Is Gravity Absent at the Earth's Core?

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So if you could pinpoint the Earth's most central atom would gravity stop there?
 
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I understand what you intend to mean, in the sense that the sum of all the forces on that particle/ atom equals 0. Therefore it doesn't experience any gravitational effects; but I don't quite understand what do you mean by stopping there, since the force of gravity acts on every mass on every other mass in the universe. It doesn't stop
 

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