The dynamics of the resonance in a 3:5 external resonant model

Abstract

Mean motion resonance sometimes ensures the stable motions of the celestial bodies in multi-planetary systems. The resonant orbits provide a stabilizing mechanism for maintaining our solar system and extrasolar planetary systems. This paper focuses on the dynamical effect of eccentricity on the stability of the 3:5 external resonant orbits in the planar circular restricted three body problem (Star–Planet–Asteroid). We computed numerically the Poincaré section of this model. We found that the initial eccentricity of the asteroid has a significant effect on the stability of the resonant orbits. The topology of this Poincaré section changes three times with increasing eccentricity. With the help of the Poincaré section, we obtained some periodic, quasi-periodic, and chaotic orbits. We also plotted the resonant region in (θ, e, a) space. θ is the angular separation of the asteroid pericenter and the planet, and e and a are the eccentricity and semimajor axis of the asteroid, respectively.