On the potential energy in a gravitationally bound two-body system with arbitrary mass distribution

Abstract

The potential energy problem in a gravitationally bound two-body system has recently been studied in the framework of a proposed impact model of gravitation \citep{WilDwi}. The result was applied to the free fall of the so-called Mintrop--Ball in G\"ottingen with the implicit assumption that the mass distribution of the system is extremely unbalanced. An attempt to generalize the study to arbitrary mass distributions indicated a conflict with the energy conservation law in a closed system. This necessitated us to reconsider an earlier assumption made in selecting a specific process out of two options \citep{Wiletal}. With the result obtained here we can now make an educated selection and reverse our choice. The consequences are presented and discussed in detail for several processes. Energy and momentum conservation could now be demonstrated in all cases.