A Pedagogical Discussion Concerning the Gravitational Energy Radiated by Keplerian Systems

TL;DR

This paper presents a simplified, pedagogical method for calculating gravitational radiation from Keplerian systems, making complex relativistic results accessible to undergraduates.

Contribution

It introduces an intuitive approach to estimate gravitational power in elliptical orbits by local circular approximations, clarifying the eccentricity dependence.

Findings

Accurately approximates gravitational power for elliptical orbits

Simplifies derivation of gravitational radiation formulas

Enhances understanding of relativistic orbital energy loss

Abstract

We first discuss the use of dimensional arguments (and of the quadrupolar emission hypothesis) in the derivation of the gravitational power radiated on a circular orbit. Then, we show how to simply obtain the instantaneous power radiated on a general Keplerian orbit by approximating it locally by a circle. This allows recovering with a good precision, in the case of an ellipse, the highly non trivial dependence on the eccentricity of the average power given by general relativity. The whole approach is understandable by undergraduate students.