I’ve searched online and many of the answers have physics or geometry jargon which I can’t wrap my head around. The last time I studied physics was in highschool & I really only studied enough to pass since I knew I wasn’t going to use it in my university major.
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A geodesic between two points is the straightest possible path between those points. In ordinary “flat” space, a geodesic is always a straight line.
https://en.m.wikipedia.org/wiki/Geodesic
> In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/)[1][2] is commonly a curve representing in some sense the shortest[a] path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a “straight line”.
People that study geodetic science do precise measurements of the earth and were, early on, involved with global positioning systems.
A geodesic is the shortest path between two points, taking into account the local geometry.
For example, let’s say you wanted to get from one side of a field to the other. In theory the shortest path would be the straight line through the middle. But if the middle of the field is all swampy that might slow you down – so the actual shortest path might involve going around the edge of the field.
Geodesics are particularly useful for long-distance travel, as they tell you the shortest route to take (particularly for ships and aeroplanes), accounting for the curvature of the Earth. It is why transatlantic flights tend to go very far North – it may look like a longer route on a map, but it is the shortest distance on a sphere.
Well, it is fundamentally a geometry concept so…
A geodesic is the generalization of a straight line in non-Euclidean geometry.
Euclidean geometry is the one we are used to in our everyday day lives. The angles of a triangle sum up to 180°, for a given line and a point off that line, there is a single line that is parallel (and co-planar if in 3D) to the first and includes the point, and parallel lines never intersect.
Turns out this isn’t the only Geometry possible. You can change any and all of these rules and still end up with consistent and useful results.
For example, if you try to do geometry on the surface of a sphere, where you can just ignore the curvature. Or on the surface of a cone. Well… You need different equations and get different results.
Cone is a pretty good example to illustrate how geodesics can appear different from straight lines on a flat surface.
Take a strip and a sheet of paper. Roll the sheet in a cone.
Lay the strip flat around the cone and trace one of its edges.
You’ve just traced a geodesic of the cone. If you unroll the sheet of paper, you will see it doesn’t look like a straight line. But the math behind it preserves the properties of a straight line we actually care about (turns out being straight when we unroll the sheet of paper is not one of them).
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