KAM torus corridor around Braik-Ross planar Resonant 2to1 Stable (R21-S) Earth-Moon resonant cycler (CR3BP, C=3.1294)

braik-ross-planar-r21-s-corridor-2026 · source: this-project · validation: V0 · known-class

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
Sense: n/a
Orbit class: Quasi-cycler
quasi-cycler (epoch-locked, finite returns)
Cycler class: non-keplerian (CR3BP)
Returns: ∞ — finite for epoch-locked classes
Validity window: — (not published)
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_PO = 6.09412703751587 TU = 26.499564292602827 d (Braik & Ross 2026 Table 2 "Resonant 2to1 Stable" row, abbrev R21-S; period_days sourced 26.5 d, matching this reproduction to the table's printed precision). Planar (z0=0) resonant Braik-Ross golden IC -- this is the ORBIT ITSELF sourced directly to the paper; only the corridor measurement below is this-project computation. years: null (CR3BP).
Priority date: 2026-07-22

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: Braik-Ross planar Resonant 2to1 Stable (R21-S) resonant Earth-Moon cycler
Mass ratio (μ): 0.0121505842705716
Jacobi constant: 3.1294
Period (non-dim): 6.0941
Stability index: —

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-family — CR3BP, CCR4BP, or CRNBP) periodic or quasi-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). Whatever identity fields the model supports (Jacobi constant, period, stability — not all apply to every model in this family; see "Model assumption" above) are tabulated above.

model: CR3BP (rotating frame)

3D view not available for rotating-frame (CR3BP-family) 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.stability_index [unknown]
Braik-Ross 2026 Table 2 labels this member stable ('R21-S' suffix -S = stable, per the paper's R{21,31,52}-S/-U convention) but does not print a numeric Barden-nu-style stability index (only period + qualitative stability designation for the resonant-family rows); this task does not separately re-derive one.

source: data/golden/braik_ross_2026_em_family_ics.yaml; Braik & Ross 2026 Table 2.

Primary citation

undefined et al. (0). . .

Corroborating sources

Braik, A. & Ross, S. D. (2026). Orbital Networks in the Three-Body Problem. arXiv preprint arXiv:2605.31543 (29 May 2026). · link
Table 2 row 'Resonant 2to1 Stable' (R21-S): sourced x0, ydot0, period. Supplies the ORBIT ITSELF (planar, resonant, stable); the corridor measurement is this-project computation, not from this source.

Notes

cycler-corridor CHARACTERIZATION, NOT a discovery. This row measures the quasi-periodic (KAM) torus corridor surrounding an ALREADY-KNOWN, LITERATURE-SOURCED periodic orbit: Braik & Ross 2026 Table 2's "Resonant 2to1 Stable" (R21-S) planar resonant Earth-Moon cycler. The orbit itself is sourced directly to the paper (via data/golden/braik_ross_2026_em_family_ics.yaml, independently computed from the authors' own MATLAB repo and verified against Table 2); ONLY the corridor measurement is this-project computation. KAM theory GUARANTEES some quasi-periodic torus family exists around any linearly-stable periodic orbit -- the open question this measurement answers is purely how BIG that corridor is, not whether it exists. Explicitly NOT conflated with this project's one confirmed novel finding (the Uranian symmetric-closure family); see data/OUTSTANDING.md's [[project_novel_findings_status]] note. Measurement result: corridor tube half-width 21741.3 km / 107.09 m/s at amplitude rung 0.06 (nondim), independent closure residual 5.598e-07 (nondim; gate 1.0e-4 = ~38.44 km equivalent). This is a LOWER BOUND -- the geometric amplitude ladder reached its top rung (6e-2 nondim) with the independent closure residual still passing; the true corridor edge (wall) was not found within the ladder's reach. Method: identical GMOS amplitude-ladder census as the C21/C32/lyapunov3d-L1 sibling rows in this same writeback -- see those rows' notes for the full method + positive-control paragraph (genome.qp_tori.correct_qp_torus; positive control tests/search/test_variational_qp_torus.py::test_l2_positive_control_reproduces_gmos_torus). Schema note: admitted as orbit_class=quasi_cycler under the schema v5.2 epoch-free CR3BP KAM-corridor carve-out (data/catalogue.schema.json v5.2; see the C21/C32 sibling rows' identical schema-note paragraph for the full rationale).