We use 16 quarters of the Kepler mission data to analyze the transit timing variations (TTVs) of the extrasolar planet . Our dynamical fits confirm that the TTVs of this planet (period P = 33.648

We characterize the radii and masses of the star and planets in the Kepler-59 system, as well as their orbital parameters. The star parameters are determined through a standard spectroscopic analysis, resulting in a mass of 1.359 ± 0.155 M and a radius of 1.367 ± 0.078 R . The planetary radii obtained are 1.5 ± 0.1 R ⊕ for the inner and 2.2 ± 0.1 R ⊕ for the outer planet. The orbital parameters and the planetary masses are determined by the inversion of Transit Timing Variations (TTV) signals. For this, we consider two different data sets, one provided by Holczer et al. (2016), with TTVs only for the planet Kepler-59c, and the other provided by Rowe et al. (2015), with TTVs signals for both planets. The inversion method is carried out by applying an algorithm of Bayesian inference (MultiNest) combined with an efficient N-body integrator (Swift). For each of the data sets, two possible solutions are found, both having the same probability according to their corresponding Bayesian evidences. All four solutions appear to be indistinguishable within their 2-σ uncertainties. Nevertheless, statistical analyses show that the solutions from Rowe et al. (2015) data better characterize the data. The first and second solutions identify masses of 5 +4 −2 M ⊕ and 4.6 +3.6 −2.0 M ⊕ , and 3.0 +0.8 −0.8 M ⊕ and 2.6 +1.9 −0.8 M ⊕ for the inner and outer planet, respectively. This points to a system with an inner super-Earth and an outer mini-Neptune. Dynamical studies show the planets have almost co-planar orbits with small eccentricities (e < 0.1), close but not into the 3:2 mean motion resonance. Stability analysis indicates that this configuration is stable over million years of evolution.

Context. The stability of satellites in the solar system is affected by the so-called evection resonance. The moons of Saturn, in particular, exhibit a complex dynamical architecture in which co-orbital configurations occur, especially close to the planet where this resonance is present. Aims. We address the dynamics of the evection resonance, with particular focus on the Saturn system, and compare the known behavior of the resonance for a single moon to that of a pair of moons in co-orbital trojan configuration. Methods. We developed an analytic expansion of the averaged Hamiltonian of a trojan pair of bodies, including the perturbation from a distant massive body. The analysis of the corresponding equilibrium points was restricted to the asymmetric apsidal corotation solution of the co-orbital dynamics. We also performed numerical N-body simulations to construct dynamical maps of the stability of the evection resonance in the Saturn system, and to study the effects of this resonance under the migration of trojan moons caused by tidal dissipation.Results. The structure of the phase space of the evection resonance for trojan satellites is similar to that of a single satellite, differing in that the libration centers are displaced from their standard positions by an angle that depends on the periastron difference 2 − 1 and on the mass ratio m2/m1 of the trojan pair. In the Saturn system, the inner evection resonance, located at ∼ 8 RS, may capture a pair of trojan moons by tidal migration; the stability of the captured system depends on the assumed values of the dissipation factor Q of the moons. On the other hand, the outer evection resonance, located at > 0.4 R Hill , cannot exist at all for trojan moons, because trojan configurations are strongly unstable at distances from Saturn longer than ∼ 0.15 R Hill .