Earth-Moon L1/L2 Halo Orbit

Source: Adapted from Genszler et al. (2026) "Surveying orbits in cislunar space for telescope-starshade observatories"

Site: https://cislunarspace.cn

Definition

Earth-Moon L1/L2 Halo Orbits (EML1 Halo and EML2 Halo) are periodic orbits around the Earth-Moon L1 and L2 Lagrange points, belonging to the Halo orbit family. In the Circular Restricted Three-Body Problem (CR3BP) model, these orbits are stable and periodic; in full force models including solar perturbations, they are quasi-stable, requiring only minimal station-keeping $\Delta v$.

Halo orbits were first described by Robert W. Farquhar in 1968. They simultaneously cross the $x-y$ plane and $x-z$ plane in the rotating frame, exhibiting a three-dimensional "cashew" or "figure-8" configuration.

Geometric Characteristics

Key geometric parameters of Halo orbits:

• $A_z$ amplitude: Out-of-plane amplitude perpendicular to the Earth-Moon orbital plane, determining the orbit's "flattening"
• $A_y$ amplitude: In-plane amplitude perpendicular to the Earth-Moon line
• Period: Ranges from approximately 7 to 25 days depending on amplitude combination

Halo orbits split into Southern and Northern families corresponding to positive and negative $z$ amplitudes.

Dynamics

EML1 Halo Orbit

• Location: Near Earth-Moon $L_1$ point, approximately 326,000 km from Earth
• Accessibility: Shorter transfer time from Earth, higher mission flexibility
• Station-keeping cost: Higher than EML2 Halo orbits

EML2 Halo Orbit

• Location: Near Earth-Moon $L_2$ point, on the far side of the Moon
• Accessibility: Relatively low transfer cost compared to SEL2
• Observation advantage: Earth and Moon on the same side of the telescope, simpler pointing constraints
• Station-keeping cost: Less than 5–10 m/s/year for orbit maintenance

Relationship with NRHO

Near-Rectilinear Halo Orbits (NRHO) are an extreme subclass of the Halo orbit family. When the $A_z/A_y$ ratio of a Halo orbit becomes very large, the orbit transitions from "cashew-shaped" to nearly linear reciprocating motion — this is the NRHO. NRHO specifically refers to members between the first and third stability changes for $L_2$, or between the first and fourth for $L_1$.

In Genszler et al. (2026):

• L1 NRHO: Period approximately 8–10 days
• L2 NRHO: Period approximately 6–10 days

Orbit Generation

Initial conditions for Halo orbits are generated using:

1. Single shooting method and continuation method
2. Differential correction algorithms
3. Dynamics propagation using CR3BP model (e.g., MATLAB's ode113)

Related Concepts

• Near-Rectilinear Halo Orbit (NRHO)
• Distant Retrograde Orbit (DRO)
• Circular Restricted Three-Body Problem (CR3BP)
• Starshade
• Lagrange Point
• Formation Flying

References

• Genszler G, Savransky D, Soto G J. Surveying orbits in cislunar space for telescope-starshade observatories[J]. 2026.
• Farquhar R W. The execution of lunar orbit and libration point missions[J]. 1972.
• Zimovan E M. Characteristics and design strategies for near rectilinear halo orbits within the Earth-Moon system[D]. Purdue University, 2017.
• Folta D C, Pavlak T A, Haapala A F, et al. Preliminary design considerations for access and operations in Earth-Moon L1/L2 orbits[C]. AAS/AIAA, 2013.
• Whitley R, Martinez R. Options for staging orbits in cislunar space[C]. IEEE Aerospace Conference, 2016.