Investigation of periodic resonant orbits in the binary stellar systems

Abstract

Resonant periodic orbits are investigated in binary star systems with three bodies. Kepler-34, Kepler-35, Kepler-413, and Kepler-16 are chosËen and surface of sections of Poincaré (SSP) is utilized in this study. As the mass ratio decreases, the amplitude of the stability regions decreases and for smaller mass ratios, the structure of the phase plane differs significantly from that observed at higher mass ratios. Using the technique of SSP, locations of the resonant periodic orbits 9:7, 7:5, 3:2, 4:3, 5:3, 1:1, and 2:3 are explored. The starting point and path of the periodic orbits around the primary are analysed for different radiation force and Jacobi constant values. The radiation pressure of the bigger primary has no effect on the resonance order. The position of the periodic orbits, however, fluctuates and significant variations in the eccentricity are observed. The inclusion of the radiation force causes the periodic orbits of resonance 9:7, 7:5, 3:2, 4:3, 5:3, 1:1 and 2:3 around the larger primary to shift in the direction of the smaller primary. Periodic orbits are used to investigate tiny binary system bodies, such comets and asteroids, whose motion can be strongly influenced by solar radiation pressure.