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The optimal shape of an object for generating maximum gravity field at a given point in space

How can we design the shape of an object, in the framework of Newtonian gravity, in order to generate maximum gravity at a given point in space? In this work we present a study on this interesting problem. We obtain compact solutions for all dimensional cases. The results are commonly characterized by a simple "physical" feature that any mass element unit on the object surface generates the same gravity strength at the considered point, in the direction along the rotational symmetry axis.