Russell-Ocampo cycler 8.049gGf2 (high-energy two-synodic ballistic)

russell-ch4-8.049gGf2 · source: literature · validation: V3

Signature

Bodies: E-M
Primary: Sun (default — heliocentric)
Sequence (canonical): 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: 4.270 yr (2 × E-M synodic)
2-synodic E-M cycler per Russell 2004 Table 4.9 row 2.
Maintenance ΔV: 0 km/s — strict ballistic
Priority date: 2003-02-09

V∞ at encounters

E (encounter 1): 8.05 km/s
Russell 2004 Table 4.9 row 2, column v_inf E = 8.05 km/s. Cycler code 8.049gGf2 — first number = max v_inf E in simple model.
M (encounter 2): 10.02 km/s
Russell 2004 Table 4.9 row 2, column v_inf M = 10.02 km/s. The high V_inf at Mars reflects the cycler's short 93-day transfer.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): 1.45
Transit times (days): 93 d, 93 d

Russell 2004 Table 4.9 row 2: aphel = 2.19 AU. Three legs (gGf) so the orbit alternates between three different Keplerian arcs.

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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

Real DE440 encounter dates (2)

2031-03-29 V∞ 8.88 / 10.35 km/s
2035-06-16 V∞ 6.91 / 10.89 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: 93 d, 0 revs
Russell 2004 Table 4.9 row 2: t_out = 93 days. The designated leg G(1.7757,279.24,U) is the second descriptor — uppercase G marks the designated Earth-Mars leg.
M → E: 93 d, 0 revs
Russell 2004 Table 4.9 row 2: t_in = 93 days (symmetric generic returns).
E → E: (TOF not published)
Intermediate Earth-Earth loop 1 of 1 for this 2-synodic cycler (sequence E-E-M-M); fills part of the 4.27-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	—	1.4951	g(1.4951,538.24,Ll)
generic	—	1.7757	G(1.7757,279.24,U)
full-rev	1:1	—	f(1:1,74.468,-180.000)

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: Russell 2-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 1 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 8.05/10.02 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.

Russell+Ocampo conference precursor to the 2004 dissertation. 8.049gGf2 is a NEW cycler in Russell 2004; not previously documented in Russell's Chapter 3 or in McConaghy 2002 (per Table 4.9 footnote — only rows 1 and 4 carry the 'a' = Ref. 15 footnote, only row 3 carries 'b' = Chapter 3).

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
Table 4.9 row 2; parent cycler 8.049gGf2 (no. 188). Featured in dissertation Figure 5.9 as a representative high-energy cycler.

Notes

Russell dissertation line 5470-5478 explicitly: "The new cycler, 8.05gGf, is composed of two generic returns and one full-rev return. The relatively high v∞ at Earth and Mars is compensated by the quick transfer time of 93 days." This is one of three cyclers Russell singles out as "debatably ha[ving] the most promising characteristics" alongside 4.991gG2 (S1L1) and 6.399G1 (Aldrin) — line 8008-8010. The leg descriptor "g(1.4951,538.24,Ll) G(1.7757,279.24,U) f(1:1,74.468,-180.000)" has a 1:1 resonant full-rev return as the third leg. Russell's Chapter 5 parent-cycler list (Table 5.5 line 7513) shows a 7-cycle ephemeris launch in Jul-42 with total delta-V = 420 m/s (so not fully ballistic in realistic ephemeris, but the simple-model parent is ballistic).

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 4.9 row 2 (8.049gGf2): aphel=2.19 AU, TR=1.45, v∞E=8.05, v∞M=10.02.
vinf_kms_at_encounters[0].vinf_kms: Russell 2004 Table 4.9 row 2: v_inf E = 8.05.
vinf_kms_at_encounters[1].vinf_kms: Russell 2004 Table 4.9 row 2: v_inf M = 10.02.
legs[0].tof_days: Russell 2004 Table 4.9 row 2: t_out = 93.
legs[1].tof_days: Russell 2004 Table 4.9 row 2: t_in = 93.
orbit_elements.aphelion_au: Russell 2004 Table 4.9 row 2: aphel = 2.19 AU.
name: Russell 2004 dissertation line 7416 lists 8.049gGf2 among the most promising cyclers; line 5470: "The new cycler, 8.05gGf, is composed of two generic returns and one full-rev return."