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

liang-2024-cgcec-111-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 period ~100 d (two ~50 d double-cycler cycle periods; switched-double-cycler construction, Sec. III.B). NOT indefinite: the paper demonstrates >= 1000 d / 10 cycles (near-resonance + chained local optimization; paper's own caveat, Conclusion pp. 19-20). Per-cycle ToF over 10 cycles 99.86-100.14 d (Fig. 5d). The heliocentric-synodic `years` convention does not apply to a Jovian moon-tour cycler -> null.
Priority date: 2024-01-01

V∞ at encounters

Callisto (encounter 1): 5.67 km/s
Liang et al. 2024 Table 3 (p. 15), first-cycle flyby 0 (initial conic-guess Callisto encounter). The 5 per-cycle V_inf are in invariants.transit_times_days companion + source_quotes.
Ganymede (encounter 2): 6.99 km/s
Liang et al. 2024 Table 3 (p. 15), flyby 1.
Europa (encounter 3): 4.67 km/s
Liang et al. 2024 Table 3 (p. 15), flyby 3.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 31.8973 d, 18.1697 d, 29.9343 d, 19.9747 d

Jovicentric (not heliocentric) patched-conic multi-rev arcs; no single (a, e) characterises the CGCEC cycle. Spacecraft period = Callisto's period (T_C ~ 16.69 d; 3T_C ~ T_S ~ 50 d, Sec. III.A); perijove r_p = r_Europa - 10000 km ~ 660,988 km (p. 14). Initial moon phases (Table 2, p. 14): Europa 0.063748 rad, Ganymede 0.70579 rad, Callisto 1.3550 rad.

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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 about Jupiter, not CR3BP; no single mass ratio governs. (Separately, mu_Jupiter itself is never printed in the paper — see the 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

Authors at NUAA (Liang, Yang, Li, Qin) and Rutgers (Bai). A portion was presented as paper IAC-23,C1,9,9,x76777 at the 74th IAC, Baku, 2-6 October 2023. Page numbers cited from the 22-page author draft.

Notes

Member A: idealized circular-coplanar CGCEC triple cycler, 1-1-1 flyby structure (Fig. 2, p. 8), high perijove (the low-energy family). Ballistic (residual Delta-v below the 1e-8 m/s threshold, p. 13). First publication of Callisto-bearing triple cyclers: Callisto is NOT in the 1:2:4 Laplace resonance, so the Laplace-resonant machinery (Lynam/Longuski, Hernandez) is unavailable; Liang et al. instead exploit a 7:4 NEAR-resonance of the (C-G, G-E) synodic periods (~50 d quasi-repeat) absorbed by a switched-double-cycler + multi-rev legs (Sec. II.A, III.B). TOLERANCE CAVEAT: mu_Jupiter is never printed; idealized-model reproductions should treat trailing digits as constant-dependent (validate ToF at ~0.01 d, V_inf at ~1e-3 km/s; mining note §5). FLYBY-ALTITUDE FICTION: the paper's Table 3 "Flyby Altitude" column (1,900,851 / 978,172 / 33,839 / 6,241 / 19,765 km) is computed from the required defect Delta-v on the moon-centered hyperbola ignoring Jupiter's gravity — a reflection of how little turning is needed, NOT physical periapses (1.9e6 km vastly exceeds Callisto's SOI). NOT ingested as altitudes (paper's own caveat, p. 16; mining note §9). Capability: this member's topology (repeated-moon CGCEC, Callisto 3x per cycle) and leg class (multi-rev Lambert legs used as phase-reshaping reservoirs) lie OUTSIDE our Phase-6 swept genome (single-ellipse zero-rev free-return loops); it does not contradict the Jovian EMPTY-region registry verdicts, which remain valid as conditioned (mining note §6). REPRODUCED 2026-06-13: same-model reconstruction (cge_scaffold.py) matches Table 3 per-flyby V_inf on both flyby sides to worst 1.52e-2 km/s and V_inf continuity to 8.1e-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 3 (p. 15): first-cycle flyby V_inf — Callisto 5.6730, Ganymede 6.9919, Callisto 5.6698, Europa 4.6685, Callisto 5.8721 km/s.
invariants.transit_times_days: Liang et al. 2024 Table 3 (p. 15): first-cycle per-leg ToF (days) — C->G 31.8973, G->C 18.1697, C->E 29.9343, E->C 19.9747 (flyby 0 at t=0).
notes: Liang et al. 2024 p. 16 caveat: the Table 3/5/7 "Flyby Altitude" values are computed from the required defect Delta-v ignoring Jupiter's gravity and are not physical periapses. Per-cycle repeat ~100 d; demonstrated 10 cycles / ~1000 d, not indefinite (Conclusion pp. 19-20).