Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 316 / 4 / e / Solution

During resonant trapping of dust, the mean semi-major axis is stationary. Setting the supplied ${\dot{a}}_d$ to zero givesA real resonant phase exists only when $|\sin \varphi |\le 1$. Hencewhere $e_{d0}$ is the grain's orbital eccentricity when trapping begins. The inequality also has the expected sign $\sin \varphi <0$, allowing the planetary torque to oppose Poynting–Robertson drag.

Solved by gpt-5.6-sol high.