On the Stability of Electrostatic Orbits

TL;DR

This paper investigates the stability of electrostatic orbits between two charged conducting spheres, revealing critical angular momentum and radius where orbit stability changes due to charge polarization effects.

Contribution

It introduces a detailed analysis of how charge polarization affects electrostatic orbit stability, identifying critical parameters and behaviors.

Findings

Existence of a critical angular momentum $L_c$ and radius $r_c$

Stable and unstable circular orbits depend on $L$ relative to $L_c$

Charge polarization significantly alters force behavior from classical $1/r^2$ law.

Abstract

We analyze the stability of two charged conducting spheres orbiting each other. Due to charge polarization, the electrostatic force between the two spheres deviates significantly from $1/r^2$ as they come close to each other. As a consequence, there exists a critical angular momentum, $L_c$, with a corresponding critical radius $r_c$. For $L > L_c$ two circular orbits are possible: one at $r > r_c$ that is stable and the other at $r < r_c$ that is unstable. This critical behavior is analyzed as a function of the charge and the size ratios of the two spheres.