Linear frictional forces cause orbits to neither circularize nor precess

TL;DR

This paper investigates how linear frictional forces influence orbital behavior in damped Kepler systems, revealing that such forces prevent orbit circularization or precession, contrary to classical expectations.

Contribution

It introduces a generalized Poisson structure to analyze the damped Kepler problem, showing the Runge-Lenz vector remains conserved under linear damping to leading order.

Findings

Linear damping prevents orbit precession.

The Runge-Lenz vector remains conserved in damped systems.

Frictional forces do not lead to orbit circularization.

Abstract

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov[1]. In this generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coe