Ross/Roberts-Tsoukkas stable Earth-Moon (3,3) prograde cycler (CR3BP)

ross-rt-em-cycler-33-2025 · 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)
T^stable = 18.14546057589189 TU (Ross Table 3, p. 11) -> 78.903311 d (our conversion; DERIVED, Table 4 prints days only for (k1,1) rows). Encounter cadence: 3 perigee + 3 perilune pass per period (k1=3, k2=3). Largest of FIVE stable windows spans perilune altitudes ~4,200-6,200 km (Delta_p_m 2041.34 km), perigee altitudes ~112,400-113,500 km (~3x GEO); family terminates both ends in lunar-surface collision (p. 14). years: null (CR3BP).
Priority date: 2025-08-01

V∞ at encounters

E (encounter 1): — (not published)
CR3BP periodic orbit: conserved quantity is the Jacobi constant, not V_inf.
Moon (encounter 2): — (not published)
Same — Jacobi-constant model.

CR3BP orbit identity

Family: (3,3) prograde Earth-Moon cycler
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.1772
Period (non-dim): 18.1455
Stability index: 0.060

Planar CR3BP rotating-frame periodic orbit; Keplerian elements inapplicable. CR3BP identity tuple below.

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 (2)

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]
No initial-state vector printed in the source (mining note §5). state_nd DERIVED by the fixed-Jacobi corrector, self-consistency-checked against the sourced T^stable + independent Radau closure; never a golden. x0 lies in the Fig. 10b family-curve bracket [-0.330, -0.315] nd.

source: scripts/cr3bp_ross_reproduce.py; tests/search/test_cr3bp_ross_families.py; 2026 journal version.
orbit_elements.cr3bp.tof_days_bounds [derive]
Table 4 (p. 13) prints the day-converted period only for the (k1,1) rows; the (3,3) day figure 78.903311 d is our conversion of the printed T^stable via the printed TU. The TU period_nd is the sourced quantity.

source: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11) T^stable in TU + p. 3 TU definition.

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 2025-07-17; 2026 journal version exists (re-verify numbering).

Notes

(3,3) stable prograde Earth-Moon cycler, nu=0 midpoint of the largest of FIVE stable windows (Delta_p_m 2041.34 km — the widest of the five families, Table 3). The window's perigee altitudes (~112,400-113,500 km, ~3x GEO) make it the most accessible. Family terminates both ends in lunar-surface collision (p. 14). Generic observation (p. 14): every (k1,k2) family examined has a stable region near C^max. Reproduced in-repo: wide window -> T within ~1.6e-9 TU of T^stable, nu=0.06001 (STABLE), independent Radau closure dJ < 1e-12. Case 2 energy regime is our derived observation. 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): (3,3) C^stable = 3.177224018696528.
orbit_elements.cr3bp.period_nd: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (3,3) T^stable = 18.14546057589189 TU.
orbit_elements.cr3bp.mass_ratio: Ross & Roberts-Tsoukkas 2025 p. 3: mu = 1.2150584270572e-2.