Establish the mass dependence of the critical-eccentricity relation

Determine whether the empirical relation $e_{\mathrm{s}}^{\mathrm{crit}}\approx5\sigma_{\mathrm{e}}^{\mathrm{crit}}$ remains valid for planetary systems with masses different from the equal-mass, Earth-mass systems studied numerically.

Background

The reported critical-eccentricity relation is obtained from simulations of five equal-mass Earth-mass planets orbiting a Solar-mass star. Because planetary masses affect secular precession, resonance widths, and the onset of dynamical instability, the inferred ratio may not be universal.

The conclusions explicitly identify testing the relation across planetary masses as unresolved.