Ross/Roberts-Tsoukkas stable Earth-Moon (1,1) prograde cycler (CR3BP)

ross-rt-em-cycler-11-2025 · source: literature · validation: V2

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
Sense: n/a
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: non-keplerian (CR3BP)
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: cr3bp
CR3BP — Jacobi-constant-conserved; signature not patched-conic comparable.
Period: — yr (1 × E-Moon synodic)
Rotating-frame period T^stable = 10.29206921007976 TU (Ross Table 3, p. 11), where 1 TU = sidereal month / 2pi = 27.321661 d / 2pi = 4.348377401631 d (p. 3) -> 44.753800 d (Table 4 day column, p. 13). Encounter cadence: 1 perigee + 1 perilune pass per period; T^stable is within ~1% of the 2:3 resonance with the synodic month (p. 11). The catalogue's heliocentric-synodic-multiple `years` convention does not apply to an Earth-Moon CR3BP periodic orbit -> null.
Priority date: 2025-08-01

V∞ at encounters

E (encounter 1): — (not published)
CR3BP periodic orbit: the conserved quantity is the Jacobi constant (C^stable), not patched-conic V_inf. Quoting V_inf would be model-mismatched (per arenstorf-em-figure8-1963 convention).
Moon (encounter 2): — (not published)
Same — Jacobi-constant model, not patched-conic.

CR3BP orbit identity

Family: (1,1) prograde Earth-Moon cycler
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.1512
Period (non-dim): 10.2921
Stability index: -0.003

Heliocentric Keplerian elements inapplicable: periodic solution in the rotating Earth-Moon barycentric frame, planar (PCR3BP). The CR3BP identity tuple below carries the orbit's identity.

Orbit view 2.5D ecliptic projection

Not renderable from current data. This is a rotating-frame (CR3BP) periodic orbit. A faithful render requires numerical propagation of the synodic-frame state, which the catalogue does not yet publish as a sampled path — so no stand-in ellipse is drawn (drawing a heliocentric ellipse here would misrepresent the dynamics). The CR3BP identity (Jacobi constant, period, stability) is tabulated above.

model: CR3BP (rotating frame)

3D view not available for rotating-frame (CR3BP) orbits.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (1)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

orbit_elements.cr3bp.state_nd [derive]
Ross & Roberts-Tsoukkas 2025 prints no initial-state vector for any member (publication gap, mining note §5). state_nd is DERIVED in-repo by the fixed-Jacobi symmetric 1-D corrector from the sourced (mu, C^stable) and self-consistency-checked against the sourced T^stable + an independent Radau closure; it is recorded with provenance, never as a golden.

source: scripts/cr3bp_ross_reproduce.py; tests/search/test_cr3bp_ross_families.py; 2026 journal version (Roberts-Tsoukkas & Ross) may print ICs.

Primary citation

Ross, S. D. & Roberts-Tsoukkas, M. (2025). Stable, Low-Energy Prograde Earth-Moon Cycler Orbits. AAS/AIAA Astrodynamics Specialist Conference, 2025, paper AAS 25-621.

URL: https://ross.aoe.vt.edu/papers/ross-roberts-tsoukkas-2025-AAS-25-621.pdf

LaTeX preprint dated 2025-07-17. A 2026 journal version exists ("Stable Prograde Earth-Moon Multi-Orbiter Cyclers via Three-Body Dynamics," Roberts-Tsoukkas & Ross); re-verify table/page numbering against it before embedding citations in code comments.

Notes

First publication of STABLE, fully ballistic, prograde Earth-Moon cyclers (the class our CR3BP lane previously lacked — all prior lane discoveries were unstable Lyapunovs). The (1,1) family's stable subfamily is extremely narrow (perilune-distance width Delta_p_m = 0.13 km, Table 3); this row is its nu=0 midpoint. Reproduced in-repo (commit 4be2375): corrector closes on (C^stable, T^stable), Barden stability nu=-0.00334 (|nu|<1), and an independent Radau integration closes the full period with dJ < 1e-12. MODEL: pure planar CR3BP (PCR3BP). No bicircular / solar-gravity / lunar-eccentricity / ephemeris refinement (the paper's stated future work); any cross-fidelity persistence claim must wait for the 2026 journal. Every number here is PCR3BP-only.

Source quotes (per-field provenance)

Every numerical value in this entry traces to a verbatim or paraphrased quote from a cited source.

orbit_elements.cr3bp.jacobi_constant: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (1,1) C^stable = 3.151175879508174.
orbit_elements.cr3bp.period_nd: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (1,1) T^stable = 10.29206921007976 TU; Table 4 (p. 13) day column 44.753800 d.
orbit_elements.cr3bp.mass_ratio: Ross & Roberts-Tsoukkas 2025 p. 3: mu = 1.2150584270572e-2.