Question

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

Answer 1

If arc length (seemingly horizontal distance) between two locations on the equator, with longitude difference `theta^o`, is S km, the equatorial radius is `(S/theta)(180/pi) km`

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 and 55^o W` and the distance in-between is 1100 km, S = 1100 km, `theta=10^o`.

Equatorial radius `R = (1100/10)(180/pi) km`= 6302 km.