Liang et al. CGE triple cycler — Member B (1-1-0, high perijove, idealized)

liang-2024-cgcec-110-highperijove · source: literature · validation: V1

Signature

Bodies: Callisto-Ganymede-Europa
Primary: Jupiter
Sequence (canonical): Callisto-Ganymede-Callisto-Europa-Callisto
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 ( × Callisto-Europa synodic)
Triple-cycler repeat ~100 d (switched-double-cycler). >= 1000 d / 10 cycles demonstrated, not indefinite (paper caveat). Same perijove as Member A; diverges from A at the Europa branch (1-1-0 structure, only Europa's flag/phase differs). years: null (Jovian moon tour).
Priority date: 2024-01-01

V∞ at encounters

Callisto (encounter 1): 5.67 km/s
Liang et al. 2024 Table 5 (p. 17), flyby 0. First two flybys (Callisto, Ganymede) identical to Member A — trajectories diverge at the Europa branch.
Ganymede (encounter 2): 6.99 km/s
Liang et al. 2024 Table 5 (p. 17), flyby 1.
Europa (encounter 3): 4.49 km/s
Liang et al. 2024 Table 5 (p. 17), flyby 3.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 31.8973 d, 18.1697 d, 30.285 d, 19.6834 d

Same perijove as Member A (r_Europa - 10000 km ~ 660,988 km). Initial moon phases (Table 4, p. 15): Europa -0.48843 rad, Ganymede 0.70579 rad, Callisto 1.3550 rad (only Europa's flag/phase differs from A). Over 10 cycles perijove drops, eccentricity grows, apse line rotates clockwise (eases the Europa encounter, p. 17).

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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.

orbit_elements.cr3bp.mass_ratio [not-applicable]
Idealized circular-coplanar patched-conic two-body model, not CR3BP. (mu_Jupiter also unprinted — tolerance caveat in notes.)

source: Liang et al. 2024 JGCD doi 10.2514/1.G008387

Primary citation

Liang, G. et al. (2024). Callisto-Ganymede-Europa Triple Cyclers. Journal of Guidance, Control, and Dynamics (Engineering Note).

DOI: 10.2514/1.G008387

URL: https://arc.aiaa.org/doi/10.2514/1.G008387

See Member A row for IAC-23 presentation provenance + page-draft note.

Notes

Member B: idealized circular-coplanar CGCEC triple cycler, 1-1-0 flyby structure (Fig. 6), high perijove. Same first two flybys as Member A; the trajectories diverge at the Europa branch (only Europa's 0/1 flag and phase differ). Ballistic (residual < 1e-8 m/s). TOLERANCE CAVEAT: mu_Jupiter unprinted; validate ToF ~0.01 d, V_inf ~1e-3 km/s. FLYBY-ALTITUDE FICTION: Table 5 "Altitude" column NOT ingested as physical periapses (paper p. 16). Topology/leg class outside our swept genome (mining note §6). REPRODUCED 2026-06-13: same-model reconstruction (cge_scaffold.py) matches Table 5 per-flyby V_inf on both flyby sides to worst 1.38e-2 km/s and V_inf continuity to 7.8e-3 km/s, inside the Table 1 print-quantization tolerance (0.017-0.14 km/s per flyby); all 4 legs 1-rev multi-rev Lambert as published; golden tests tests/search/test_liang_cge_reproduction.py.

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: Liang et al. 2024 Table 5 (p. 17): first-cycle flyby V_inf — Callisto 5.6730, Ganymede 6.9919, Callisto 5.6698, Europa 4.4853, Callisto 5.7914 km/s.
invariants.transit_times_days: Liang et al. 2024 Table 5 (p. 17): first-cycle per-leg ToF (days) — C->G 31.8973, G->C 18.1697, C->E 30.2850, E->C 19.6834 (flyby 0 at t=0).
notes: Liang et al. 2024 p. 16 "Flyby Altitude" Delta-v-fiction caveat; p. 17 apse-line rotation observation; ~100 d repeat, 10-cycle/~1000 d demonstrated (not indefinite).