**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 x 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:***(a)**

Distance from

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