Where is a planet's gravity maximum?

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    Gravity Maximum
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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?
 
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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