Cislunar Resonant Transport and Heteroclinic Pathways: From 3:1 to 2:1 to L1

TL;DR

The paper develops a dynamical framework for cislunar transport by computing interior resonant periodic orbits of the Earth–Moon PCR3BP for the 4:1, 3:1, and 2:1 MMRs, constructing their invariant manifolds, and identifying zero-$\Delta v$ heteroclinic connections including to lunar $L_1$ orbits. Through a perigee Poincaré map and a generalized distance metric, it quantifies practical transfer times and maps a network of accessible semi-major axes, revealing both natural transport pathways and barriers such as rotational invariant circles. Key findings include robust 3:1–2:1 heteroclinics enabling efficient resonance-to-resonance transitions, and notable L1-tube interactions that connect resonant dynamics to lunar capture—highlighting viable low-energy routes to the Moon within the planar CR3BP. The work sets the stage for extending to spatial models and higher-fidelity perturbations, which are essential for translating these dynamical highways into operational mission designs in the Earth–Moon system.

Abstract

Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is critical for both lunar exploration and for high-Earth-orbiting trajectories. In this study, we investigate the role of mean-motion resonances and their associated heteroclinic connections in enabling natural semi-major axis transport in the Earth-Moon system. Working within the planar circular restricted three-body problem, we compute and analyze families of periodic orbits associated with the interior 4:1, 3:1, and 2:1 lunar resonances. These families exhibit a rich bifurcation structure, including transitions between prograde and retrograde branches and connections through collision orbits. We construct stable and unstable manifolds of the unstable resonant orbits using a perigee-based Poincaré map, and identify heteroclinic connections - both between resonant orbits and with lunar $L_1$ libration-point orbits - across a range of Jacobi constant values. Using a new generalized distance metric to quantify the closeness between trajectories, we establish operational times-of-flight for such heteroclinic-type orbit-to-orbit transfers. These connections reveal ballistic, zero-$Δv$ pathways that achieve major orbit changes within reasonable times-of-flight, thus defining a network of accessible semi-major axes. Our results provide a new dynamical framework for long-term spacecraft evolution and cislunar mission design, particularly in regimes where lunar gravity strongly perturbs distant circumterrestrial orbits.

Figures (28)

• Figure 1: (a) PCR3BP barycentered rotating $(x,y)$ frame in normalized units. (b) The geocentric osculating orbital elements showing inertial longitude of perigee ($\omega$) and synodic longitude of perigee ($g$).
• Figure 2: Illustration of perpendicular $x$-axis crossings method for computing PCR3BP periodic orbits perpCrossing.
• Figure 3: Illustration of the definition of distance metric between two orbits $\Gamma_B$ and $\Gamma_C$.
• Figure 4: Illustration of definition of distance metric $D(\mathscr{M},\Gamma_f)$ between a state $\mathscr{M}$ on the stable manifold $\Gamma_{\mathscr{M}}$ of an orbit $\Gamma_f$ and the orbit $\Gamma_f$ itself.
• Figure 5: Poincaré section plot at perigee ($\ell=0$) for $C = 3.10$. The “identify” indicates that the synodic longitude of perigee is an angle that maps back to itself.

Theorems & Definitions (2)

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