<p>This paper investigates the continuation and bifurcation of cis-lunar resonant periodic orbits from the Circular Restricted Three-Body Problem to the Elliptic Restricted Three-Body Problem. The study focuses on distant retrograde orbits, along with planar/vertical Lyapunov orbits and halo orbits, given their relevance in dynamical prototypes and cis-lunar missions. Each continuation is categorized into two groups (for distant retrograde orbits, planar Lyapunov orbits and halo orbits) or four groups (for vertical Lyapunov orbits) depending on the resonant order of the investigated orbit. Characteristic curves and stability transitions, along the continuation with respect to eccentricity of the Earth-Moon system, are systematically examined. Special attention is given to tangent and period-doubling bifurcations, which lead to the emergence of new orbit branches. These findings offer enhanced insight into the structural evolution and bifurcation dynamics of resonant periodic orbits within the Earth-Moon system. Notably, the ER3BP serves as an ideal intermediate model during orbit transitions, and the geometry of the ER3BP orbits can serve as a qualitative indicator for identifying either regular or challenging transition regions.</p>

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Continuation and bifurcation of cis-lunar resonant periodic orbits in the Elliptic Restricted Three-Body Problem

  • Chen Gao,
  • Ruilong Li,
  • Josep J. Masdemont,
  • Yu Cheng,
  • Lei Liu

摘要

This paper investigates the continuation and bifurcation of cis-lunar resonant periodic orbits from the Circular Restricted Three-Body Problem to the Elliptic Restricted Three-Body Problem. The study focuses on distant retrograde orbits, along with planar/vertical Lyapunov orbits and halo orbits, given their relevance in dynamical prototypes and cis-lunar missions. Each continuation is categorized into two groups (for distant retrograde orbits, planar Lyapunov orbits and halo orbits) or four groups (for vertical Lyapunov orbits) depending on the resonant order of the investigated orbit. Characteristic curves and stability transitions, along the continuation with respect to eccentricity of the Earth-Moon system, are systematically examined. Special attention is given to tangent and period-doubling bifurcations, which lead to the emergence of new orbit branches. These findings offer enhanced insight into the structural evolution and bifurcation dynamics of resonant periodic orbits within the Earth-Moon system. Notably, the ER3BP serves as an ideal intermediate model during orbit transitions, and the geometry of the ER3BP orbits can serve as a qualitative indicator for identifying either regular or challenging transition regions.