= Repeated fission hierarchy
{title2=$a'/a=2\alpha^2/(1+\alpha)^2$}
If each daughter subsequently conserves its own spin while contracting at fixed outer separation, its next critical radius is $a/8$. A local repetition of the <synchronous fission model for binary formation> gives the displayed inner-to-outer separation ratio. Continuous <tidal locking> throughout the contraction would instead keep the spin frequency fixed and decrease its centrifugal-to-gravity ratio as the cube of its radius; the repeated fission would not follow. Spin-orbit torque assumptions must therefore be explicit.
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