Analysis of the dynamics of the resonant planetary system HD 45364

Abstract

The aim of this work is to analyse the orbital dynamics and stability of exoplanetary system in which two planets are in nearly 3:2 MMR. We have taken HD 45364 system for our study in which two planets are most likely in a 3:2 MMR. We have plotted two resonant angles and the relative apsidal longitudes and it is observed that they are librating around a constant value. From this observation our opinion is that there exist nearly 3:2 MMR between HD 45364b and HD 45364c. The perturbative solution is obtained for the time variation of the semi-major axes. The short and long term variations of semimajor axes are studied. For the validation of our analytical results we have compared our analytical solutions with the numerical solutions. The effect of planetary perturbations on eccentricity is studied with the help of secular resonance dynamics theory. The short and long term variations of eccentricities of HD 45364b and HD 45364c are shown graphically. Moreover, using the latest stability criteria, we have studied the dynamical stability of HD 45364 system.