Braik-Ross common-energy (1,1)b Earth-Moon cycler (CR3BP, C=3.1294)

braik-ross-c11b-cycler-2026 · source: literature · validation: V1

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)
Period T_PO = 55.995 d (Braik & Ross 2026 Table 2 "(1,1)b-cycler" row); reproduced in-repo at 55.9590 d (-0.064%). The 0.06% gap is the largest of the three Braik-Ross cyclers reproduced here; the C11b branch sits closer to the (1,1) family's saddle-center fold than C11a, so the seed bracket is tighter and the corrector's recovered period lands slightly off the published rounded value (mining-note discussion in docs/notes/2026-06-14-249-unstable-member-recovery-plan.md). Encounter cadence: k1=1, k2=1 (same family as C11a, different branch). years: null (CR3BP).
Priority date: 2026-05-29

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: (1,1) prograde Earth-Moon cycler — long-period branch (C11b)
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.1294
Period (non-dim): 12.8690
Stability index: 3.244

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 source. state_nd DERIVED in-repo by the fixed-Jacobi symmetric corrector from the seed region (x0~-0.7684981, ydot0_sign=-1, half-period at the 6th x-axis crossing) pinned in src/cyclerfinder/search/reachable_representatives.py::_CYCLER_SEEDS and confirmed against the sourced T_PO + (1,1) topology by the reproduction harness.

source: src/cyclerfinder/search/reachable_representatives.py + docs/notes/2026-06-14-249-unstable-member-recovery-plan.md.
orbit_elements.cr3bp.period_nd [uncertain]
Reproduced period 55.9593 d lands 0.06% (-0.036 d) below Braik-Ross's Table-2 sourced 55.995 d -- the largest period-error of the three Braik-Ross cyclers reproduced here. The C11b branch sits closer to the (1,1) family's saddle-center fold than C11a (mining note), so the seed region is more sensitive and the corrected member lands a hair off the printed rounded value. Topology, Jacobi, and UNSTABLE verdict are exact; the period difference is within the 0.5 d source-confirmation tolerance used by recover_all_cyclers_braik_ross.

source: docs/notes/2026-06-14-249-unstable-member-recovery-plan.md (GRIND RESULT section).

Primary citation

Braik, A. & Ross, S. D. (2026). Orbital Networks in the Three-Body Problem. arXiv preprint arXiv:2605.31543 (29 May 2026).

URL: https://arxiv.org/abs/2605.31543

Same source as braik-ross-c11a-cycler-2026. Table 2 row "(1,1)b-cycler": T_PO=55.995 d, sigma=0.9255 TU^-1 (sigma_d=0.2128 d^-1).

Corroborating sources

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. · link
Family anchor: same continuous (1,1) family as ross-rt-em-cycler-11-2025 (Ross-RT 2025 Def. 1, Table 3), DIFFERENT branch at a DIFFERENT energy. C11b is the long-period branch of the (1,1) family at C=3.1294 (paired with C11a's short-period branch across a saddle-center fold). Same family identity (k1=1, k2=1, prograde); different orbit (UNSTABLE, T=55.995 d vs the anchor's STABLE T=44.754 d).

Notes

Common-energy (1,1)b-cycler from Braik & Ross 2026 Table 2, the LONG-PERIOD branch of the (1,1) family at C_J=3.1294. Paired with C11a across the family's saddle-center fold (mining). Like C11a it is UNSTABLE at this energy (sigma=0.9255 TU^-1, slightly weaker than C11a's sigma=1.0482). REPRODUCTION (2026-06-14): symmetric corrector at C=3.1294 from seed x0=-0.7684981 (ydot0_sign=-1, 6th x-axis crossing) -> T=55.959 d (sourced 55.995, error -0.064%; the largest period-gap of the three Braik-Ross cyclers reproduced, flagged as data_gap "uncertain" above); Jacobi 3.1294 enforced to machine eps; topology (1,1) prograde confirmed. Independent Radau closes Jacobi (dJ=1.3e-12) and full state to ~3e-11. MODEL: pure PCR3BP at the Braik-Ross common Jacobi. See the C11a row for the framework context (Braik-Ross reachable-set accessibility study).

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.period_nd: Braik & Ross 2026 Table 2 (p. 12): (1,1)b-cycler T_PO=55.995 d at C_J=3.1294.
orbit_elements.cr3bp.braik_ross_sigma_per_tu: Braik & Ross 2026 Table 2 (p. 12): (1,1)b-cycler instability rate sigma=0.9255 TU^-1.
orbit_elements.cr3bp.braik_ross_sigma_per_day: Braik & Ross 2026 Table 2 (p. 12): (1,1)b-cycler instability rate sigma_d=0.2128 day^-1.
orbit_elements.cr3bp.jacobi_constant: Braik & Ross 2026 Sec. 2.4 / Table 2 header: common Jacobi level C_J=3.1294.
orbit_elements.cr3bp.mass_ratio: Braik & Ross 2026 Table 1 (p. 8): mu = 0.012150584270572.