surface departs from it by nearly 9 km at Everest and 11 km in the Mariana Trench. Use it for escape velocity, surface gravity and great-circle distances; use the equatorial or polar radius when the 21 km difference matters.