The average radius of an ellipse is the diagonal between major and minor axes. Hence one has the ratio of circumference of ellipse to 2 x the elliptical average radius. As the ellipse approaches the limiting case of a circle, at what rate (if any) does the ratio change? For Kepler’s Third Law, one should have period^2 proportional to average radius^3. So at what rate would such constant change (?) as circularity is approached?

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