Retrograde near-circular periodic orbits near equatorial planes of small irregular bodies

Research on the stabilities of periodic orbits is useful for selection of parking orbits in asteroid and comet missions. In this paper, retrograde near-circular periodic orbits near equatorial planes (RNPOEP) of small irregular bodies are discussed, especially for their bifurcations and stabilities. RNPOEPs of six bodies are calculated based on a polyhedral method. The results reflect that two Period-Doubling Bifurcations (PDBs) cause the annular unstable regions, where RNPOEPs are all unstable, in the gravitational fields of some bodies. The unstable annular regions in the gravitational field of some bodies such as 243 Ida are wide, while those of some other bodies such as 216 Kleopatra are narrow. Based on the bodies' shapes, they are classified as two categories. Bodies of the first category have straight shapes which are approximately symmetric about the x-axis, such as 216 Kleopatra. Bodies of the second category have arched shapes which are approximately symmetric about the y-axis, such as 243 Ida. In order to provide insight of the dominating factors for the range of unstable annular regions, simplified models are proposed in the analysis. Specifically, a double-particle-linkage model is used for the first category while a triple-particle-linkage model is used for the second category. It is found that the distribution of the unstable annular regions in the gravitational field of simplified models is similar to those of the polyhedral models. Numerical results validate that the mass distribution dominates the range of the annular regions for both types of small bodies.