Two countries are halfway around the world from each other (by E to W) and lie on the 17 degree north latitude. Earth's radius is 3790 miles at that latitude. Would flying west to the other country be shorter, or would flying directly north be shorter?
1 Answer
Go north, not east or west, for the shortest route in this case.4
Explanation:
On a globe, draw the arc that goes north from one city through the North Pole, then south to the other city. Note that the plane where the arc lies passes through the center whereas any other plane through the same two cities does not. The route through the North Pole, with its plane passing through the center, is called the Great Circle Route.
It has been known for centuries that the Great Circle Route with its arc measuring less than 180°, in this example going through the North Pole, is the shortest possible route on a spherical globe. The Great Circle, having a bigger radius than any smaller circle on the sphere, curves less going from point A to point B.
This principle applies even when the cities are not exactly halfway around a latitude from each other. In that case the route does not go right over a pole but can gp to places that seem fantastic if you are not used to thinking in terms of great circles. As an experiment, take a piece of string and stretch it taut on a globe from New York to Tokyo. The taut string, forced to cover the shortest route, follows a great circle -- and you see that it goes through northern Alaska!
