= Circular relative motion of a neutral Coulomb pair
{title2=$\omega_\pm=e^*B/\mu\pm\sqrt{e^2B^2/(4\mu^2)+e^2/(\mu R^3)}$}
In the zero-pseudomomentum sector, a planar relative circular orbit has two signed angular-frequency branches. Here $\mu=m_1m_2/(m_1+m_2)$, $e^*=e(m_1-m_2)/[2(m_1+m_2)]$, $R$ is separation, and the Coulomb constant is absorbed into $e^2$. The <centre of mass> also circles: $\mathbf R_{\rm cm}=\mathbf R_0+eB\mathbf r/[(m_1+m_2)\omega]$. This distinction is essential when reconstructing individual particle orbits.
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