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#


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.