Pre-giant Roche-lobe-filling period limit
= Pre-giant Roche-lobe-filling period limit
{title2=$P_i<2\pi\sqrt{R_{\rm BGB}^3/(C^3GM_d)}$}
For $R_L=Ca(M_d/M)^{1/3}$, the period when a donor reaches radius $R$ is $P=2\pi\sqrt{R^3/(C^3GM_d)}$. Requiring overflow before a specified evolutionary radius therefore bounds the initial period independently of companion mass in this lobe approximation. If that radius scales as $M_d^{5/3}$, the bound scales as $M_d^2$.