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

TL;DR

This paper investigates the optimal shape of an object to produce the maximum gravitational field at a specific point, providing compact solutions across dimensions and revealing a uniform surface gravity contribution feature.

Contribution

It offers a comprehensive analysis and explicit solutions for the shape optimization problem in Newtonian gravity across all dimensions.

Findings

Derived compact solutions for all dimensional cases.

Identified that surface mass elements contribute equally to gravity at the point.

Revealed a simple physical principle governing optimal shapes.

Abstract

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.