Retrograde resonances at high mass ratio in the circular restricted 3-body problem

Abstract

Studies involving retrograde orbits have been an emerging field in recent years, particularly in the case where there are resonances between objects orbiting in opposite directions. The high amount of data from space exploration missions increases the possibility of observing binary stellar systems which may have additional bodies with retrograde orbits. Furthermore, such orbits are relevant to understanding the dynamics of spacecrafts around binary asteroids, being essential to planning exploratory missions. In this work, we survey retrograde orbits around binary systems with mass ratio between 0.01 (hierarchical) and 0.5 (equal masses) in the framework of the planar circular restricted three-body problem (PCR3BP). We build surfaces of section and identify retrograde resonances up to fifth order, namely the 2/−1, 3/−2, 1/−1, 2/−3, 1/−2, 1/−3 and 1/−4 resonances. We conclude that retrograde resonances occur in binary systems at high mass ratio, including the co-orbital (1/−1) resonance. Period doubling bifurcations occur for the 1/−1 resonance, and period doubling and period tripling bifurcations are observed for the 1/−2 resonance. Asymmetric retrograde resonances of the type 1/−n occur for almost equal masses of the binary system. This study may be used for identifying retrograde planets in extrasolar systems and may possibly have applications to astrodynamics mission planning.