Resonant semi-major axis
= Resonant semi-major axis
{title2=$a_r=a_p((p+q)/p)^{2/3}$}
The nominal <semi-major axis> of an exterior $(p+q):p$ <mean-motion resonance> follows from $(p+q)n_r=pn_p$ and <Kepler's third law>. Apsidal precession displaces the actual libration center because stationarity of the <resonant argument> requires $(p+q)n-pn_p-q\dot\varpi=0$.