 Differential-gravity disruption limit of a uniform satellite

A point-mass host creates radial differential acceleration $2GMx/D^3$, while a uniform satellite restores with $4\pi G\rho x/3$. Equality gives $D=[3M/(2\pi \rho ){]}^{1/3}$. The displacement cancels; the robust scaling is $(M/\rho {)}^{1/3}$. A rotating circular-orbit Jacobi calculation changes the radial coefficient from two to three.