User:Michael Retriever/Earth radius mean
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A radius mean for the Earth which isn't used but is interesting to know is the one that you would get distributing all the area of the Earth's ellipsoid over an adapted sphere.
Given the equatorial radius
and the polar radius
the Earth's great ellipse eccentricity would be
Being the formula for the longitude of an ellipse
where
![z = \left[{1 - \left({1\over 2}\right)^2e^2 - \left({1\cdot 3\over 2\cdot 4}\right)^2{e^4\over 3} - \left({1\cdot 3\cdot 5\over 2\cdot 4\cdot 6}\right)^2{e^6\over5} - \dots}\right]\!\,](../../../math/3/2/4/3249975c80042381bf3566d774ce68e3.png)
we can say that
thus
After calculating the decreasing function z with a precision of 8 diminishing terms, we find that
Note that the result is extremely similar to the quadratic mean.
