Ross/Roberts-Tsoukkas stable Earth-Moon (2,1) prograde cycler (CR3BP)

ross-rt-em-cycler-21-2025 · source: literature · validation: V2

Assumed erratum recorded for this row's source: Table 3 (p. 11), C^stable lower bound for the (2,1) family, vs Eq. 8 with Table 1's tangency constants (p. 8) — published so the authors can verify or refute; see errata.

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 = 19.44043166795154 TU (Ross Table 3, p. 11) -> 84.534335 d (Table 4, p. 13). Encounter cadence: 2 perigee + 1 perilune pass per period (k1=2, k2=1). T^stable ~ 3.09 sidereal months — not an integer multiple, so the orbit does not close in the Earth-centered inertial frame (p. 11, Fig. 7b). years: null (CR3BP, see (1,1) row).
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: (2,1) prograde Earth-Moon cycler
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.1294
Period (non-dim): 19.4404
Stability index: 0.050

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 from sourced (mu, C^stable), self-consistency-checked; never a golden. (2,1) is a razor-thin stable window (Delta_p_m 4.23 km): the exact nu=0 x0 sits a hair off the published 16-digit C, so the reproduced T lands ~2.7e-4 TU from T^stable (results note §1).

source: scripts/cr3bp_ross_reproduce.py; tests/search/test_cr3bp_ross_families.py; 2026 journal version.
orbit_elements.cr3bp.jacobi_max [conflict]
Ross Table 3 C_(2,1) BOUND column = 3.1297495000000 disagrees with Eq. 8 + Table 1 min{3.129751730201047, 3.1833333078762} = 3.129751730201047 (Delta 2.23e-6; mining note §4). The C^stable/C^max/T^stable columns used here are internally consistent and catalogue-grade; only the C_(k1,k2) bound column is inconsistent. Pinned by tests/search/test_cr3bp_ross_families.py::test_data_gap_c21_bound_inconsistency. Re-verify against the 2026 journal.

source: Ross & Roberts-Tsoukkas 2026 journal version (Roberts-Tsoukkas & Ross).

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

Braik, A. & Ross, S. D. (2026). Orbital Networks in the Three-Body Problem. arXiv preprint arXiv:2605.31543 (29 May 2026). · link
Braik & Ross 2026 confirms the (2,1) stable cycler in their common-energy Table 2 as "C21", period T=84.533 d, instability rate sigma=0.1358 TU^-1 (the LOWEST sigma of the 4 cyclers tabulated — consistent with the published stable verdict). Their stated common Jacobi C_J=3.1294 is the 5-sig-fig display rounding of THIS row's C^stable=3.129389531088256 (the (2,1) family's full Jacobi extent DeltaC ~ 4e-12 is sub-resolution at 4 d.p., so 3.1294 IS this family's Jacobi to that precision — verified by our reproduction harness which only recovered C21 at the unrounded 3.129389531088256, not at literal 3.1294). 4-of-4 reproduction and the rounded-vs-literal disposition are recorded in docs/notes/2026-06-14-249-unstable-member-recovery-plan.md (final section, commits a19eb24, 4a20243, f608c6b, 325c8a2). Three other common-energy (1,1)/(3,2) members from the same Table 2 (C11a, C11b, C32) enter as separate catalogue rows (braik-ross-c11a-cycler-2026, braik-ross-c11b-cycler-2026, braik-ross-c32-cycler-2026) -- those are new family members at a DIFFERENT Jacobi (C=3.1294) from the (1,1)/(3,2) anchors ross-rt-em-cycler-11-2025 / ross-rt-em-cycler-32-2025 (which sit at the per-family stable midpoint, not the common energy).

Notes

(2,1) stable prograde Earth-Moon cycler, nu=0 midpoint of a narrow stable subfamily (Delta_p_m 4.23 km, Table 3). Reproduced in-repo: the enforced C is exact, the corrected member lands ~2.7e-4 TU off the printed T^stable (the razor-thin window displaces the exact-midpoint x0 a hair along the family), verdict STABLE (nu=0.05007, |nu|<1), independent Radau closure dJ < 1e-12. PCR3BP-only; see (1,1) row model note.

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): (2,1) C^stable = 3.129389531088256.
orbit_elements.cr3bp.period_nd: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (2,1) T^stable = 19.44043166795154 TU; Table 4 (p. 13) 84.534335 d.
orbit_elements.cr3bp.mass_ratio: Ross & Roberts-Tsoukkas 2025 p. 3: mu = 1.2150584270572e-2.