Analysing the dynamics of the Kepler-90 planetary system

Abstract

Kepler-90 system has a set of eight planets in a hierarchical structure. In this work, we used frequency analysis to study several Kepler-90 analogues to analyse in detail how the values of the eccentricity of each planet can alter the stability of the system. The system was formed by the star and eight planets for three different intervals of eccentricity (e). Our results show that for the first and second intervals, all the systems are stable. However, no set of Kepler-90 systems with large values of e survived up to 105 orbits of Kepler-90h. In the low-eccentricity interval, planets Kepler-90b and Kepler-90c were found to be in a 5:4 mean motion resonance, and the pair Kepler-90g and Kepler-90h in a 3:2 mean motion resonance, although these two pairs are in resonance in different Kepler-90 analogues. In the medium-eccentricity interval, only the pair Kepler-90g and Kepler-90h is in resonance. Kepler-90b and Kepler-90c are in quasi-resonance 5:4; the critical angle circulates and librates intermittently in different periods of time. The results statistically indicate that these resonances directly affect the most of them. The influence covers a wide range of possibilities: (i) a strong resonant mean motion coupling added to a coupling of the longitude of the pericentres; (ii) just a single resonant argument librating; (iii) intermittent behaviour, interleaving libration, and circulation of the resonant arguments; and (iv) the quasi-resonant influence due to the near commensurability