  For a singleton planet $P$ with gravitational potential $V$, we show that for
each $\varepsilon > 0$ there exists a planet $P'$ with gravitational potential
$V'$, with $(P',V')$ "$\varepsilon$-close" to $(P,V)$ (in an appropriate
$C^0$-sense) for which the spherical harmonic expansion of $V'$ does not extend
more than a distance $\varepsilon$ below the Brillouin sphere of $P'$.
