If gravity is curvature of space, and everything is traveling in a straight line in the curved space, then why do two objects traveling with different speed in same direction from same point take different trajectory?
Q2) Curvature explains orbiting satellites, but then how does simple falling of objects is described?
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Ok, first off, it’s true that objects in spacetime not under external forces follow “shortest paths” (called *geodesics*) through spacetime (I don’t think it’s helpful to think of this as a ‘straight line’). That said:
– These geodesics aren’t *unique*. A geodesic is a *local* minimum, meaning every *small* perturbation from that path is longer. There can be multiple geodesics connecting two points, as long as both are locally minimize the path.
– Even if objects follow “straight lines”, if they end up at different points they follow *different straight lines*. Even if they end up at the same point they can follow different “straight lines”, but if they end up at different points they certainly follow different paths.
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