Corotating tidal-disruption estimate for a uniform sphere ($R_{\min }\simeq [9M/(4\pi \rho ){]}^{1/3}$)

A small cohesionless spherical body of radius $s$ and density $\rho$ has surface self-gravitational acceleration $4\pi G\rho s/3$. The radial stretching of the corotating point-mass tidal field is $3GMs/R^3$. Equating them gives the displayed survival-distance estimate. The size $s$ cancels because both accelerations are linear in $s$ at fixed density. This is a local spherical force-balance estimate, not the exact fluid Roche figure: shape deformation, material strength and nonsynchronous spin can change its numerical coefficient.