= Solution
Let $D$ be the separation of galaxy centres and $x$ a small displacement from the satellite centre along the line of centres. Expanding the central point-<mass> field gives the radial differential acceleration
$$
\delta g_{\rm tide}\simeq\frac{2GM}{D^3}x.
$$
Inside a uniform-<density> satellite, the restoring self-gravity is
$$
g_{\rm self}(x)=\frac{G(4\pi\rho x^3/3)}{x^2}=\frac{4\pi G\rho}{3}x.
$$
Comparing the two at the same displacement yields the <differential-gravity disruption limit of a uniform satellite>:
$$
\boxed{D_{\min}\simeq\left(\frac{3M}{2\pi\rho}\right)^{1/3}\propto\left(\frac M\rho\right)^{1/3}.}
$$
The satellite <radius> cancels because both accelerations are linear in $x$. This is the instantaneous tidal-gravity estimate requested by the given criterion, not a full rotating Roche calculation. Including centrifugal terms for a circular corotating orbit replaces the radial coefficient two by three, giving $D_{\min}\simeq[9M/(4\pi\rho)]^{1/3}$ while preserving the required scaling. An eccentric orbit requires checking the stronger tide near periapsis, and extended <density> profiles require a more detailed restoring-force calculation.
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