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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The curving of space is not just in space, but also time. Better combined together into _spacetime_. Lets explore why this answers your question:
All things are moving both in space and time. Even more, within this setup (and only then the curvature truly makes sense), everything is actually moving _exactly at the speed of light_! This may sound very weird at first, but normally almost all your speed is forward in time! Only if you get really _really_ fast in space can we notice that it now automatically moves slower in time: you age slower, things around you seem to speed up. Your temporal speed gets reduced.
Only with this realization will the weirdness of general relativity really make sense. Gravity is bending spacetime, both aspects of it. However, you are completely correct that two things with the same starting position and direction should travel the same path! Yet this seems to contradict observations, even basic ball throws, more so orbital mechanics.
The resolution of this paradox lies within the above: spacetime, and that everything always moves at the speed of light. When two objects start in the same direction but at different speeds, the one faster in space is actually slower in time! Put differently, their directions in spacetime are actually not the same; one moves faster “sideways” (in space), while the other moves quicker “forwards” (in time). And as a result of this, their resulting paths throughout bent spacetime will differ.
Edit: for the experts: yes I am aware that the sign for time is different; the above has been written in such a way to still be technically correct while obviously not dabbling in metrics and manifolds.
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