Gravitational potential formulae between two bodies with finite dimensions

Abstract

The aim of this paper is to analyze and shed light on the potential relations between two bodies of finite dimensions and different shapes. After explaining the properties of different shaped bodies, we analyze the gravitational potential between an irregular body and a point mass, followed by the potential relation between two irregular bodies with discussion of its different properties. We also explore the potential relation between two solid cylinders, which can be degraded to 16 potential relations; one of these relations is the potential relation between two finite straight segments. With a new development for the potential relation, we evaluate the gravitational potential between a heterogeneous irregular body and a point mass followed by the potential between two heterogeneous irregular bodies with N−layers, which also can be reduced to the potential between two oblate or prolate heterogeneous bodies. We demonstrate that this relation can be degraded to many potential relations between two bodies, because it depends on the moments of inertia of the body's shape. Finally, we emphasize that this relation is considered a golden relation, which can be developed to generate the potential relation between different shaped bodies, either natural celestial bodies or between celestial and artificial bodies.

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