Circular relative motion of a neutral Coulomb pair (${\omega }_{\pm }=e^{\ast }B/\mu \pm \sqrt{e^2{B}^2/(4{\mu }^2)+e^2/(\mu R^3)}$)

In the zero-pseudomomentum sector, a planar relative circular orbit has two signed angular-frequency branches. Here $\mu =m_1{m}_2/(m_1+m_2)$, $e^{\ast }=e(m_1-m_2)/[2(m_1+m_2)]$, $R$ is separation, and the Coulomb constant is absorbed into $e^2$. The centre of mass also circles: ${\mathbf{R}}_{\mathrm{cm}}={\mathbf{R}}_0+eB\mathbf{r}/[(m_1+m_2)\omega ]$. This distinction is essential when reconstructing individual particle orbits.