Axial Orbit
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
An axial orbit is a three-dimensional periodic orbit family among the libration point orbits (LPOs). At the collinear points, the axial family and the halo family bifurcate from the planar Lyapunov family at different locations; the axial family is symmetric about the x-axis and accordingly splits into two branches, axial-1 and axial-2 (He 2026). At the triangular points, the L4/L5 axial family bifurcates from the vertical Lyapunov family and no longer has any symmetry (He 2026). In periodic-orbit catalogs, the axial family stands alongside the Lyapunov, vertical, and halo families as a standard LPO family (Folta 2015, Guzzetti 2016).
Stability
L1/L2 axial orbits are strongly unstable throughout the family, with no center subspace (so they cannot host torus-based formations) (Guzzetti 2016); L4 axial orbits are linearly stable and remain bounded in a 120-year extrapolation (Vaquero & Howell 2014). Early catalogs give L1/L2 axial-family stability indices on the order of hundreds (strongly unstable), consistent with these qualitative conclusions.
Axial Resonant Orbits
Three-dimensional asymmetric resonant orbits are called axial resonant orbits, computed by perturbing a bifurcating orbit in the z direction (Vaquero & Howell 2014). Its 3:1 member can be migrated directly from the Earth–Moon system to other three-body systems (such as Saturn–Titan) by system translation (continuation in the mass parameter μ) without redoing the initial-guess–bifurcation–continuation pipeline in the new system (Vaquero & Howell 2014). Two caveats:
- Resonance ratios have two conventions: Vaquero & Howell's 3:1 means 3 spacecraft revolutions per 1 lunar revolution, while Parker & Anderson 2014 and Guzzetti 2016 use the p:q convention p lunar revolutions : q spacecraft revolutions; the same orbit carries reversed labels under the two conventions, so state the convention when citing.
- System translation does not preserve stability: the Earth–Moon 4:3 resonant family is entirely unstable, while the same family at Saturn–Titan is mostly linearly stable (Vaquero & Howell 2014).
Applications
- Transfers to L4 axial orbits: a three-dimensional transfer from LEO to an L4 axial orbit, patching the stable manifold of an L2 axial orbit (which passes near the Earth naturally) to the unstable manifold of a 3:2 axial resonant orbit, at ΔV 3.27 km/s over 22.54 days; the L4 axial orbit is linearly stable, covers both Earth and Moon, and never loses communication (Vaquero & Howell 2014).
- Space domain awareness: L4/L5 axial orbits traverse large volumes of cislunar space and are frequently selected in space domain awareness architecture optimization, favoring persistent detection of targets maneuvering in the plane (Klonowski 2024).
Terminology Variants
| Term | Meaning | Source |
|---|---|---|
| axial-1 / axial-2 branches | The two branches into which the collinear axial family splits by its x-axis symmetry | He 2026 |
| Axial resonant orbit | Three-dimensional asymmetric resonant orbit obtained by z-direction perturbation of a bifurcating orbit | Vaquero & Howell 2014 |
| 3:1 axial resonant orbit | Resonant member migratable to other three-body systems by system translation | Vaquero & Howell 2014 |
Related Concepts
References
- Vaquero & Howell, 2014, Leveraging resonant-orbit manifolds to design transfers between libration-point orbits
- Folta et al., 2015, An Earth-Moon system trajectory design reference catalog
- Guzzetti et al., 2016, Rapid trajectory design in the Earth–Moon ephemeris system via an interactive catalog of periodic and quasi-periodic orbits
- Klonowski et al., 2024, Cislunar space domain awareness architecture design and analysis for cooperative agents
- He et al., 2026, A review of cislunar constellation design and optimization