Ross/Roberts-Tsoukkas stable Earth-Moon (3,2) prograde cycler (CR3BP)

ross-rt-em-cycler-32-2025 · 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 = 17.90058010350006 TU (Ross Table 3, p. 11) -> 77.838478 d (our conversion via the printed TU; Table 4 prints days only for the (k1,1) rows, so this day figure is DERIVED, mining note §8). Encounter cadence: 3 perigee + 2 perilune pass per period (k1=3, k2=2). Two stable windows, the larger ~40 km wide (Delta_p_m 42.08 km); the near-2:5 synodic-resonance member (Fig. 9b, ~74 d) is a DIFFERENT, unstable member of this family, NOT this nu=0 Table-3 member (p. 13). 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: (3,2) prograde Earth-Moon cycler
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.1828
Period (non-dim): 17.9006
Stability index: -0.012

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; never a golden. (3,2) requires crossing-index selection at the 6th x-axis crossing (results note §2).

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 (3,2) day figure 77.838478 d is our conversion of the printed T^stable via the printed TU (1 TU = 4.348377401631 d). 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).

Corroborating sources

Leiva, A. M. & Briozzo, C. B. (2008). Extension of fast periodic transfer orbits in the Sun-perturbed Earth-Moon system (quasi-bicircular persistence of a (3,2)-class member). Celestial Mechanics and Dynamical Astronomy 101, pp. 225-245.
Ross p. 13 (spelled 'Leiva and Brizzolara') notes a member of the (3,2) family was previously identified by Leiva & Briozzo and shown to persist under solar perturbation (Sun-Earth-Moon quasi-bicircular model) — the only prior sighting, as a single unstable orbit. If ever ingested, parent it to this (3,2) family (mining note §6).

Notes

(3,2) stable prograde Earth-Moon cycler, nu=0 midpoint of the larger of two stable windows (Delta_p_m 42.08 km, Table 3). An earlier pass deferred this family as integrator-cost-prohibitive; the deferral is RETRACTED — fixing the half-period crossing index (the 6th x-axis crossing) resolves it (results note §2): reproduced T = 17.9005801151 (+1.2e-8 TU), nu=-0.01175 (STABLE), independent Radau closure dJ = 5.3e-13. The near-2:5-synodic member (Fig. 9b) is a different, unstable member — do not conflate. Case 2 energy regime (C^stable > C2) is our derived observation, not stated by the paper. 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): (3,2) C^stable = 3.182762663084288.
orbit_elements.cr3bp.period_nd: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (3,2) T^stable = 17.90058010350006 TU.
orbit_elements.cr3bp.mass_ratio: Ross & Roberts-Tsoukkas 2025 p. 3: mu = 1.2150584270572e-2.