Bicircular Four-Body Problem

Author: CislunarSpace

Website: https://cislunarspace.cn

Definition

The Bicircular Four-Body Problem is a four-body dynamical model that accounts for solar gravitational influence. It treats the Earth-Moon system and the Sun-Earth-Moon barycenter system as two independent Circular Restricted Three-Body Problem (CR3BP) systems. The Moon orbits the Earth-Moon barycenter in a circular orbit, while the Earth-Moon barycenter orbits the Sun in another circular orbit. While this model has a self-consistency issue — the two three-body systems are independent and do not satisfy Newton's second law simultaneously — it is useful for analyzing motion near equilibrium points under solar perturbation.

Key Properties

  • Incorporates solar gravity as a perturbation on the Earth-Moon CR3BP.
  • Two independent circular orbits define the motion: Moon around Earth-Moon barycenter, and barycenter around the Sun.
  • The model is not fully self-consistent, as the combined system violates Newton's second law.
  • Useful for qualitative studies of libration point dynamics under solar influence.

References

  • Gómez, G., Llibre, J., Martínez, R., and Simó, C. "Dynamics and Mission Design Near Libration Points." World Scientific, 2001.