Where is a planet's gravity maximum?

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rootone
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An object approaching Earth (or any planet) experiences increasing gravity as it gets nearer.
However, If the object could continue until reaching the center it would find itself again in a net zero gravity field.
At what point will it experience the maximum amount of gravity?
 
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One way to get the answer would be to model the Earth's density versus depth analytically and use an equivalent form of Gauss' law.
 
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