**9.4.3 Shortest Distance between Two Points**

**1.**The

**shortest distance**between two points on the surface of the earth is the distance measured along a great circle.

Shortest distance between points
D and M =
( θ × 60 ) nautical miles |

**Example:**

In the above diagram, calculate

(a) The distance from

*P*to*Q*, measured along the parallel of latitude 48^{o}S,(b) The distance from

*P*to*Q*, measured along the route*PSQ*, where S is the South Pole. State the shorter distance.

Solution:

Solution:

**(a)**

Distance from

*P*to*Q*, measured along the parallel of latitude 48^{o}S= 180 × 60 × cos 48

^{o}← (angle*PMQ*= 180^{o})=

**7266.61 n.m.**

**(b)**

Distance from

*P*to*Q*, measured along the route*PSQ*, where S is the South Pole= 84 × 60 ← (angle

*POQ*= 180^{o}– 48^{o}– 48^{o }= 84^{o})=

**5040 n.m.**

The distance from

*P*to*Q*, measured along the route*PSQ*in**(b)**, where S is the South Pole, is**shorter**than the distance measured along the parallel of latitude in (a).
The
shortest distance in the above example is the distance along the arc of a great circle,
which passes through the
South (or North) Pole. |