Computed Ganymede-Callisto two-working-body ballistic cycler gc4-28 (k = 4, both moons bend)

ganymede-callisto-two-working-body-cycler-gc4-28-2026 · source: this-project · validation: V1 · candidate

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 (4 × Ganymede-Callisto synodic)
DERIVED (this project): 4 Ganymede-Callisto synodic periods = 50.093 d in the Russell & Strange 2009 Table 2 ideal model.
Source ephemeris: ideal circular-coplanar Galilean model (Russell & Strange 2009 Table 2 constants); continuous-gravity ideal-model rung
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-10-07

V∞ at encounters

Ganymede (encounter 1): 8.86 km/s
DERIVED (this project, ideal-model patched-conic zero; data/973_gc/k4_gauntlet.json). Largest demanded/available turn ratio 0.880 at the 100-km floor.
Callisto (encounter 2): 5.55 km/s
DERIVED (this project). Largest demanded/available turn ratio 0.797 at the 200-km floor.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 23.407 d, 3.392 d, 19.903 d, 3.392 d

Multi-arc (no single ellipse). Distance from Jupiter 320,944-2,601,280 km (extents, all legs).

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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 [unknown]
Real-ephemeris standing untested. The patched-conic real-ephemeris chain (rung (d)) was not run for this member (note), and real-ephemeris continuous gravity is untested (lane limit: the open-chain n-body formulation does not converge across a full-revolution return).

source: docs/notes/2026-10-07-973-two-working-body-k-extension.md; docs/notes/2026-10-08-1025-sigma-batch.md sec. 10

Primary citation

No primary citation recorded; see the provenance tags below.

orbit fidelity circular-coplanar V∞ fidelity circular-coplanar

Corroborating sources

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, generalised here to the Jovian moons (as for gc-1).
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
MODEL source: the ideal circular-coplanar Galilean model; their cyclers have one working body and a massless target (AAS 07-118 p.2), and AAS 07-118 p.18 names removing that assumption as future work.
Campagnola, S. et al. (2019). Tour Design Techniques for the Europa Clipper Mission. Journal of Guidance, Control, and Dynamics 42(12):2615-2626. DOI: 10.2514/1.G004309
PRIOR ART: the one published two-working-body Ganymede-Callisto cycler (GCGC, a single trajectory, not a searched class); as for gc-1.

Notes

Member gc4-28 of the two-working-body Ganymede-Callisto class of gc-1 (ganymede-callisto-two-working-body-cycler-gc1-2026): both moons bend; k = 4 (50.093 d); structure k4|LGanymede>Ganymede/2h|LGanymede>Callisto/0s|LCallisto>Callisto/1h|LCallisto>Ganymede/0s. Ideal-model Lambert-leg starts 7.081532, 30.488173, 33.880028, 53.782616 d (model epoch: all bodies at angle 0 at t = 0). Worst demanded/available turn ratio 0.880. V1 evidence (data/1025_writeback_v1.json): lamberthub <= 8.0e-10 m/s on every Lambert leg; DOP853 re-fly 2.2e-05 km, gate passes on the integrated vectors. Continuous gravity (docs/notes/2026-10-08-1025-sigma-batch.md sec. 10; ideal model with point-mass moons at real GMs, not the ephemeris): EXISTS. The joint-mass branch reaches the full masses (identity by the limit, IAS15 re-fly 5.4e-06 km, no unscheduled minimum inside 3 Hill radii). Full-mass nodes: G 8.810 km/s, altitude 510 km, turn 4.5 deg; C 5.551 km/s, altitude 926 km, turn 7.5 deg; C 5.551 km/s, altitude 926 km, turn 7.5 deg; G 8.810 km/s, altitude 510 km, turn 4.5 deg. Patched-conic values above. Real ephemeris: untested. Rung (d) (the patched-conic chain tool) was not run for this member, and real-ephemeris continuous gravity is untested (lane limit). Literature: literature_check v3-A1: "inconclusive", naming the Russell-Strange 2009 Ganymede-Callisto ideal-model moon cycler (one working body; rule F7). Resolving notes: as for gc-1 (docs/notes/2026-10-06-943-gc-prior-art-search.md) and docs/notes/2026-10-08-1025-literature-step.md. OWNER DECISION 2026-10-08: written candidate-novel as a member of gc-1's class, with gc-1's attribution (Hollister & Menning 1970 method; Russell & Strange 2007/2009 model; Campagnola et al. 2019 nearest prior art). Wording: "first computed", never "new class".