Umbriel 1:2-exterior resonant torus homoclinic connection (Titania-forced CCR4BP)

umbriel-1-2-torus-homoclinic-uranus-2026 · source: discovered · validation: V1

Signature

Bodies: Uranus-Umbriel-Titania
Primary: Uranus
Sequence (canonical): not applicable — a quasi-periodic torus has no repeating encounter sequence to state; see quasi-periodic tori
Sense: n/a
Orbit class: Torus (connected)
quasi-periodic invariant torus WITH a computed manifold connection (departs unstable, returns stable — see /about/#quasi-periodic-torus)

What is a quasi-periodic invariant torus? →
Cycler class: non-keplerian (CR3BP)
Returns: 1 — finite for epoch-locked classes
Validity window: 2000-01-01 → 2083-01-01
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: ccr4bp
CCR4BP — restricted four-body: the base three-body pair plus ONE periodic third-body forcing term; no exact conserved quantity (Jacobi constant does not carry over).
Period: — yr ( × synodic)
No beat-period / encounter-pair concept applies to a torus-homoclinic connection (there is no repeating multi-body flyby cycle to state a pair/k/years for). The connection's own timing (unstable-departure to stable-arrival elapsed flow time) is carried in ccr4bp_provenance.connection.t_u_tu/t_s_tu (nondimensional TU) and their _days conversions. Left null rather than fabricated, matching the sequence_canonical null convention below.
Source ephemeris: URA111 (JPL/NAIF Uranian satellite SPK kernel) + DE440 (Uranus barycentric state)
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-07-24

V∞ at encounters

No encounter V∞ values published in accessible sources.

CR3BP orbit identity

Family: umbriel-spacecraft-1:2-exterior-resonant-torus
Mass ratio (μ): 0.000014685981867903303
Jacobi constant: —
Period (non-dim): 11.9911
Stability index: —

Uranus-centered torus-homoclinic connection; heliocentric/planetcentric Keplerian elements inapplicable. The CR3BP identity tuple below carries the BASE resonant periodic orbit the torus is built around (Sec 3); the torus + connection's own identity is in ccr4bp_provenance.

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: CCR4BP (rotating frame, one periodic forcing term)

3D view not available for rotating-frame (CR3BP-family) orbits.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (5)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

sequence_canonical [not-applicable]
This is a torus-homoclinic connection (departs the SAME quasi-periodic torus's unstable manifold, returns via its stable manifold) -- there is no alternating named-body flyby sequence for this field's convention to describe. Neither Umbriel nor Titania is closely encountered (see ccr4bp_provenance.real_ephemeris_evidence closest_approach_km, always >181,000 km / >534,000 km respectively, far outside either moon's physical radius). Left null rather than fabricated, per the (umbriel-oberon-1-1-uranian-quasi-cycler-2026) row's own precedent for invariants.aphelion_ratio / orbit_elements.cr3bp.
orbit_elements.cr3bp.jacobi_constant [not-applicable]
The CCR4BP (time-periodic Titania forcing) has NO exact conserved quantity -- see search.ccr4bp_heteroclinic_search.quasi_jacobi_gap's own docstring. The approximate substitute (ccr4bp_provenance.connection.quasi_jacobi_gap) is reported there instead.
orbit_elements.cr3bp.stability_index [unknown]
No Floquet/monodromy stability index has been separately computed for the base torus's underlying periodic orbit by this task chain.
validity_window.synodic_duty_cycle_pct [unknown]
Only 10 discrete real-ephemeris anchor epochs have been tested, each densely scanned across its own single ~7.9-day synodic cycle (300 points, the methodology) -- NOT a continuous multi-year daily scan across the whole calendar span the way the family's first-documented member's own synodic_duty_cycle_pct was measured. A denser continuous scan (daily sampling across the full 2000-2083 span, matching the family's first-documented member's own evidence density) is a natural next step, not yet run. The within-cycle duty structure at the one representative anchor that has been densely scanned is instead recorded as a threshold ladder in ccr4bp_provenance.real_ephemeris_evidence.synodic_duty_cycle_bands_pct, since "feasible" for this connection is a continuous correction-budget threshold, not the binary hard-physical-wall criterion.
vinf_kms_at_encounters [not-applicable]
No named-body encounter exists for a torus-homoclinic connection (neither moon is closely approached -- see ccr4bp_provenance.real_ephemeris_evidence closest_approach_km). vinf_fidelity is still recorded (real-de440) to reflect which fidelity tier the row's own headline real-ephemeris connection-gap evidence (ccr4bp_provenance.real_ephemeris_evidence) is stated at, per the family's first-documented member's own recommendation, even though no vinf_kms_at_encounters array exists to pair it with.

Primary citation

cyclerfinder discovery campaign (2026). Umbriel 1:2-exterior resonant torus homoclinic connection -- CCR4BP (Uranus-Umbriel-Titania). cyclerfinder project.

orbit source derived orbit fidelity circular-coplanar V∞ source derived V∞ fidelity real-de440

Notes

NEW dynamical species for this catalogue: a homoclinic connection to a quasi-periodic invariant TORUS in the CCR4BP (Concentric Circular Restricted 4-Body Problem), not a discrete multi-encounter Lambert-arc tour and not a single strictly-periodic orbit. A spacecraft riding the 2-D invariant torus around the spacecraft:Umbriel 1:2-exterior resonant periodic orbit (Titania-forced) can depart along the torus's unstable manifold, flow for t_u ~19.0 TU (~12.53 d), and return along the stable manifold of the SAME torus after t_s ~19.09 TU (~12.59 d) -- closing the idealized position/velocity gap to machine precision (corrected_pos_gap_km = 5.66e-10 km, corrected_vel_gap_km_s = 5.11e-14 km/s). Ghost-guard verified: independent Radau vs. DOP853 integrator agreement to ~1.05e-7 km; off-torus sanity distance ~1928 km (rules out a trivial near-departure pseudo-match). Real-ephemeris consistency: the idealized connection does NOT survive verbatim under real DE440/URA111 ephemeris (headline 2030-01-01 gap: 174,709 km / 1.458 km/s) -- but a narrow synodic-phase window exists near each synodic cycle where the mismatch collapses to a comparable near-miss (best 2030 point: 84.5 km / 5.9 m/s, a ~2069x/247x reduction from the headline naive-epoch gap). Epoch-robustness scan: this narrow-window structure RECURS at all 10 independently-tested anchor epochs spanning 2000-2083 (~9-year spacing; per-epoch local-minimum gaps 5.4-142.8 km / 1.0-13.1 m/s), all 10/10 passing the pre-declared "comparable to the 2030 reference" gate (844.6 km / 0.059 km/s, 10x the reference). Closest approach to either moon across all 10 epochs stays far outside its physical radius (Umbriel ~181,200-181,800 km vs. ~584 km; Titania ~534,600-828,600 km vs. ~788 km) -- no collision-course degeneracy. This is evidence of a real, recurring, correctable near-connection, not a one-off numerical coincidence, though the evidence is 10 sparse discrete epochs with their own dense within-cycle scans, NOT a continuous multi-year daily scan (see data_gaps). Literature clearance: the deep novelty check (10 live queries + full corpus scan + full-text check of the closest adjacent paper, Kumar arXiv:2509.03655, whose Uranus CCR4BP work covers Oberon/Titania secondary resonances, NOT Umbriel-Titania) found no disqualifying prior CCR4BP/torus/heteroclinic work on this pair. independently re-verified this same-day for the SHARPER claim (a real-ephemeris-survivable, epoch-recurring homoclinic connection across 10 epochs, not merely "does some CCR4BP structure exist on this pair") -- verdict STILL CLEAR (docs/notes/2026-07-24-706-umbriel-titania-writeback-litcheck-refresh.md). our_status is left absent (matching the row's own precedent) rather than asserted, since no independent verification gauntlet analogous to spec §16.4's candidate-novel/ verified-novel ladder has been run for this object class. Schema: admitted under schema v5.3, which added orbit_class= torus_homoclinic, model_assumption=ccr4bp, and the additive ccr4bp_provenance block -- see data/catalogue.schema.json's own v5.3 changelog entry and docs/notes/2026-07-24-707-ccr4bp-catalogue-schema-design.md for the full design reasoning (approved by the user as proposed). Discovery + verification chain: (CCR4BP infra, JEG positive control) -> (cross-solar-system moon-pair screening) -> (reuse-only pipeline extension) -> (deep novelty check) -> (Umbriel-Titania torus + homoclinic connection search, ghost-guard verified) -> (n/a / intermediate) -> (real-ephemeris consistency check) -> (epoch-robustness recurrence scan) -> (fresh literature-clearance re-check) -> (catalogue schema design proposal, user- approved) -> (this writeback: schema implementation + row).

Source quotes (per-field provenance)

Every numerical value in this entry traces to a verbatim or paraphrased quote from a cited source.

ccr4bp_provenance.connection.idealized_pos_gap_km: data/found/701_ccr4bp_umbriel_titania_search/result.json:best_robust_genuine_connection_corrected.corrected_pos_gap_km = 5.661540346264633e-10.
ccr4bp_provenance.connection.integrator_delta_km: data/found/701_ccr4bp_umbriel_titania_search/result.json:best_robust_genuine_connection_corrected.corrected_integrator_delta_km = 1.0512238869207226e-07 -- the ghost-guard independent Radau-vs-DOP853 cross-check this row's V1 validation_level rests on.
ccr4bp_provenance.real_ephemeris_evidence.n_epochs_comparable: data/found/705_ccr4bp_epoch_robustness_scan/result.json:summary.n_epochs_comparable_to_704 = 10 (of 10 tested).
validity_window.synodic_period_days: data/found/705_ccr4bp_epoch_robustness_scan/result.json:real_umbriel_titania_synodic_period_days = 7.908977583921671.