How is the great circle and great circle route the same?

Answer 1

They are very closely related. Any great circle route moves along the circumference of a great circle around the globe. If a route does not stay on the circumference of a great circle, it is not a great circle route.

It is easy to see what great circles are on the earth, and you can easily demonstrate them if you have a globe handy*. First, imagine a sphere with no lines or markings on it of any kind. You can draw many different circles on the globe, from very tiny to very large. As you think about how large circles can get on a globe, something may occur to you. There is clearly a limit to how big a circle can get on any given globe. Not only that, but if you think about it it is clear that the largest circle you can draw on a globe will cut the globe into two exactly equal halves. Just like the equator.

Imagine that you are standing up right on the rim of a circle, as if you were standing at the equator. Imagine the circle getting bigger and bigger, way beyond the limits of the earth. As the imaginary circle gets bigger and bigger, your little part of it gets closer and closer to a straight line! If you're clever and coordinated enough to be able to stand on a ball, you can see that your little part of the circumference is very curved in comparison.

Putting these ideas together, you see that if you want to go from one point on earth's equator to another point on the equator, following the equator (in the right direction of course) will be the shortest possible way to go. The equator and all lines of longitude (including the parts on the other side of the poles) are great circles. But any two points on the globe can be connected by part of the circumference of a great circle. This is what leads some great circle routes to look very curved if they are plotted out on most standard map projections.

*Go to your globe, and have a length of strong thread handy. Any thin, very flexible cord will do. Find Washington, DC, and also find Moscow, Russia. Take your cord and extend it over the globe with one thumb holding the cord at Moscow and the other holding it at Washington. Keep taking up the slack as you gently move the cord back and forth. The cord is plotting out for you the great circle route between the cities. Obviously, the shortest length of your cord will represent the shortest path. Whenever you do this with a globe, the path your cord traces will be part of a great circle. Go to a map and see how odd looking your plotted route would look.