What is the arc length formula and how would it be used to find the radius of the earth?

Apr 17, 2016

If arc length (seemingly horizontal distance) between two locations on the equator, with longitude difference ${\theta}^{o}$, is S km, the equatorial radius is $\left(\frac{S}{\theta}\right) \left(\frac{180}{\pi}\right) k m$

Explanation:

The formula used is (circular arc length) = radius X (angle subtended at the center in radian)
Sample data, for explication:

If two locations, near the equator, in Brazil, have longitudes ${45}^{o} W \mathmr{and} {55}^{o} W$ and the distance in-between is 1100 km, S = 1100 km, $\theta = {10}^{o}$.

Equatorial radius $R = \left(\frac{1100}{10}\right) \left(\frac{180}{\pi}\right) k m$= 6302 km.