The gravitational field of a cube

TL;DR

This paper explores the theoretical gravitational properties of a hypothetical perfect cube-shaped planet, analyzing its potential, surface features, and orbital dynamics, with implications for modeling complex shapes through superposition.

Contribution

It introduces a novel theoretical analysis of the gravitational field of a cube-shaped object and proposes a method to model complex shapes by superimposing simpler cubic fields.

Findings

Calculated gravitational potential of a cube

Deduced surface lake formations on a cube

Analyzed orbital behavior around a cube

Abstract

Large astronomical objects such as stars or planets, produce approximately spherical shapes due to the large gravitational forces, and if the object is rotating rapidly, it becomes an oblate spheroid. In juxtaposition to this, we conduct a thought experiment regarding the properties of a planet being in the form of a perfect cube. We firstly calculate the gravitational potential and from the equipotentials, we deduce the shape of the lakes that would form on the surface of such an object. We then consider the formation of orbits around such objects both with a static and a rotating cube. A possible practical application of these results is that, because cuboid objects can be easily stacked together, we can calculate the field of more complicated shapes, using the principle of superposition, by simply adding the field from a set of component shapes.