Computed 3D out-of-plane (2,1) Earth-Moon resonant periodic orbit — spatial extension of ross-rt-em-cycler-21-2025 (CR3BP, KNOWN-CLASS member of the Antoniadou-Libert spatial-resonant family; libration-class, NO transport utility per Region B)

em-cycler-21-3d-spatial-2026 · source: this-project · validation: V2 · known-class

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
Sense: n/a
Orbit class: Resonant PO
resonant periodic orbit (stable, no transport utility)
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)
Full nondim period T = 18.167169790651315 TU. The 3D out-of-plane branch of the planar (2,1) cycler (ross-rt-em-cycler-21-2025); the spatial family bifurcates from the planar family's vertical-critical orbit (Antoniadou & Libert 2019 mechanism). years: null (CR3BP).
Priority date: 2026-06-25

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, 3D out-of-plane spatial extension (winding k1=2, k2=0, k_z=10)
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.0258
Period (non-dim): 18.1672
Stability index: 0.000

3D CR3BP rotating-frame periodic orbit (genuinely out-of-plane, z0~-0.206); 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 (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.state_nd [derive]
No published IC for THIS Earth-Moon spatial member (Antoniadou & Libert 2019 is mu=0.001 planetary, no Earth-Moon ICs; JPL no match). state_nd DERIVED by our 3D corrector from the broken-plane lift of the planar (2,1) cycler, V1/V2 re-verified. Never a golden. This is WHY our_status is known-class-member, not known-reproduction.

source: scripts/scan_434_3d_broken_plane_em.py; src/cyclerfinder/data/validation/v1_3d.py + v2_3d.py; tests/data/test_em_cycler_21_3d_knownclass.py.

Primary citation

undefined et al. (0). . .

Corroborating sources

Antoniadou, K. I. & Libert, A.-S. (2019). Spatial resonant periodic orbits in the restricted three-body problem. Monthly Notices of the Royal Astronomical Society 483(3):2923-2940. DOI: 10.1093/mnras/sty3195
The published CLASS source (NOT first_published): stable spatial resonant periodic families exist for the 2/1 (and 3/2,5/2,3/1,4/1,5/1) resonances, born from the vertical-critical orbits of the planar resonant family. Computed at mu=0.001 (planetary); supplies NO Earth-Moon IC — so this specific EM-mu member is a computed known-class member, not a literal reproduction.
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
The PLANAR parent (ross-rt-em-cycler-21-2025) whose vertical-critical orbit this 3D family bifurcates from.

Notes

KNOWN-CLASS MEMBER (spec §16.4). A computed, V1+V2-verified, Floquet- STABLE 3D out-of-plane Earth-Moon resonant/libration periodic orbit (orbit_class resonant_po, schema v4.9, — NOT a transport cycler): the spatial extension of the planar (2,1) cycler ross-rt-em-cycler-21-2025. RECHARACTERIZED from orbit_class cycler after Region B showed it has NO transport utility — the closest lunar pass is 122,628 km vs the lunar SOI 66,183 km, so the orbit never encounters the Moon (nor Earth); it is a stable libration-class resonant PO, not a transport cycler. Member of the PUBLISHED spatial- resonant family CLASS (Antoniadou & Libert 2019) but NOT a literal copy of any published orbit (that paper is mu=0.001 with no Earth-Moon IC; JPL's three-body catalogue has no match). NOT novelty-claimable (class known) AND NOT a known- reproduction (no specific published orbit) -> our_status known-class-member. Verification: run_v1_3d full-asymmetric 6D closure n_iter=1, independent Radau 3.2e-12 km/s, degenerate_planar=False; run_v2_3d 6-cycle drift 1.7 mm (linear) vs 50000 km floor; Floquet all six |ev|=1.0000. CR3BP-only; no real- ephemeris claim.

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.mass_ratio: Ross & Roberts-Tsoukkas 2025 p. 3: mu = 1.2150584270572e-2 (shared with the planar parent ross-rt-em-cycler-21-2025).