= Synchronous fission model for binary formation
{title2=$a/R_c=16\alpha^2/(1+\alpha)^2$}
In this idealized model, a critically rotating spherical cloud splits into two equal-mass homologous spheres of radius $a/2$ that share the orbital frequency of their touching circular binary. Their combined orbital and spin inertia is $(1+\alpha)Ma^2/4$. Equating post-fission angular momentum to $\alpha M\sqrt{GMR_c}$ gives the displayed separation relation. A compact outcome $a<R_c$ requires $0<\alpha<1/3$. The model is an angular-momentum budget, not a hydrodynamic proof that stellar fission occurs.
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