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Parameterize the trajectory by the decreasing orbital eccentricity. The Poynting–Robertson drag invariant givesFor $Q_0\gg q_0$, $C\simeq 2q_0$. Initially $e\simeq 1$, and the orbit moves almost vertically down a plot of $Q/q_0$ against $q/q_0$: the apocentre distance shrinks rapidly while the pericentre distance changes little. Integrating the high-eccentricity slope givesOnce the orbit has moderate orbital eccentricity, both distances change appreciably. For example $e=1/2$ gives $q\simeq 0.766q_0$ and $Q\simeq 2.30q_0$ in the $Q_0/q_0\to \infty$ limit. Eventually $e\ll 1$, $q\simeq Q\simeq C{e}^{4/5}$, and the trajectory approaches the diagonal $Q=q$ before reaching the origin. Thus the two approximate phases are apocentre contraction at nearly fixed pericentre, followed by nearly circular inward migration. They are a smooth crossover, not two separate exact solutions.

Using $q=a(1-e)$ and $Q=a(1+e)$, differentiate each apsidal distance. The apsidal evolution under Poynting–Robertson drag isBoth the pericentre distance and apocentre distance decrease. Since $a=(Q+q)/2$ and $e=(Q-q)/(Q+q)$, the same rates areTheir ratio isIn particular $Q\gg q$ gives $dQ/dq\simeq (5/3)(Q/q{)}^2$, whereas the circular limit gives slope $1$.