Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of Newton's 3rd law, but let’s consider Einsteinian gravity. My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.
So do I pull Earth with the same force it pulls me? If yes, how?
Answer
You both fall toward the common center of mass. Because the mass of the Earth is quite a bit larger than yours, the center of mass is very close to the center of the Earth, but rather far away from you. Thus, as you both fall to the common center, the Earth hardly moves while you fly until you hit the ground.
More specifically, you are talking about the two-body solution. Both bodies curve spacetime and move in this curved spacetime. As you justly stated, your contribution is small and for this reason the Earth movement toward you is very small as well.
However, when you interact with the Earth, the momentum you get equals the momentum the Earth gets. And yes, in the classical view, you attract the Earth with the same force as the Earth attracts you. While your gravity is very weak, the mass of the Earth attracted by it is enormous. Therefore the forces work out to be the same, as expected.
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