Umbriel-Titania-Umbriel (1,1) Uranian symmetric-closure quasi-cycler

umbriel-titania-1-1-uranian-quasi-cycler-2026 · source: discovered · validation: V4

Signature

Bodies: Uranus-Umbriel-Titania
Primary: Uranus
Sequence (canonical): Umbriel-Titania-Umbriel
Sense: n/a
Orbit class: Quasi-cycler
quasi-cycler (epoch-locked, finite returns)
Cycler class: multi-arc
Returns: 10 — finite for epoch-locked classes
Validity window: 2000-06-21 → 2083-06-21
Launch epoch: 2000-06-21T00:00:00Z
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: cr3bp
CR3BP — Jacobi-constant-conserved; signature not patched-conic comparable.
Period: not strictly periodic (no published period)
Source ephemeris: URA111 (JPL/NAIF Uranian satellite SPK kernel, 1900-2099 coverage)
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-07-11

V∞ at encounters

Umbriel (encounter 1): 1.23 km/s
Per gauntlet-passing IC (data/gauntlet_566_five_representatives.jsonl, candidate enum563-line26-umbriel-titania-umbriel); exact symmetric closure at rel_offset=0 deg.
Titania (encounter 2): 1.01 km/s
Per gauntlet-passing IC. Mid-cycle encounter of the Umbriel-Titania-Umbriel symmetric closure.
Umbriel (encounter 3): 1.23 km/s
Per gauntlet-passing IC. Returns to the first Umbriel encounter within the 4.44e-15 km/s symmetric-closure residual.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 3.9544738760575804 d, 3.9544738760575804 d

Orbit view 2.5D ecliptic projection

Not renderable from current data. This entry is a multi-arc tour across several distinct moon-pair systems, with each leg computed under its own restricted three-body approximation — not a single rotating-frame periodic orbit. A faithful render requires numerical propagation of each leg's synodic-frame state, which the catalogue does not yet publish as a sampled path, so no stand-in ellipse is drawn. Unlike a single CR3BP orbit, this entry has no single Jacobi constant, period, or stability index — a multi-moon-pair tour has no one restricted three-body system to define them against. See the notes below for per-leg details.

model: CR3BP (rotating frame)

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

Legs

→ : 3.9544738760575804 d, 0 revs
→ : 3.9544738760575804 d, 0 revs

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (3)

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

invariants.aphelion_ratio [not-applicable]
This is a Uranus-centered multi-moon-pair patched-conic tour, not a single heliocentric ellipse — the heliocentric aphelion-ratio concept this field is designed for does not apply here. Left null rather than fabricated.
invariants.turn_ratio [unknown]
The achieved turn angle per encounter has not been separately computed against the max-bend physical-sanity ceiling, so a turn_ratio (achieved/max) cannot be stated yet.
orbit_elements.cr3bp [not-applicable]
model_assumption=cr3bp here means each leg's V_inf is matched via a restricted-three-body (Uranus-moon) approximation, NOT that this row is a single CR3BP rotating-frame periodic orbit — it is a multi-arc tour across two different Uranus-moon pairs, each with its own mass ratio. No single Jacobi constant/period/stability triple describes the whole tour, matching the precedent already recorded for the Jovian/Saturnian Tisserand-graph tours ('Jacobi constant is not conserved in this model'). The cr3bp identity schema field applies only to cycler_class=non-keplerian rows (a single periodic orbit); this row is cycler_class=multi-arc, so that field is correctly absent, not missing.

Primary citation

cyclerfinder discovery campaign (2026). Umbriel-Titania-Umbriel (1,1) Uranian symmetric-closure quasi-cycler -- representative of the 30-member symmetric-closure family (first-documented member: Umbriel-Oberon-Umbriel). cyclerfinder project.

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

Notes

Representative Umbriel-Titania-Umbriel member of the Uranian symmetric-closure quasi-cycler family. This is an INTERNALLY-ENUMERATED family within this project's own search space: the direct symmetric-closure enumeration found 30 exact 0-deg/180-deg symmetric periodic closures spread across the six non-Miranda Uranian moon-pair directions (Ariel/Umbriel/Titania/Oberon pairs). the Umbriel-Oberon-Umbriel (1,1) row was the FIRST-DOCUMENTED member of this family; this row is the census-minimum single representative for the Umbriel-Titania pair direction (Sec 2/4: one rep per pair, the other same-pair-redundant closures are not separately catalogued). Genericity WITHIN this project's own search density is not prior art -- the family being internally enumerable does not change any literature-novelty verdict. Validation (V4, windowed): the gauntlet ran this candidate through the same frozen V2->V3->V4-scipy->V4-strict chain the earlier row itself cleared, at the reference launch epoch 2000-06-21 and n_cycles in {3, 5, 10}. Verdict PASS_AS_QUASI_CYCLER: strict V2 is FAIL_QUASI_BOUNDED by design (the bounded-drift quasi_cycler signature exceeds the 50,000 km strict-periodic floor -- the same admission path used), with V3, V4-scipy and V4-strict all passing at all three n_cycles. Windowed validity (the characterization, NOT continuous validity): the feasible synodic DUTY CYCLE is 68.5% -- the fraction of synodic phase for which the transfer is V4-strict-feasible (its osculating periapsis stays outside Uranus's r_eq = 25,559 km). Measured over the combined daily-2000 + daily-2030 epoch scans (N=731). Every failure in the scan is the genuine planet_crossing_infeasible geometry boundary recurring every 7.9 d (full synodic period; MEASURED Sec 4, not a derived halving rule) -- zero lambert_no_solution, zero integrator_failure, zero drift-floor failures (cleaner on the drift axis than the earlier row, which has its own ~1.3% secondary drift-floor population; this representative has none). The calendar span {2000-06-21 -> 2083-06-21} is the shared URA111-kernel-coverage- bounded interior span (same bounds convention as the family's first-documented member's own row, whose 2084+ failures are kernel-edge extrapolation artifacts); it is NOT an independently swept per-representative annual pass run. A low duty cycle is a launch-epoch- must-be-timed-to-synodic-phase constraint (like an interplanetary launch window), a legitimate validity_window characteristic, not a validation defect (Sec 5). Literature clearance: the offline literature_check.py KNOWN_CORPUS adjudication returns NOT-FOUND under the repeated-moon topology fingerprint; the only body-set-overlapping anchors are the Uranus mga-tour / mission-concept entries (Heaton-Longuski 2003, Sims 2014, Jarmak 2020, UOP Flagship), all a different topology (non-repeating flyby tours), correctly discriminated. No moon-pair symmetric-closure quasi-cycler anchor exists for this pair. Discovery + adjudication chain: (family census via the discovery genome) -> (Fable-corrected continuous-tof commensurability refinement -> direct symmetric-closure enumeration; the 30-member family) -> (Opus+Fable survivor-list adjudication, 5-representative selection) -> (V1-V4-strict gauntlet) -> (epoch-robustness duty-cycle scan) -> (writeback-readiness verdict) -> (this writeback).

Source quotes (per-field provenance)

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

vinf_kms_at_encounters.0.vinf_kms: Per data/gauntlet_566_five_representatives.jsonl candidate enum563-line26-umbriel-titania-umbriel: V_inf at first Umbriel = 1.2295656768416439 km/s; reported 1.2296 (4 decimals) for display.
vinf_kms_at_encounters.1.vinf_kms: Per : V_inf at Titania = 1.0058255988095806 km/s; reported 1.0058.
vinf_kms_at_encounters.2.vinf_kms: Per : V_inf at second Umbriel = 1.229565676841644 km/s; reported 1.2296. Symmetric-closure residual vs first Umbriel = 4.44e-15 km/s.
validity_window.synodic_duty_cycle_pct: Per verdict Sec 2 (data/scan_567_epoch_robustness.jsonl): feasible synodic duty cycle = n_PASS / (n_PASS + n_planet_crossing_infeasible) over daily-2000+daily-2030 (N=731) = 68.5%.
validity_window.synodic_boundary_period_days: Per verdict Sec 4: MEASURED FFT dominant period of the daily planet_crossing_infeasible boundary series = 7.9 d (full synodic period).
validity_window.start: URA111-kernel-coverage-bounded interior span; same bounds convention as the row (longest interior PASS run start 2000).
validity_window.end: URA111-kernel-coverage-bounded interior span; same bounds convention as the row (interior PASS run end 2083; 2084+ are kernel-edge artifacts).
n_returns: Per : PASS_AS_QUASI_CYCLER at n_cycles in {3,5,10}; n_returns=10 mirrors the family's first-documented member's own convergent-with-bounded-drift count (NOT a strict-periodic infinity).