**DISCLAIMER!!**
**I’m not asking y’all to do classwork for me**
I just have a question to better understand geography. So we’re learning about great circles and such and how great circles bisect the earth and all that and anything that doesn’t equally bisect the earth is a small circle. North to south pole great circle. Equator is a great circle. My question is, how does that relate to flight navigation? I understand that great circles offer the shortest distance but how? And why? Some graphs from the lecture video I watch with a straight line path visually match the distance of the arc. Does the rotation of the earth also play a factor in this as well? And what is the rhumb line exactly?
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OK, a couple of geometry principles:
* If you pick two points on a (flat) sheet of paper, you can only draw ONE (straight) line through them. There’s no multiple straight lines going through two points. Two points determine a line.
* On a sphere, a line instead of going on “forever” will just wrap around the surface and form a GREAT circle. [Two points on a sphere determine a great circle](https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Illustration_of_great-circle_distance.svg/1200px-Illustration_of_great-circle_distance.svg.png). You can have [other circles going through those two points](https://qph.fs.quoracdn.net/main-qimg-fac28e0ee9bb7015beaf143db150a6ef.webp) but they will NOT be great circles.
So the shortest path on a flat piece of paper is the one line that’s formed by the two points. On a sphere (like the Earth), it’s the great circle, not any of the little circles.
To see what airplanes do when they fly, you’ll need [an actual globe](https://upload.wikimedia.org/wikipedia/commons/9/90/World_Globe_Map.jpg), but basically airplanes fly from “Point A” to “Point B”, so they just fly on the great circle determined by those two points.
What’s confusing is that [a map like this](https://geology.com/world/world-map.gif) is actually very stretched at the top and at the bottom; they had to deform the globe surface features to flatten them. So what looks like the shortest path on that map actually isn’t in reality. For example, satellites [orbit like this](https://www.esri.com/content/dam/esrisites/en-us/maps-we-love/46-solar-eclipse-finder/related-1.jpg), but on a flattened map they appear to [“fly” like this](https://www.scienceabc.com/wp-content/uploads/ext-www.scienceabc.com/wp-content/uploads/2017/03/ISS-Orbit-on-world-map.jpg-.jpg).
Wiki article about [the rhumb line](https://en.wikipedia.org/wiki/Rhumb_line). It has to do with ship navigation, where they can use that compass to go “30 degrees left of true north” and achieve a “rhumb line path” towards their destination if they keep that compass angle always the same.
Equator is a great circle, but if you walk due east constantly at any other latitude, your path is a circle, but you’ll have to curve to stay pointing east. For an extreme example, imagine you’re 10 meters from the south pole, if you walk perfectly east, the pole stays 10 meters away from you, and is always on your right side. That’s a small circle. If you were to maintain some other heading, like 85 degrees (5 degrees to the left of east), that’s a rhumb line, and you’d spiral away from the pole.
If you look at a map that shows the border between day and night, that wavy line on the map represents the great circle that separates daytime from nighttime.
As for how it relates to navigation, if you take a string and pull it tight between two points on a globe, that path is part of a great circle. When you unwrap the globe to fit on a flat map, it gets distorted(unless it also happens to be the equator or due north/south, which is still straight on a mercator projection).
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