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I do believe that might be at the top of the largest mountain. Of course, what goes on in the changing interior of the earth probably makes much more difference. The point is: that place where the most mass is between you and the center of the earth's center of gravity (the center). Think about it. If you were at the very center of the earth (and there was a hole there rather than a very solid blob of metal) the great gravity of the mass of the earth would be approximately equal in all directions; so, you would float there.

It would be on poles, because due to Earth's slighly deflated shape they are closest to Earth's center. Mind you, the gravitational force is in inverse square proportion with distance.

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Q: Where is the weight of an object maximum on earth?
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