Gps Great Circle
Calculus/Geometry Question?
So in my AP Calc class we are using GPS to do some calculations.
During the lecture the teacher said something like.. “The shortest path of travel is around the greatest circle”. and I don’t quite understand.. can someone fill me in on this?
The correct statement is closer to: “Given any two points on the earth’s surface, the shortest path of travel along the earth’s surface is along the great circle containing both points.”
A “great circle” is a circle drawn along the surface of the earth that has the same center as the center of the earth (this is assuming the earth a perfect sphere, which it is not, but it is close). Basically, it is the largest circle that can be drawn around the earth through those two points.
The effect of this is that the shortest path is not a straight line on most maps, since maps are usually Mercator projections which preserve direction. But unless your points are at the exact same longitude, you will need to change direction along the shortest path to follow the great circle.
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