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I was trying to understand the Einstein's explanation for gravity (gravitational force), and while I am able to understand why two moving masses will be attracted, due to the curving of the space, I am not quite able to understand what would make an apple fall, i.e., how will Einstein model explain the gravitational force between two stationary objects?

(Please correct me if I am wrong anywhere. I am a computer scientist; hence physics is not my forte! :D)

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Related: – Qmechanic Sep 21 '12 at 12:24
Einstein's model says that all particles will naturally travel along geodesics. These are effectively the straightest path possible in curved space-time. It turns out that it is a straighter path to move closer to another object with mass as time increases, than to be stationary. – Mew Sep 21 '12 at 12:30
up vote 4 down vote accepted

I think the picture you have of space being curved is incomplete. In GR, it's spacetime that is curved, not just space.

To visualize GR, you must learn to picture worldlines instead of trajectories. Worldlines are paths of objects through spacetime. The worldlines of freely falling objects are geodesics.

In GR, the presence of mass-energy results in geodesic deviation which roughly means that two initially parallel geodesics will not remain parallel.

So, here's the picture you should have. In flat spacetime, the worldlines of two spatially separated objects that are not moving with respect to each other are parallel.

In the curved spacetime of GR, the geometry is such that the these two worldines converge even if they were "parallel" (not moving with respect to each other) at some point in the past.

Viewed as a trajectory in space rather than a worldline in spacetime, you see two objects falling radially towards one another.

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This sounds good in theory but do you know if it is possible to compute orbits by using geodesics and curved spacetime? – Zeynel Sep 22 '12 at 12:22

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