An aircraft flies over the North Pole at 900 km h-1 and continues south at a constant speed along a particular line of longitude. Estimate the angle between a plumb line hanging freely in the aircraft and the true radius vector from the centre of the Earth to the aircraft when the aircraft is
(a) At the North Pole,
(b) At the equator, and
(c) At latitude 45° N.
Indicate the orientation of the plumb line in each case. You may assume the Earth to be a sphere of radius 6.4 x 103 km.