Multi-Revolution Halo Orbit

Author: CislunarSpace

Website: https://cislunarspace.cn

Definition

Multi-revolution halo orbits are periodic orbits that exist in the Elliptic Restricted Three-Body Problem (ERTBP). In the ERTBP, the eccentricity of the smaller primary's orbit introduces periodic perturbations that break the continuous symmetry present in the Circular Restricted Three-Body Problem (CR3BP). As a result, only orbits whose periods are integer multiples of the smaller primary's orbital period can exist as periodic solutions.

Peng et al. employed arc-length continuation methods to compute these multi-revolution halo orbits, effectively resolving singularity issues that arise in single-parameter eccentricity continuation. This approach treats the eccentricity and orbital period as coupled parameters, allowing smooth continuation from CR3BP halo orbits to ERTBP periodic orbits as eccentricity increases from zero.

Key Properties

  • Discrete symmetry: Only specific period ratios (integer multiples of the primary's period) yield periodic solutions
  • Arc-length continuation: Computed by parameterizing the solution branch with arc length rather than eccentricity alone
  • Singularity resolution: The arc-length method avoids the fold bifurcations encountered in direct eccentricity continuation
  • Practical relevance: More realistic than CR3BP halo orbits for systems with significant eccentricity, such as the Sun-Earth system

References

  • Peng, H., et al. "Multi-Revolution Halo Orbits in the Elliptic Restricted Three-Body Problem."