Continuation with Distance along the parallel of latitude

Distance Along the Parallel of latitudes

Giving X (30⁰ N, 45⁰ E), Y (30⁰ N, 45⁰ W) and Z (30⁰ N, 15⁰ E)

                                                                                                                I.            Find the distance between X &Y

                                                                                                             II.            Find the distance between X & Z

                                                                                                           III.            Find the distance between Y & Z

Solution

        I.            Since X, Y and Z are on latitude 30⁰ N which is a small circle.

The radius of the circle in relation to the great circle radius is as shown below:

r= R Cos α, where α is the latitude angle

To find the distance is like finding the length of an arc

The angle subtended at center is the longitude difference/ angular distance between two places e.g.

e.g. between X & Y it is 90⁰ (It takes 45⁰ to reach the meridian and 45⁰ to get to 45 ⁰ W)

X and Y distance can now be calculated as follow taken R= 6400 km

90/360 x 2 x 3.142 x 6400 cos 30= 8707.37 km

Can you try the next two?