Calculating Distances Along the Great Circles

Note that the shortest distance between two points on the surface of the earth lies on the arc length of a great circle connecting the two points.

Let the arc length, l, be \( \scriptsize \overline{AB} \), then

\( \scriptsize l = \overline {AB} = \normalsize \frac{θ°}{360°} \scriptsize \times 2 \pi R\)

Where 

• θ° = angular difference
• R = radius of the earth = 6,400 km
• π = \( \frac{22}{7} \)

Example 6.3.1:

A and B are two places on the earth's surface on the same meridian. B has a Latitude of 20° N and A is a point north of B such that the distance AB measured along the meridian is 800 km.

Calculate the Latitude of A