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

1 Answer
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 (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.