A Comparative Floquet–Lyapunov Study of Perturbation-Induced Halo Orbit Instability in the Earth–Moon System

Abstract

Halo orbits around the Earth–Moon collinear Lagrange points L1, L2, and L3 underpin the next decade of cislunar activity, from NASA's Artemis Lunar Gateway to China's Queqiao lunar communication relay. Their operational viability depends on how strongly non-idealised forces reshape their intrinsic instability. Yet, while the linear stability of these orbits in the Circular Restricted Three-Body Problem (CR3BP) is well established, the relative impact of the perturbations a real mission actually encounters has not been systematically ranked within a single self-consistent framework. This preprint addresses that gap. Numerically refined halo orbits at L1–L3 are constructed via Richardson third-order approximations and multiple-shooting differential correction (periodicity errors < 10⁻¹⁰; Jacobi deviations < 10⁻¹²), then subjected to a unified Floquet–Lyapunov analysis under solar radiation pressure (SRP), lunar oblateness (J2), Earth's albedo and thermal radiation, and third-body solar gravity, each applied independently within identical numerical settings so that resulting shifts in Floquet multipliers and Lyapunov exponents can be directly compared. Monte-Carlo sampling of initial conditions maps sensitivity thresholds and bifurcation zones. The comparative results yield a clear hierarchy: third-body solar gravity dominates, driving Floquet-multiplier shifts of up to 88% and collapsing the L1 maximum Lyapunov exponent from 0.478 to 0.200; SRP and lunar J2 act as mild regularisers, reducing chaotic divergence at L1 and L2 while leaving L3 largely unaffected; Earth's albedo produces only marginal shifts. Results are benchmarked against Jorba & Masdemont (1999), Kolemen et al. (2012), and Richardson (1980), with L3 identified as the quasi-stable exception, reducing station-keeping cadence by roughly half relative to L1 and L2.