Secular eigenmode amplitude product (source code)

= Secular eigenmode amplitude product
{title2=$r_pr_m=A_{12}/A_{21}$}

For a real two-planet <Laplace-Lagrange secular matrix> with negative off-diagonal entries, the upper <secular eigenmode> has anti-aligned apsides and the lower has aligned apsides. Their positive planet-1 to planet-2 amplitude ratios obey $r_pr_m=A_{12}/A_{21}$. Under the conventional <angular momentum deficit> normalization this is $L_2/L_1$.