Computed Ganymede-Callisto two-working-body ballistic cycler gc-2 (k = 3; a GanCal-family relative of Russell & Strange GanCal#5)

ganymede-callisto-two-working-body-cycler-gc2-2026 · source: this-project · validation: V2 · known-class

Signature

Bodies: Ganymede-Callisto
Primary: Jupiter
Sequence (canonical): Ganymede-Callisto-Callisto-Ganymede
Sense: n/a
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: multi-arc
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: circular-coplanar
Idealised: planets on circles, coplanar ecliptic.
Period: — yr (3 × Ganymede-Callisto synodic)
DERIVED (this project): 3 Ganymede-Callisto synodic periods = 37.570 d (R-S 2009 Table 2 ideal model). Encounters per period: Ganymede 2, Callisto 2.
Source ephemeris: ideal circular-coplanar Galilean model (Russell & Strange 2009 Table 2 constants); real-ephemeris patched-conic rung on NAIF jup365; continuous-gravity ideal-model continuation
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-10-06

V∞ at encounters

Ganymede (encounter 1): 3.62 km/s
DERIVED (this project, ideal-model patched-conic zero; data/943_cell_gc_gauntlet.json). Ganymede turn 2 x 19.72 deg, ratio 0.788, required altitude 1,024 km.
Callisto (encounter 2): 3.04 km/s
DERIVED (this project). Callisto turn 2 x 6.87 deg, ratio 0.259, required altitude 9,800 km; needs at least 0.214 of Callisto's GM (results note 6.21).

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 10.846 d, 2.605 d, 21.514 d, 2.605 d

Multi-arc. Distance from Jupiter 791,455-2,337,392 km (Lambert-only cycle).

Orbit view 2.5D ecliptic projection

spacecraft: idealized coplanar ellipse planets: J2000 osculating ellipse (Standish & Williams Table 1) orientation: coplanar-idealized (no Ω/ω published — in-plane ellipse)

3D view not available for multi-arc trajectories yet. The 3D system can now render a numerically-sampled polyline (n-body or multi-arc), but no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them). The button will appear here once a sampled path is exported for this trajectory; we never interpolate one from the catalogue's per-leg (a, e).

— — planet orbit (true J2000 ellipse)

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.

vinf_kms_at_encounters [uncertain]
No full-mass counterpart on gc-2's own branch in continuous gravity: the branch FOLDS at sigma = 0.164 of the real moon masses. An isola or another seed is untested.

source: docs/notes/2026-10-07-1004-gc2-gancal5-callisto-gm-continuation.md sec. 9; data/1004_gc2/

Primary citation

No primary citation recorded; see the provenance tags below.

orbit fidelity circular-coplanar V∞ fidelity circular-coplanar

Corroborating sources

Russell, R. P. & Strange, N. J. (2009). Cycler Trajectories in Planetary Moon Systems. Journal of Guidance, Control, and Dynamics 32(1):143-157. DOI: 10.2514/1.36610
CLASS source (owner ruling 2026-10-07): gc-2 keeps GanCalthe skeleton (the shared G-G 1-rev low return and the 37.6-d period). GanCalthe 24.25-d G->C leg is replaced by a G->C leg plus a Callisto 1-rev return. That inserts one Callisto encounter, which has no counterpart on GanCalthe leg (results note 6.20-6.21).
Hollister, W. M. & Menning, M. D. (1970). Periodic Swing-By Orbits between Earth and Venus. Journal of Spacecraft and Rockets 7(10):1193-1199. DOI: 10.2514/3.30134
METHOD source: the two-working-body date-residual corrector.

Notes

Two-working-body Ganymede-Callisto cycler, k = 3 (37.570 d). Legs: a Ganymede 1-rev low return, G->C and C->G of 2.605 d each, and a Callisto 1-rev high return. Ideal-model state: Lambert-leg starts 0.838679, 11.684556, 14.289304, 35.803635 d. Owner ruling (2026-10-07): a GanCal-family relative of R-S GanCal#5, recorded as known-class-member, NOT candidate-novel. - The ruling departs from the spec §16.4 letter ("same architecture"). gc-2's Callisto bends 6.87 deg and needs at least 0.214 of its GM. The owner ruling is the basis. - It is not a literal GanCal member. In the patched conic no Callisto-mass path joins them, and the inserted Callisto encounter has no counterpart on GanCalthe leg (4.5 SOI away). Results note 6.11, 6.14, 6.20-6.21. Real-ephemeris standing (patched conic, NAIF jup365, 10 cycles): - Ballistic and gate-passing at 5/5 epochs 2030-2056 (worst 0.813-0.823). - DOP853 re-fly <= 2.4e-5 km. The Lambert-only path is validated by VenMar#45 and GanEur#316. - screen (data/973_screen_943_gc.json): passes. Continuous gravity (docs/notes/2026-10-07-1004-gc2-gancal5-callisto-gm-continuation.md sec. 9; ideal R-S model with point-mass moons): gc-2's branch FOLDS at sigma = 0.164 of the real moon masses (fold bracket 0.16393/0.16395). - There is no full-mass gc-2 on that branch. Checks: two distinct solutions at fixed sigma, the fold bracket, an IAS15 re-fly, and a direct Newton at sigma = 1 that stalls at 0.4 km/s. - So the patched-conic real-ephemeris PASS above does not imply existence in continuous gravity. - Limits: absence on one branch is not absence; an isola or another seed is untested. - The owner's relative ruling is refined, not reopened: in continuous gravity the patched-conic relation has no full-mass counterpart on gc-2's own branch. - Real-ephemeris continuous-gravity standing untested. covered gc-1 and the GanCal#1 control; the open-chain n-body formulation does not converge across a full-revolution return, so neither has a verdict. The real-ephemeris pass above is the patched-conic chain tool (rung (d)). V2-ballistic (spec §14 owner amendment 2026-10-08, same-phase drift wording of 2026-10-11; docs/notes/2026-10-08-1007-v2-ballistic-chain-campaign.md secs. 8.4b, 8.11-8.12): PASS at 5 of 5 jup365 epochs, 10 continuous cycles each (L = 4; first and last cycle excluded). - Junction continuity 9.2e-8 km/s; re-fly <= 2.4e-5 km. - Same-phase drift: dates 0.012-0.057 d against a 0.13-d band; |V_inf| 0.005-0.006 km/s against 0.30. - Slope diagnostics (handed to V3): dates -0.0005 to +0.0006 d per cycle; |V_inf| -0.0011 to +0.0008 km/s per cycle. - Systematic real-versus-ideal |V_inf| offset (recorded, not banded): 0.16-0.36 km/s. Under the sec. 2 pre-registered rules it was 2/5 (the 10 % band on that offset). Note: in continuous gravity gc-2's branch folds; V2 here is the patched-conic chain only. Literature: - Scripted gate (literature_check v2,; data/942_943_litcheck_scope.json): INCONCLUSIVE. Named anchor: "Russell-Strange 2009 Ganymede-Callisto ideal-model moon cycler" (one working body; rule F7). - Resolving notes: docs/notes/2026-10-06-943-gc-prior-art-search.md; results note 6.20-6.21. - Owner decision 2026-10-08: the gate's inconclusive is decided by the 2026-10-07 ruling (GanCal-family relative, known-class-member). - Further prior art (corpus review, docs/notes/2026-10-07-971-fable-corpus-review-2.md lines 54-76): - Minovitch 1972 (p.755, periodic GT trajectories, none computed). - Grushevskii, Golubev et al. ISSFD 2017 (p.3, a closed G-C Tisserand loop inside a one-way descent). - Boutonnet et al. 2024 (JUICE C-G-C round trip, pp.33-34, 38, 40). - Takubo et al. 2026 (AIAA 2026-1262 p.4). - The Callisto 1-rev leg has flown-design precedent: Europa-bracketed Callisto 1:1 returns at V_inf 2.81-3.08 km/s (Buffington 2014 Table 3; Lam et al. 2018 Table 3; values per the review, from the PDFs) and 3.53-3.59 km/s (Cangahuala et al. 2025 Table 2, p.13). None has a Ganymede element.