Separation of Potentials in the Two-Body Problem

TL;DR

This paper introduces a novel approach to the two-body problem by separating potentials, allowing trajectory calculations without using reduced mass, and demonstrates that each body moves in its own stationary potential well.

Contribution

It proposes a new method involving potential separation for solving the two-body problem, differing from traditional reduced mass techniques.

Findings

Each body moves in its own stationary potential well.

Energy and angular momentum laws hold for each body separately.

Potentials enable direct trajectory calculations.

Abstract

In contrast to the well-known solution of the two-body problem through the use of the concept of reduced mass, a solution is proposed involving separation of potentials. It is shown that each of the two point bodies moves in its own stationary potential well generated by the other body, and the magnitudes of these potentials are calculated. It is shown also that for each body separately the energy and the angular momentum laws are valid. The knowledge of the potentials in which the bodies are moving permits calculation of the trajectories of each body without resorting to the reduced mass. Key words: mechanics, two-body problem, gravitational potential, virial theorem.