Leveraging of bicircular restricted four-body problem for enhancing satellite formation dynamics in cislunar space

This study analyzes relative motion dynamics for formation flying in cislunar space using the Bicircular Restricted Four-Body Problem (BCR4BP), incorporating solar gravitational attraction and Solar Radiation Pressure (SRP). Numerical simulations across Halo, Lyapunov, DRO, DPO, and LPO orbit families reveal that the stability and growth of relative motion are fundamentally determined by the choice of chief reference orbit. Solar gravity is the dominant mechanism, reducing the Lyapunov exponent by up to 91% for LPOs and L₂ Halos (enabling passive formation flying with λ ≈ 0.026-0.034 day^-1, final separation ≤ 6 km, doubling time ≈ 20-26 days) while increasing it by over 1,000% for DROs (causing catastrophic divergence to 10⁸-10¹¹ km). SRP plays a secondary role, modifying λ by at most 30%. Critically, the CR3BP is fundamentally misleading: it overestimates DRO stability by six orders of magnitude and underestimates LPO/L₂ Halo stability by similar margins. The BCR4BP is not an optional refinement but an operational necessity for correct orbit selection, accurate stability assessment, and fuel-efficient formation flying mission design in the Earth-Moon system.