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 as they come close to each other. As a consequence, there exists a critical angular momentum, , with a corresponding critical radius . For two circular orbits are possible: one at that is stable and the other at that is unstable. This critical behavior is analyzed as a function of the charge and the size ratios of the two spheres.
The results are yet to be published.
The ratio of the lifetime to the orbital period is of order , where is the orbital speed and is the speed of light.
At the critical point the centrifugal force is of the same order as but is not exactly equal to the Coulomb force.
Ground based tests showed that the orbiting sphere received only about 80% of the maximum possible charge at that voltage due to the small but finite size of the electrode which “shared” the charge with the sphere.