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Now start the simulation and let the moon fall. The deepest portion of Earth’s core and the center of the softball-sized moon will quickly displace the less dense materials between them and merge, with the little moon traveling the most distance and the core moving slightly for the merging. There will be some oscillation as the gravity well attains hydrostatic equilibrium again, but the dropped "softball moon" will quickly occupy the center of the core, driving the Earth’s well ever deeper with its added mass. And due to its ultra-density, it will reside at the point of greatest acceleration - the center.
An acceleration tapering to zero at the core is a physics recipe for a hollow Earth rather than the home for the densest matter in the well.
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