Orbital Dynamics of Exoplanetary Systems Kepler-62, HD 200964 and Kepler-11

Orbital Dynamics of Exoplanetary Systems Kepler-62, HD 200964 and Kepler-11

Authors:

Mia et al

Abstract:

The presence of mean-motion resonances (MMR) in exoplanetary systems is a new exciting field of celestial mechanics which motivate us to consider the present work to study the dynamical behaviour of exoplanetary systems by time evolution of the orbital elements of the planets. Mainly we study the influence of planetary perturbations on semi-major axis and eccentricity. We identify (r+1):r mean-motion resonance terms in the expression of disturbing function and obtain the perturbations from the truncated disturbing function. Using the expansion of the disturbing function of three body problem and an analytical approach, we solve the equations of motion. The solution which is obtained analytically is compared with that of obtained by numerical method to validate our analytical result. In the present work we consider three exoplanetary systems namely Kepler-62, HD 200964 and Kepler-11. We have plotted the evolution of the resonant angles and found that they librate around constant value. In view of this, our opinion is that two planets of each system Kepler-62, HD 200964 and Kepler-11 are in 2:1, 4:3 and 5:4 mean motion resonances respectively.