Secular apsidal configuration of non-resonant exoplanetary systems

Using a high-order (order 12) expansion of the perturbative potential in powers of eccentricities [Libert, A.-S., Henrard, J., 2005. Celest. Mech. Dynam. Astron. 93, 187–200], we study the secular effects of two coplanar planets which are not in mean motion resonances. The main results concern eccentricity variations, oscillation amplitude of the angular difference of the apsidal lines (Δϖ) and frequency of such an oscillation. We show that this analytical approach describes correctly the behaviour of most of the exosystems and underlines the known limitations of the linear Laplace–Lagrange theory. Apsidal configuration of υ Andromedae, HD 168443, HD 169830, HD 38529, HD 74156 and HD 12661 are examined. We also point out the great sensitivity of the υ   Andromedae system to the initial values (e1(0)e1(0), e2(0)e2(0) or Δϖ(0)Δϖ(0)).