The planetary system Kepler-90 has eight planets b, c, i, d, e, f, g, and h, in increasing distance from the star. The outer planet has an orbital distance equals to 1 AU, and planets b and c are about to 2 Earth radii. Planets g and h are similar to gas giants, while planets d, e, and f are similar to super-Earths. Small planets are closer to the star and the larger ones are distant from the star, similar to our solar system.
Numerical simulations performed by Cabrera et al (2014) and Granados et al (2018) showed that some of these planets are in mean motion resonances (MMR) between them. For example, planets b and c are in 4:5 MMR. Granados et al (2018) also showed that the planets g and h are in 2:3 MMR.
Through frequency analysis and long-term evolution, we analyse their stability for a sample of parameters of the planets, such as their masses, semi-major axes and eccentricities. We performed simulations numerical to analyze three different intervals of eccentricity: the first interval from 0 to 1x10-3, the second interval from 1x10-3 to 1x10-2 and the third interval from 1x10-2 to 1x10-1. The values of eccentricity, argument of pericentre, longitude of the ascending node, and mean longitude were randomly chosen in each eccentricity interval.
Our results showed that the planets which eccentricities belong to the first and second intervals are stable, while most of the planets with large eccentricity, 1x10-2 to 1x10-1, are ejected from the system. The variation of the eccentricity of the planets in the two first intervals indicate that the planet h is dominant in the nominal systems being important for the stability of the system Kepler-90.
The first interval of eccentricity has two nominal systems where the MMRs appear among the planets, b and c are in 4:5 MMR, and the planets g and h are near 2:3 MMR, corroborating the results obtained by Granados et al (2018). These resonances are also found in a nominal system of the second interval of eccentricity.
We also analysed a sample of particles located in this system through the frequency map analysis. We will present the stable and unstable regions, along with the islands of resonance.
Acknowledgement: SMGW, OW and DMGG thank CNPq (313043/2020-5), Fapesp (2016/24561-0) and CAPES for the financial support.