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

TL;DR

This paper investigates the orbital dynamics of exoplanetary systems Kepler-62, HD 200964, and Kepler-11 by analyzing mean-motion resonances through analytical and numerical methods, revealing specific resonant relationships in these systems.

Contribution

It introduces an analytical approach to study mean-motion resonances in exoplanetary systems and validates it with numerical simulations, identifying specific resonances in three systems.

Findings

Kepler-62 exhibits a 2:1 resonance.

HD 200964 exhibits a 4:3 resonance.

Kepler-11 exhibits a 5:4 resonance.

Abstract

The presence of mean-motion resonances (MMRs) in exoplanetary systems is a new exciting field of celestial mechanics which motivates us to consider this 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 semimajor axis and eccentricity. We identify $(r+1):r$ MMR 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 this 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. Keywords:astrometry - celestial mechanics - planetary systems.