Fixed-point eccentricity ratio as a function of system inclination for a two-planet system with m ₁ = 10 ⁻⁵ M _☉, m ₂ = 10 ⁻² M _☉, a ₁ = 0.03 AU, and a ₂ = 0.3 AU(α = 0.1; see Figure  1). The black curve, labeled LL was computed directly from the Laplace–Lagrange eigenvector solution. The blue dashed curve is the approximation to the LL solution, given by Equation (19), corresponding to e ₂ = 0.1. The curves with eccentricity labels demonstrate the dependence of the eccentricity ratios on the stationary eccentricity of the outer secondary, as dictated by the secular perturbation theory, developed by Mardling (2007). Recall that refers to the RV minimum mass.