

I’m not an expert, but from my understanding it’s kind of something like this:
So a geodesic is a line of shortest length between two points on a curved surface, like two points on a ball, the geodesic would be the shortest line that connects the two.
If you look at flight paths compared to a flat representation of Earth, you’ll see that aircraft seem to follow a very strange arc, that’s because they’re actually flying the geodesic of their route, which looks funny when presented flat.
If you imagine Earth as the aircraft and spacetime as the globe, that’s essentially what is meant. However do keep in mind that aircraft follow a two-dimensional geodesic, whereas we would follow a three-dimensional one due to spacetime being four-dimensional; due to how reductions work. (3D object casts 2D shadow, 4D object casts 3D shadow).
My knowledge is rather vague past this point, but essentially orbits are geodesics against 4D spacetime, and gravity affects that temporal component.











We do actually, just at a very small scale compared to what you may see around black holes.
Satellites in LTO need their clocks adjusted by a few dozen picoseconds I believe. Very cool.