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

Abstract

Halo orbits around the Earth–Moon L1–L3 underpin near-term cislunar infrastructure, from the Artemis Lunar Gateway to lunar communication relays, yet their operational viability depends on how strongly non-idealized forces reshape their intrinsic instability. While the linear stability of these orbits in the Circular Restricted Three-Body Problem (CRTBP) is well established, the relative impact of the perturbations a real mission actually encounters (solar radiation pressure, lunar oblateness, Earth's albedo and thermal radiation, and third-body solar gravity) has not been systematically ranked within a single, self-consistent framework. This study addresses that gap. Numerically refined halo orbits at L1–L3 are constructed via Richardson third-order approximations and single-shooting differential correction (periodicity errors < 10⁻¹⁰; Jacobi deviations < 10⁻¹²), then subjected to a unified Floquet–Lyapunov analysis under each perturbation. Linear stability is quantified through the monodromy matrix and Floquet multipliers; nonlinear behavior is probed through Poincaré maps and Lyapunov exponents; and sensitivity thresholds are mapped via Monte-Carlo sampling of initial conditions. 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 exponent from 0.4783 to 0.2003; SRP and lunar J2 act as mild regularizers, reducing chaotic divergence at L1 and L2 while leaving L3 largely unaffected; Earth's albedo produces only marginal shifts across all three orbits. The dominance of solar gravity is shown to be the operative constraint on unmaintained cislunar stationkeeping, and L3 is identified as the quasi-stable exception, requiring substantially less frequent correction than L1 and L2. Results are benchmarked against Jorba & Masdemont (1999), Kolemen et al. (2012), and Richardson (1980), with future extensions to full-ephemeris models identified as the next step toward mission-grade fidelity.