On gravitational interactions between two bodies

TL;DR

This paper explores the mathematical structure of gravitational interactions between two bodies, discussing historical developments and the broader context of physical theories, with a focus on the quest for a unified understanding of fundamental forces.

Contribution

It provides a historical and conceptual analysis of the mathematical modeling of two-body gravitational interactions, highlighting recent developments and their implications for theoretical physics.

Findings

Historical insights into gravitational theory evolution

Discussion of recent mathematical approaches to two-body problems

Reflection on the nature of physical laws and mathematical structures

Abstract

Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only empirically determinable. We do not know if such a theory exists. Moreover, if it exists, there seems to be no reason for it to be comprehensible for the human mind. On the other hand, as pointed out in Wigner's famous paper, human mathematics is unbelievably successful in natural science. This seeming paradox may be mitigated by assuming that the mathematical structure of physical reality has many `layers'. As time goes by, physicists discover new theories that correspond to the physical reality on the deeper and deeper level. In this essay, I will take a narrow approach and discuss the mathematical structure behind a single physical phenomenon - gravitational interaction between two bodies. The main aim of this essay is to put some recent developments of this topic in a broader context. For the author it is an exercise - to investigate history of his scientific topic in depth.