Solution (source code)

= Solution

<Poynting–Robertson drag> removes <angular momentum>, so a trapped grain requires positive resonant <torque> from the planet. Part (c) shows that conjunction must occur after the dust has passed apoapsis. In the planet's rotating frame, the four-lobed pattern is therefore rotated so that the relevant outer lobe lags the fixed planet in the direction of orbital motion. Equivalently,
$$
\boxed{\sin\phi<0},
$$
with the stable phase displaced beyond $\phi=\pi$ rather than sitting at the torque-free value $\phi=\pi$.