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.

HD 200946's Two Giant Planets in an 4/3 Orbital Resonance

Formation and evolution of the two 4/3 resonant giants planets in HD 200946

Authors:

Tadeu dos Santos et al

Abstract:

It has been suggested that HD 200964 is the first exoplanetary system with two Jovian planets evolving in the 4/3 mean- motion resonance. Previous scenarios to simulate the formation of two giant planets in the stable 4/3 resonance configuration have failed. Moreover, the orbital parameters available in the literature point out an unstable configuration of the planetary pair.

The purpose of this paper is i) to determine the orbits of the planets from the RV measurements and update the value of the stellar mass (1.57 M), ii) to analyse the stability of the planetary evolution in the vicinity and inside the 4/3 MMR, and iii) to elaborate a possible scenario for the formation of systems in the 4/3 MMR.

The results of the formation simulations are able to very closely reproduce the 4/3 resonant dynamics of the best-fit config- uration obtained in this paper. Moreover, the confidence interval of the fit matches well with the very narrow stable region of the 4/3 mean-motion resonance. The formation process of the HD 200964 system is very sensitive to the planetary masses and protoplanetary disk parameters. Only a thin, flat disk allows the embryo-sized planets to reach the 4/3 resonant configuration. The stable evolution of the resonant planets is also sensitive to the mass of the central star, because of overlapping high-order resonances inside the 4/3 resonance. Regardless of the very narrow domain of stable motion, the confidence interval of our fit closely matches the stability area.