= Solution
In the frame rotating with the planet, put the planet at fixed radius $a_p$. At periapsis the planetesimal moves prograde faster than the planet and passes just outside it. Its relative longitude initially increases, reaches a turning point near $r=2^{1/4}a_p$ at a lead of about $10^\circ$, and then decreases because its angular speed has fallen below the frame rate. Meanwhile its radius continues to grow along the outgoing parabolic branch. A sketch should therefore show an exterior cusp-like closest passage, a short prograde sweep to maximum lead, and a long outward trail that bends retrograde in the rotating frame.
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