9.4.3 Shortest Distance between Two Points


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 48o 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 48o S
= 180 x 60 x cos 48o ← (angle PMQ = 180o)
= 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 = 180o – 48o – 48o = 84o)
= 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.