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 1r2 as they come close to each other. As a consequence, there exists a critical angular momentum, Lc, with a corresponding critical radius rc. For L>Lc two circular orbits are possible: one at r>rc that is stable and the other at r<rc that is unstable. This critical behavior is analyzed as a function of the charge and the size ratios of the two spheres.

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13.

The ratio of the lifetime to the orbital period is of order c3v3, where v is the orbital speed and c is the speed of light.

14.

The polarization force, defined as the right-hand side of Eq. (7), comes from substituting the non-Coulombic terms in Eq. (2) into Eq. (6). It is not equal to the total force minus the Coulomb force.

15.

At the critical point the centrifugal force is of the same order as but is not exactly equal to the Coulomb force.

16.

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.

17.
In addition to the parameters listed in Table I of Ref. 1 the launch velocities obtained from the video of the orbits were used in calculating the values of L̃2. A link to the video is provided in Ref. 1.
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