Question

Qantas flies a non-stop route from London, UK (51.5 N,0 E) to Perth, Australia (32 S,115.9 E). Assume the Earth is perfect sphere with radius of 6371 km.

Calculate the total length of the flight first fly due east until reach longitude 115.9 degree east and then fly due south.

Calculate the total length by first fly due south then due east.

Calculate the arc angle of the great circle and therefore the shortest flight path.

Answer 1

given, latlong for London (a1, b1) = (51.5N, 0E)

latlong for perth (a2,b2) = (32S, 115.9 E)

a. length of flight route east then south = l

radius of earth R = 6,371,000 m

hence

l = Rcos(a1)(b2 - b1) + R(a2 - a1)

l = 6,371,000(cos(51.5)(115.9 - 0)*pi/180 + (32 - (- 51.5))*pi/180)

l = 17196233.8465462 m = 17196.233846 km

b. for the path south then east

l = R(a2 - a1) + Rcos(a2)(b2 - b1)

l = 6,371,000(cos(32)(115.9 - 0)*pi/180 + (32 - (- 51.5))*pi/180)

l = 20102.7945 km

c. arc angle of greatest circle = c

cos(c) = sin(a1)sin(a2) + cos(a1)cos(a2)cos(b2 - b1)

hence

c = 130.189414674 deg

hence

arclentgh = c*R = 14476.40241462 km