= Radiation-pressure shift of a mean-motion resonance
{title2=$a/a_p=(1-\beta)^{1/3}((j+1)/j)^{2/3}$}
A grain with <radiation-pressure coefficient> $\beta<1$ feels effective central <gravitational parameter> $GM_\star(1-\beta)$. Combining its <mean motion> with the planet's <mean motion> at an exterior-type $(j+1):j$ frequency commensurability gives the displayed <semi-major axis>. The commensurability lies geometrically exterior only for $j<\sqrt{1-\beta}/(1-\sqrt{1-\beta})$. Radiation changes the grain's attraction, so the same frequency ratio need not imply the usual radial ordering.
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