Study of the Dynamical Evolution of the Compact Planetary System Kepler-51

This paper examines the dynamic evolution of the compact three-planet system Kepler-51. Possible resonant states of the system are analyzed and a search for potential chains of mean motion resonances is carried out. Using the Posidonius software package the dynamic evolution of the system is studied over a time interval of 100 Myr, taking into account tidal interaction. Also, for various initial values of eccentricities, inclinations, arguments of periapsis and longitudes of the ascending nodes of orbits, modeling of the dynamic evolution of the planetary system is carried out within the framework of the semi-analytical theory of motion. It is shown that the compact planetary system Kepler-51 is not resonant. Under initial conditions corresponding to the masses and elements of the planets’ orbits, determined from observations taking into account their errors, the evolution of the system is stable and regular over the studied interval of 100 Myr.