Mean-motion resonance

A mean-motion resonance has $j{n}_2-k{n}_1\simeq 0$ for small integers $j,k$. Its slow resonant angle combines mean longitudes with apsidal or nodal longitudes.

A first-order mean-motion resonance has $|j-k|=1$. For small eccentricity its leading eccentric resonant term is linear in eccentricity.

A resonant argument is a slow angular combination whose libration diagnoses resonance. For an exterior $j:(j-1)$ eccentric resonance it can be $\varphi =j\lambda -(j-1){\lambda }_p-\varpi$.

Resonance capture occurs when slow orbital migration carries a body into a resonance and the resonant argument begins to librate, so resonant torque can balance the migration torque.