Geodesics and how someone can end up in New Orleans by traveling East from the westernmost point in Alaska?
In: Planetary Science
If you assume the Earth is a sphere, then if you head in any direction going in a straight line, you will travel along a great circle, which is a circle the same size as the equator. Which of those circles you follow will depend on your starting point and your starting direction. But the fact that you follow such a circle is pretty intuitive. Consider a smaller ball that’s perfectly symmetric, and if you leave any point you’re going to go around an equator of the ball and back where you started.
If you look at a globe, you’ll see that none of the lines of constant latitude are great circles, except the equator. They’re all smaller circles, all the way down to a single point at the poles. So it should be clear that if you set off traveling east from anywhere, and keep going in a straight line, those constant latitude circles can’t be paths you will follow. In particular, if you start at the North Pole, you’ll go all the way around through the south pole, regardless of which direction you go, so you won’t stay on the same latitude at all.
So then, to figure out the path from any starting point, you can imagine the starting point being a “pole” of the globe. No matter which direction you go, you’ll end up following a great circle that goes through the antipode of your starting point, which has the same latitude but south instead of North. So you’ll have that whole range of latitudes on your trip.
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