Russell-Ocampo cycler 3.64gGg3 (low-energy three-synodic ballistic, bolded promising)

russell-ch4-3.64gGg3 · source: literature · validation: V1

Signature

Bodies: E-M
Primary: Sun (default — heliocentric)
Sequence (canonical): E-E-E-M-M
Sense: outbound
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: 6.410 yr (3 × E-M synodic)
3-synodic E-M cycler = 3 * 2.135 yr = 6.41 yr.
Maintenance ΔV: 0 km/s — strict ballistic
Priority date: 2003-02-09

V∞ at encounters

E (encounter 1): 3.64 km/s
Russell 2004 Table 4.10 row 'low-energy bold cluster' (~line 5321): v_inf E = 3.64.
M (encounter 2): 4.59 km/s
Russell 2004 Table 4.10: v_inf M = 4.59.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): 1.62
Transit times (days): 175 d, 175 d

Russell 2004 Table 4.10: aphel = 1.62 AU. Three generic legs gGg, the second G is designated.

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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

Not-published gaps (never interpolated):

E → M — segment elements (a, e) not published; no curve drawn.
M → E — segment elements (a, e) not published; no curve drawn.
E → E — segment elements (a, e) not published; no curve drawn.
E → E — segment elements (a, e) not published; no curve drawn.

Real DE440 encounter dates (5)

2029-01-08 V∞ 4.29 / 6.13 km/s
2031-02-27 V∞ 4.19 / 4.68 km/s
2033-03-28 V∞ 2.96 / 4.51 km/s
2033-05-07 V∞ 3.80 / 3.47 km/s
2035-05-27 V∞ 3.94 / 3.85 km/s

Real, verifiable JPL DE440 geometric-match dates (see Launch windows). Positions on the map are idealized; these are the true dates.

Legs (trajectory segments)

E → M: 175 d, 0 revs
Russell 2004 Table 4.10: t_out = 175 days.
M → E: 175 d, 0 revs
Russell 2004 Table 4.10: t_in = 175 days (symmetric).
E → E: (TOF not published)
Intermediate Earth-Earth loop 1 of 2 for this 3-synodic cycler (sequence E-E-E-M-M); fills part of the 6.41-yr period between Mars encounters. Multi-rev arc — tof_days / n_revs / branch / (a,e) to be set by the multi-rev Lambert solver.
E → E: (TOF not published)
Intermediate Earth-Earth loop 2 of 2 for this 3-synodic cycler (sequence E-E-E-M-M); fills part of the 6.41-yr period between Mars encounters. Multi-rev arc — tof_days / n_revs / branch / (a,e) to be set by the multi-rev Lambert solver.

Free-return arcs (Russell decomposition)

Russell's Earth-to-Earth free-return arcs (spec §16.7.7) — a decomposition distinct from the encounter legs above. A single arc spans what the catalogue models as two or more encounter segments.

Arc type	Resonance	TOF (yr)	Raw descriptor
generic	—	2.4845	g(2.4845,894.42,Ll)
generic	—	2.9217	G(2.9217,691.79,U)
full-rev	1:1	—	f(1:1,82.995,-180.000)

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: Russell 3-synodic Earth-Mars ballistic · Russell-Ocampo cycler code

Known-unknowns (3)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

trajectory.segments[loop-ee-*] [derive]
The 2 intermediate Earth-Earth loop arc(s) tof_days / n_revs / branch / (a,e) are computable once the multi-rev Lambert solver closes the arc(s) to the published 3.64/4.59 km/s V-infinity; not yet derived. Russell 2004 tabulates only t_out/t_in + the aggregate aphelion, not the loop arc(s).

source: multi-rev Lambert solver; Russell 2004 Table 4.x leg descriptors
trajectory.segments[out-em].a_au [unknown]
Per-segment (a,e) of the outbound generic-return arc not tabulated by Russell 2004 (orbit_elements.a_au/e are null for the same reason — each generic-return arc has its own (a,e); only the aggregate aphelion is well-defined).

source: Russell 2004 dissertation Table 4.x leg descriptors g(...)/G(...)
trajectory.segments[ret-me].a_au [unknown]
Per-segment (a,e) of the return generic-return arc not tabulated by Russell 2004; same source gap as out-em.

source: Russell 2004 dissertation Table 4.x leg descriptors g(...)/G(...)

Primary citation

Russell, R. P. & Ocampo, C. A. (2003). Global Search and Optimization for Free-Return Earth-Mars Cyclers. AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 03-145.

orbit source Russell 2004, Tables 4.9 / 4.13 orbit fidelity circular-coplanar V∞ source Russell 2004, Tables 4.9 / 4.13 V∞ fidelity circular-coplanar

Corroborating sources

Russell, R. P. (2004). Global Search and Optimization for Free-Return Earth-Mars Cyclers. PhD dissertation, UT Austin. · link
Russell 2004 dissertation §4.8 line 5512: 'Cyclers 3.64gGg, 3.77Gh, and 3.78Gg, in particular, have favorable turning angle characteristics.' Table 4.10 with TR = 1.62 (high).

Notes

One of the few three-synodic ballistic cyclers Russell singles out as "the first six bold cyclers from Table 4.10 [that] have remarkable low values of v∞ at both Earth and Mars" (dissertation line 5510). Specifically called out at line 5512 for "favorable turning angle characteristics" (TR = 1.62). Leg descriptor: g(2.4845,894.42,Ll) G(2.9217,691.79,U) f(1:1,82.995,-180.000) — extracted from Table 4.10 line 5321.

Source quotes (per-field provenance)

Every numerical value in this entry traces to a verbatim or paraphrased quote from a cited source.

delta_v_kms: Derived from Russell 2004's tabulated AR / TR via the M2 powered-flyby surrogate (src/cyclerfinder/core/flyby.py): ΔV ≈ (V∞_E + V∞_M) × max(0, 1 − TR) + (1 − AR) × (V∞_E + V∞_M) × 0.025 [AR-correction term active only when AR < 1]. Upper bound; biases near-ballistic entries toward 'requires nudge'. Strict-ballistic rows (AR ≥ 1 AND TR ≥ 1) give ΔV = 0 exactly. AR/TR primary values: Russell 2004 Table 4.10 (low-energy bold cluster row 3.64): aphel=1.62 AU, TR=1.62, v∞E=3.64, v∞M=4.59.
vinf_kms_at_encounters[0].vinf_kms: Russell 2004 Table 4.10 row 'low-energy bold cluster': v_inf E = 3.64.
vinf_kms_at_encounters[1].vinf_kms: Russell 2004 Table 4.10: v_inf M = 4.59.
legs[0].tof_days: Russell 2004 Table 4.10: t_out = 175.
legs[1].tof_days: Russell 2004 Table 4.10: t_in = 175.
orbit_elements.aphelion_au: Russell 2004 Table 4.10: aphel = 1.62 AU.
name: Russell 2004 dissertation line 5512: "Cyclers 3.64gGg, 3.77Gh, and 3.78Gg, in particular, have favorable turning angle characteristics." Bolded in Russell Table 4.10.