Quasi-Bicircular Four-Body Problem

Author: CislunarSpace

Website: https://cislunarspace.cn

Definition

The Quasi-Bicircular Four-Body Problem is a self-consistent four-body dynamical model proposed by Andreu. Unlike the bicircular model, it ensures the Sun-Earth-Moon motion satisfies the three-body problem solution. The Earth-Moon barycenter follows a quasi-periodic orbit near the Sun-Earth L₁ or L₂ point rather than a simple circular orbit, maintaining dynamical consistency. Based on this model, invariant manifolds and low-energy transfers near equilibrium points can be analyzed, and periodic or quasi-periodic orbits near Earth-Moon libration points can be designed with results closely matching real ephemeris models.

Key Properties

  • Self-consistent: the Sun-Earth-Moon configuration satisfies the equations of motion.
  • The Earth-Moon barycenter traces a quasi-periodic orbit, not a perfect circle.
  • Enables accurate computation of invariant manifolds under solar perturbation.
  • Results closely match full-ephemeris models, making it valuable for mission design.

References

  • Andreu, M. A. "The Quasi-Bicircular Problem." Ph.D. Thesis, University of Barcelona, 1998.