Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies

Yu Jiang,Hexi Baoyin

doi:10.1016/j.rinp.2018.11.049

Yu Jiang, Hexi Baoyin

Open Access

https://doi.org/10.1016/j.rinp.2018.11.049

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Abstract

Abstract We presented an overview of detailed continuation results of periodic orbit families which emanate from the equilibrium points (EPs) of irregular-shaped minor celestial bodies (hereafter called minor bodies). The generation and annihilation of periodic orbits (POs) related to the EPs are discussed in detail. The branch points of families of POs are also investigated. We presented 3D bifurcation diagrams for periodic orbits families emanating from the EPs of minor bodies which have five EPs totally. Structures of the 3D bifurcation diagrams depend on the distribution of EPs with different topological classifications. We calculated orbit families emanating from the EPs of asteroids 433 Eros and 216 Kleopatra, including the Lyapunov orbit family, the Vertical orbit family, the orbit families bifurcating from the Vertical orbit family, as well as the nonplanar orbit family.

Highlights

The study of dynamics around irregular-shaped bodies is useful for understanding the motion of stars and clusters of galaxies, the origin, evolution, and stability of moonlets of multiple asteroid systems, as well as the design of deep space missions to minor celestial bodies
If the equilibrium point belongs to Case O4, the equilibrium point is unstable and only one periodic orbit family emanating from the equilibrium point
Generation and annihilation of periodic orbits related to the equilibrium points we investigate the generation and annihilation of POs related to the EPs during the continuation

Summary

Introduction

The study of dynamics around irregular-shaped bodies is useful for understanding the motion of stars and clusters of galaxies, the origin, evolution, and stability of moonlets of multiple asteroid systems, as well as the design of deep space missions to minor celestial bodies. Chanut et al [12] plotted the zero velocity surfaces of asteroid 216 Kleopatra and analyzed the stability of the asteroid’s seven EPs. This paper investigates the periodic orbit families originating from the EPs of an irregular-shaped celestial body, and analyzes the bifurcation diagram of the periodic orbit families.

Results

Conclusion