family A: (5,2) prograde asymmetric resonant Earth-Moon cycler (CR3BP, C=2.4819, periselene 13,243 km alt; known-class member)

earth-moon-5-2-prograde-asymmetric-cycler-1000a-2026 · source: this-project · validation: V1 · known-class

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 = 12.712603845043912 TU nondim (about 2 pi x 2 = 12.5664: the p-q resonance); 55.204226 d via this project's registry t* (375190.2619 s). years: null (CR3BP, rotating-frame periodic orbit).
Priority date: 2026-10-08

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: family A: (5,2) prograde asymmetric resonant Earth-Moon cycler (winding E 3, M 0); member of the Casoliva 2010 Class 1 p-q resonant class
Mass ratio (μ): 0.01215058439469525
Jacobi constant: 2.4819
Period (non-dim): 12.7126
Stability index: -110.096

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 (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 published IC for this orbit or its family (literal table). state_nd DERIVED: the multiple-shooting grid member that seeded the family's continuation, re-closed with cyclerfinder.search.cr3bp_periodic.correct_periodic at the registry mu. Never a golden. This is why our_status is known-class-member, not known-reproduction.

source: scripts/run_1000_shooting.py; scripts/run_1000_continue.py; scripts/writeback_1047_rows.py; data/1047_rows/writeback_v1.json.
orbit_elements.cr3bp.stability_index [derive]
Casoliva 2010 Eq. 6-8 convention, as on the casoliva-7-3b/7-3c rows: k = max(|k_par|, |k_perp|) with its sign, from the full-period monodromy (earth_moon_resonant_families.planar_stability_index; k_par -110.096, k_perp -8.418). The product of 20 per-arc STMs gives k_par -110.097. Not comparable number-for-number with the Barden half-period nu rows.

source: src/cyclerfinder/search/earth_moon_resonant_families.py::planar_stability_index; data/1047_rows/writeback_v1.json.

Primary citation

No primary citation recorded; see the provenance tags below.

Corroborating sources

Casoliva, J. et al. (2010). Two Classes of Cycler Trajectories in the Earth-Moon System. Journal of Guidance, Control, and Dynamics 33(5), pp. 1623-1640. DOI: 10.2514/1.46856
The published CLASS source (not first_published): Class 1, near-Keplerian p-q resonant Earth-Moon cyclers, including the asymmetric 7-3b/7-3c pair. Table 3 tabulates p-q = 1-2, 2-1, 3-2 and 7-3 only; it has no (5,2) prograde orbit.

Notes

KNOWN-CLASS MEMBER (spec sec. 16.4; (iii); owner decision 2026-10-11, 'Rows for A, B, D only'). family A: 5:2 prograde (inertial), winding about the Earth 3, about the Moon 0, asymmetric. A computed member of the published class of near-Keplerian p-q resonant Earth-Moon cyclers (Casoliva et al. 2010 Class 1, which includes the asymmetric 7-3b/7-3c pair); NOT a literal copy of any published orbit and NOT novel. FAMILY: full computed C range 2.4022-3.0968 (low end: Earth floor; high end: loss of convergence, unexplained, 0.003 below Liang 2017's 5:2 C); cycler-class candidates over C 2.4034-2.9423 (perigee 225-35,752 km alt, periselene 11,637-35,997 km alt, T 12.696-13.093, b -275 to -103 from arc STMs). This row is the grid member that seeded the continuation (data/1000_complement/continuation/5_2_pro_wE3_wM0_p.jsonl (line 1, k = 0)), re-closed with correct_periodic. LITERATURE (docs/notes/2026-10-11-1047-earth-moon-families-literal-table-and-v3-gate.md): literal table (every published Earth-Moon p:q orbit held as numbers: Casoliva 2010 Table 3, Vaquero 2013, Newton 1959, Casoliva 2008 seeds, Liang 2017, Liang 2020, Hoelker-Winston 1968, Genova-Aldrin 2015) has NO member of this family. The v3 literature gate returns 'published' at class level (Earth primary, Moon, topology resonant); the gate does not compare p:q, sense or symmetry. Restrepo & Russell 2018: excluded by construction (their database holds planar axisymmetric orbits only; this orbit is asymmetric). Franz & Russell 2022: excluded by construction (their database drops orbits that go more than about 350,000 km from the Moon; this orbit reaches 795,600 km). VERIFICATION (V1; scripts/writeback_1047_rows.py, data/1047_rows/writeback_v1.json, tests/search/test_1047_rows_writeback_v1.py): full-state single-shooting Newton closure 3.7e-11; independent Radau re-propagation keeps the Jacobi constant to 1.9e-12 over one period and agrees with DOP853 arc by arc (20 arcs) to 4.6e-11. The orbit is strongly unstable (k = -110.1), so a whole-period closure depends on the integrator's step sequence: 9.9e-08 for a plain DOP853 run and 1.6e-09 for Radau (error amplification, not a closure failure; the reason uses multiple shooting). Dense DOP853 re-propagation: perigee 3,332 km alt, periselene 13,243 km alt (inside the Hill radius 61,274 km: a lunar encounter every period, orbit_class cycler), winding about the Earth 3 and about the Moon 0, no perpendicular x-axis crossing (asymmetric). NOT V2 (an unstable orbit cannot satisfy V2-ballistic bounded drift). MIRROR: the mirror image (x, -y, -vx, vy) of this orbit is a different orbit of the same C and period (minimum state distance 0.099 nondim); it is not a separate row (owner decision: one row per family). MODEL: planar CR3BP at this project's registry mu, l* and t*. No ephemeris claim.