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.

中文翻译：

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有限尺寸的两个物体之间的引力势公式

本文的目的是分析和阐明有限尺寸和不同形状的两个物体之间的潜在关系。在解释了不同形状的物体的特性之后，我们分析了一个不规则物体和一个点质量之间的重力势能，然后分析了两个不规则物体之间的重力关系，并讨论了它们的不同特性。我们还探讨了两个实心圆柱之间的势能关系，可以将其降级为16个势能关系。这些关系之一是两个有限直线段之间的潜在关系。随着电位关系的新发展，我们评估了异质不规则体和点质量之间的重力势，然后评估了两个N异质不规则体之间的势-层，也可以减少到两个扁圆形或长圆形异质体之间的电位。我们证明该关系可以降级为两个物体之间的许多潜在关系，因为它取决于物体形状的惯性矩。最后，我们强调该关系被认为是黄金关系，可以发展为在不同形状的物体之间（天然天体或天体与人造物之间）产生潜在的关系。