Repeated fission hierarchy ($a^{\prime }/a=2{\alpha }^2/(1+\alpha {)}^2$)

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.