I'm a secondary student who never studied any general relativity level maths (yet!), but I heard that in general relativity objects with mass and energy deform space-time, and therefore bodies move in the shortest path in this deformed space. At least this is what I think this article means.
There is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow. The curvature is, in turn, caused by the energy–momentum of matter.
Here's my question: If this is the case how come objects moving initially in the same direction but at different speeds, have end up having different trajectories? I mean, the length of a path doesn't depend on the speed you traverse it with? Unless some relativistic phenomena is at work?