 Equal-mass Coulomb circular orbit

For two particles of equal mass $m$ and opposite charges $\pm q$ separated by $s$, the centre of mass lies halfway between them. In a nonradiating classical model, each radius is $s/2$ and $k_e{q}^2/s^2=m{\omega }^{2}s/2$. Hence ${\omega }^2=2k_e{q}^2/(m{s}^3)$ and $T=2\pi \sqrt{m{s}^3/(2k_e{q}^2)}$. Equivalently, relative motion has reduced mass $m/2$. Radiation and quantum binding invalidate an indefinitely stable classical orbit for actual microscopic charges.