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Jupiter-Europa 3:4 exterior resonant torus substitute, Laplace-locked N=5 CRNBP (Io+Ganymede forced)

europa-3-4-crnbp-torus-jupiter-2026 · source: discovered · validation: V1

Signature

Bodies

Jupiter-Europa-Io-Ganymede

Primary

Jupiter

Sequence (canonical)

not applicable — a quasi-periodic torus has no repeating encounter sequence to state; see quasi-periodic tori

Sense

n/a

Orbit class

Quasi-periodic torus

quasi-periodic invariant torus, no encounter sequence, no computed connection yet — existence/structural discovery only (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

crnbp

CRNBP — restricted N-body: the base three-body pair plus TWO simultaneous periodic forcing terms; no exact conserved quantity (Jacobi constant does not carry over).

Period

— yr ( × synodic)

No beat-period/encounter-pair concept applies to a bare quasi-periodic torus (no alternating named-body flyby cycle to state a pair/k/years for). The stroboscopic forcing period (theta1 clock) is carried in crnbp_provenance.torus.period_tu; the motion itself is quasi-periodic (irrational rotation number, crnbp_provenance.torus. rotation_number), so no single orbital period exists to state here.

Source ephemeris

jup365.bsp (JPL/NAIF Galilean satellite SPK) via core.ephemeris; naif0012.tls

Ephemeris model the source states its numbers were computed against.

Priority date

2026-07-27

V∞ at encounters

No encounter V∞ values published in accessible sources.

CR3BP orbit identity

Family

europa-spacecraft-3:4-exterior-resonant-torus (Kumar et al. 2021 seed class; EXTERIOR, never 'interior' -- #724 correction)

Mass ratio (μ)

0.00002528017724591319

Jacobi constant

—

Period (non-dim)

12.4777

Stability index

—

Jupiter-Europa rotating-frame quasi-periodic torus; Keplerian elements inapplicable. The cr3bp tuple carries the BASE resonant orbit's identity; the torus's own identity (Fourier coefficients, rotation number, seed lineage) is in crnbp_provenance.torus.

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]
  Bare quasi-periodic torus -- no alternating named-body flyby sequence exists. No moon is closely encountered (closest approaches across the three NARROW model-shadowing torus points x all 10 epochs: Europa >=4.14e5 km, Io >=2.03e5 km, Ganymede >=2.16e5 km -- see crnbp_provenance.real_ephemeris_evidence.torus_points -- all far outside every SOI; the two genuinely-collapsing points' divergent real-SPICE trajectories, which are NOT the catalogued object, come as close as 3.2e3 km to Ganymede). Left null rather than fabricated, per the rows' own precedent.
• orbit_elements.cr3bp.jacobi_constant [not-applicable]
  The CRNBP (two simultaneous time-periodic forcings, Io+Ganymede) has NO exact conserved quantity; unlike the row there is not even a quasi-Jacobi connection-endpoint gap to report (no connection exists for this object).
• orbit_elements.cr3bp.stability_index [unknown]
  No Floquet/stability, manifold, or transfer computation exists for this object (mandatory qualifier; TCP has all three for THEIR Lyapunov-substitute tori -- this row must not imply parity). shortlist item 3 (manifold/connection work) is gated and not dispatched.
• validity_window.synodic_duty_cycle_pct [unknown]
  10 sparse anchors with per-anchor dense synodic scans, not a continuous daily scan (same evidence-shape mismatch as the row, Q4 / Sec 7). Within-cycle structure is recorded as the threshold ladder in crnbp_provenance.real_ephemeris_evidence.synodic_duty_cycle_bands_pct.
• vinf_kms_at_encounters [not-applicable]
  No named-body encounter exists. vinf_fidelity (real-de440) records the fidelity tier of the row's headline real-SPICE model-shadowing evidence, per the row's convention.

Primary citation

cyclerfinder discovery campaign (2026). Quasi-periodic invariant-torus substitute of the Jupiter-Europa 3:4 exterior resonant orbit in a Laplace-locked restricted five-body model. cyclerfinder project.

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

Corroborating sources

• Baresi, N. et al. (2023). Exploiting the Laplace Resonance for Designing Trajectories in the Jupiter-Io-Europa-Ganymede System. AAS/AIAA Astrodynamics Specialist Conference, Big Sky, MT, AAS 23-201.
  MODEL-CLASS source (mandatory citation): the Tri-Circular/Laplace-locked N=5 idea is theirs; first N=5 tori (L1/L2 Lyapunov-family substitutes), Floquet stability, manifolds. Our object differs on exactly two axes: orbit family substituted (mean-motion-resonant vs Lyapunov) and rate model (physical Ganymede synodic rate vs both rates idealized to exact rationals -- their own 2*pi*k periodicity construction requires the idealization). No stability, manifold, or transfer computation exists for OUR object (they have all three for theirs).
• Owen, D. et al. (2024). Transfer Trajectory Design in the Jupiter-Io-Europa-Ganymede Tri-circular Problem. 29th International Symposium on Space Flight Dynamics (ISSFD), Darmstadt, Germany.
  MODEL-CLASS source (mandatory citation): planar TCP QPO continuation (70th/75th Lyapunov members) + Europa<->Ganymede transfers; its own SSVI future-work text confirms beyond-Lyapunov substitutes were NOT computed.
• Kumar, B. et al. (2021). Computation and Analysis of Jupiter-Europa and Jupiter-Ganymede Resonant Orbits in the Planar Concentric Circular Restricted 4-Body Problem. AAS/AIAA Astrodynamics Specialist Conference, AAS 21-651; arXiv:2109.14815.
  SEED source: the planar Jupiter-Europa 3:4 EXTERIOR resonant orbit/torus class this object substitutes (their own abstract's 'exterior Jupiter-Europa' terminology -- never 'interior', correction). Their model is N=4 CCR4BP; no N=5/multi-perturber extension attempted (confirmed by the full-text read of their own 2023 Acta Astronautica follow-on paper, which is also entirely N=4).

Notes

First computed quasi-periodic invariant-torus substitute of a mean-motion-resonant periodic orbit in a Laplace-locked Jupiter-Io-Europa-Ganymede restricted five-body model: the planar Jupiter-Europa 3:4 resonant orbit of Kumar et al. 2021 (exterior to Europa, a ~= 1.211 Europa SMA), continued to the physical Io mass with Ganymede at its physical (non-rate-idealized) synodic rate and Io exactly Laplace-slaved (omega_Io = -2*omega_Gan), at the physical libration-center phase (Phi_L = 180 deg), via 2D pseudospectral Fourier collocation (n1=2, n2=20; on-grid residual RMS 1.23e-4, off-grid invariance ~2.1e-3). [Verbatim SS4 headline claim.] Mandatory qualifiers (verbatim SS4): - The MODEL class is Baresi, Owen & Scheeres's (AAS 23-201, 2023; ISSFD 2024) -- cite both; the Tri-Circular/Laplace-locked idea is theirs, and they computed the first N=5 tori (L1/L2 Lyapunov-family substitutes), Floquet stability, manifolds, and Europa<->Ganymede transfers in it. - Distinct from TCP on exactly TWO evidence-backed axes: (i) orbit family substituted (mean-motion-resonant, Kumar-class, vs L1/L2 Lyapunov planar); (ii) rate model (physical Ganymede synodic rate vs both rates idealized to exact rationals -- TCP's own periodicity construction requires the idealization). Method (pseudospectral PDE vs stroboscopic map+DFT) is a difference but NOT independently novelty-bearing. Phase is NOT a differentiator (TCP already used 180 deg). - Say "exterior Jupiter-Europa 3:4" or plain "Jupiter-Europa 3:4"; NEVER "interior" (the orbit lies BETWEEN Europa and Ganymede, 1.2114 Europa units = 0.759 Ganymede units -- the/the dispatch's own draft language used "interior" in error; corrected here). - No stability, manifold, or transfer computation exists for OUR object yet (TCP has all three for theirs) -- do not imply otherwise. shortlist item 3 (N=5 manifold/connection work) is gated and not dispatched. - Never "first N=5 CRNBP torus" or "first torus in the Laplace-locked model". - Novelty is conditional on the literature searched to date (the sweep + the full read + the family's first-documented member's own follow-on search + the full-text read of Kumar/Anderson/de la Llave 2023, confirmed entirely N=4). search/literature_check.py has NOT been run for this object -- not (whose note explicitly deferred that gate to writeback time) and not by this writeback task; note the module's own scoping caveat flags its cycler-vocabulary matcher as unsuited to a raw non-cycler dynamical object like a bare torus. The operative clearance is the manual literature sweeps above (the substance of the gate); a class-appropriate scripted re-check at any future re-verification would be prudent. Real-ephemeris standing: the idealized torus does NOT survive real SPICE ephemeris generically (headline collapse at torus point (0,0), naive 2030-01-01 epoch: 3.68e5 km / 8.19 km/s over one Ganymede-synodic forcing period, comparable to Ganymede's own orbital radius) -- but a narrow recurring near-miss window exists at 3 of 5 tested torus points: (0,0) and (pi,pi) both 10/10 narrow (refined per-epoch minima 502.9-1950.4 km and 790.2-1719.3 km respectively), (pi/2,pi/2) also 10/10 narrow (2409.9-4042.4 km); (pi,0) and (0,pi) GENUINELY collapse 10/10 (2.55e4-1.31e6 km and 3.32e4-4.00e4 km respectively). The narrow/collapse dichotomy is torus-point-dependent but PERFECTLY epoch-stable across all 10 tested anchors spanning 2000-2083 -- the family's first-documented member's own strongest evidence that this is real dynamical structure, not noise. This differs in KIND from the Umbriel-Titania row's own evidence: there is no departure/target manifold pair here, no connection has been computed or attempted, and the gap measured is a model-shadowing mismatch (idealized CRNBP forward flow of a torus point vs real-SPICE propagation of the same departure state), not a connection-quality metric. validation_level=V1 (2026-07-28): the Sec 8 gap closed -- an independent Radau-vs-DOP853 integrator cross-check of the torus's own short-time flow-consistency claim, at the identical sample anchors the corrector's own closure_residual was computed from, agrees to integrator_delta_max_km=7.11e-8 km (crnbp_provenance.torus. radau_cross_check; seven orders of magnitude below the Umbriel-Titania row's own 1.0 km ghost_guard V1 gate). our_status left absent, matching the rows' own precedent, since no independent novelty-verification gauntlet has been run for this object class (orthogonal to validation_level, which gates mechanical correctness not novelty). Schema: admitted under schema v5.4, which added orbit_class= quasi_periodic_torus, model_assumption=crnbp, and the additive crnbp_provenance block (a NEW block, not an extension of ccr4bp_provenance, since it needs an N-body perturbers[] LIST) -- see data/catalogue.schema.json's own v5.4 changelog entry and docs/notes/2026-07-27-735-n5-crnbp-torus-catalogue-schema-design.md for the full design reasoning (approved by the user as proposed). Discovery + verification chain: (shortlist/scoping) -> (N=4 seed) -> (mu_Io continuation to the physical torus) -> (novelty sweep) -> (refined verdict, corrected a citation error) -> (physical-phase correction) -> (independent re-confirmation, corrected "interior"->"exterior", precise claim language) -> (real-ephemeris consistency check, first-pass generic collapse) -> (Kumar/Anderson/de la Llave 2023 cross-check, novelty unaffected) -> (epoch(+ torus-point) robustness scan, found the recurring narrow window) -> (catalogue schema design proposal, user-approved) -> (writeback: schema implementation + row, validation_level=V0) -> (Radau independent-integrator cross-check, validation_level V0 -> V1).

Source quotes (per-field provenance)

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

crnbp_provenance.torus.residual_rms

data/found/729_crnbp_epoch_torus_robustness_scan/result.json:torus_residual_rms = 0.00012343143649488024; independently re-reproduced this session (scripts/verify_724_rerun_continuation.py, extended) to 1.2343143649480972e-04, matching /the family's first-documented member's own quoted 1.2343143649e-04 to 4e-11 relative.

crnbp_provenance.real_ephemeris_evidence.generic_collapse_reference.pos_gap_km

data/OUTSTANDING.md entry: 'Headline result: a real, GENERIC COLLAPSE (torus point theta1=theta2=0, epoch 2030-01-01, one Ganymede-synodic period = 12.478 TU/7.05 days): pos_gap=3.68e5 km, vel_gap=8.19 km/s -- comparable to Ganymede's own orbital radius (1.07e6 km).'

crnbp_provenance.real_ephemeris_evidence.torus_points[0].n_epochs_narrow

data/found/729_crnbp_epoch_torus_robustness_scan/result.json:summary.n_primary_epochs_narrow = 10 (of 10 tested); fraction_primary_epochs_narrow = 1.0.

orbit_elements.cr3bp.mass_ratio

core.crnbp.jupiter_europa_io_ganymede_default.mu, live-printed this session (PYTHONPATH=src python3 -c "from cyclerfinder.core.crnbp import jupiter_europa_io_ganymede_default as f; print(f.mu)") = 2.528017724591319e-05.

crnbp_provenance.torus.radau_cross_check.integrator_delta_max_km

data/found/738_crnbp_torus_radau_ghost_guard/result.json:check.integrator_delta_max_km = 7.112659620276295e-08 -- the independent Radau-vs-DOP853 cross-check this row's V1 validation_level rests on.