Liang et al. CGE triple cycler — Member C (1-1-1, low perijove, idealized)

liang-2024-cgcec-111-lowperijove · 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; 10-cycle/~1000 d demonstrated, not indefinite. Low-perijove (high-energy) contrast member: r_p = (r_Europa - 10000 km)/2 ~ 330,494 km, roughly doubling the V_inf vs the high-perijove A/B family. years: null (Jovian moon tour).
Priority date: 2024-01-01

V∞ at encounters

Callisto (encounter 1): 7.64 km/s
Liang et al. 2024 Table 7 (p. 18), flyby 0. Lower perijove ~ doubled V_inf vs Members A/B — confirms high-perijove is the low-energy family.
Ganymede (encounter 2): 10.49 km/s
Liang et al. 2024 Table 7 (p. 18), flyby 1.
Europa (encounter 3): 12.02 km/s
Liang et al. 2024 Table 7 (p. 18), flyby 3.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 32.2542 d, 17.8127 d, 31.1267 d, 18.9362 d

Low perijove r_p = (r_Europa - 10000 km)/2 ~ 330,494 km. Initial moon phases (Table 6, p. 18): Europa 0.94281 rad, Ganymede 1.3883 rad, Callisto 1.7936 rad. Across all three idealized members ToF(G->C)+ToF(C->G) ~ 50 d and likewise for the C/E pair; cycle-ToF spread <= 0.35 d; all cycle ToFs ~100 d (p. 18).

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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 C: idealized circular-coplanar CGCEC triple cycler, 1-1-1 flyby structure (Fig. 7), LOW perijove — the high-V_inf contrast member (lower perijove ~ doubled V_inf, confirming the high-perijove A/B family is the low-energy one). 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 7 "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 7 per-flyby V_inf on both flyby sides to worst 4.82e-2 km/s and V_inf continuity to 9.0e-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 7 (p. 18): first-cycle flyby V_inf — Callisto 7.6433, Ganymede 10.4922, Callisto 7.6409, Europa 12.0213, Callisto 7.7838 km/s.
invariants.transit_times_days: Liang et al. 2024 Table 7 (p. 18): first-cycle per-leg ToF (days) — C->G 32.2542, G->C 17.8127, C->E 31.1267, E->C 18.9362 (flyby 0 at t=0).
notes: Liang et al. 2024 p. 16 "Flyby Altitude" Delta-v-fiction caveat; p. 18 across-member ToF regularities; ~100 d repeat, 10-cycle/~1000 d demonstrated (not indefinite).