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Russell 2004 dissertation Chapter 4 ballistic and near-ballistic Earth-Mars cycler tables (broad-class family)

russell-2004-ch4-broadclass-family · source: literature · validation: V0

Signature

Bodies
E-M
Primary
Sun (default — heliocentric)
Sequence (canonical)
Sense
Orbit class
Cycler
strict cycler (infinite returns)
Cycler class
single-ellipse
Trajectory regime
ballistic
Maintenance ΔV band
unclassified
Model assumption
circular-coplanar
Idealised: planets on circles, coplanar ecliptic.
Period
— yr ( × E-M synodic)
Family seed covering 2-, 3-synodic period cyclers (k in {2, 3}). Per-member catalogue entries pick the specific period.
Priority date
2003-02-09

V∞ at encounters

No encounter V∞ values published in accessible sources.

Orbit elements (heliocentric)

Semi-major axis a
— AU
Eccentricity e
—
Perihelion
— AU
Aphelion
— AU
Inclination
0.00°

Family seed: no specific orbital elements. Individual member cyclers carry their own aphelion.

Orbit view 2.5D ecliptic projection

Top-down ecliptic view: the Sun at centre, true J2000 ellipses for Earth, Mars, and the cycler's heliocentric ellipse (a=null, e=null). E M Sun
spacecraft: idealized coplanar ellipse planets: J2000 osculating ellipse (Standish & Williams Table 1) clock: idealized phase clock (no epoch) orientation: coplanar-idealized (no Ω/ω published — in-plane ellipse) encounters: time-true on the idealized phase clock (real mean motions, phase chosen so the geometry's encounters occur)
— — planet orbit (true J2000 ellipse) ——— cycler ellipse

Definition status

incomplete — core fields missing or known-unknowns tracked below

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 introducing the global-search method.

Corroborating sources

Notes

FAMILY SEED ENTRY for Russell 2004 dissertation Chapter 4 cycler tables. Russell's global search enumerates 202 total ballistic + near-ballistic Earth-Mars cyclers with periods up to 3 synodic periods (dissertation Table 4.14): - Table 4.9 (page 127): 5 ballistic 2-synodic cyclers (4 generic transit-leg rows tabulated; the 5 count in Table 4.14 includes one variant not tabulated separately). The McConaghy 2006 "Notable" cycler is row 1 = 4.991gG2 (catalogued individually as `russell-ch4-4.991gG2`). The high-energy 8.049gGf2 is row 2. - Tables 4.10-4.11 (pages 128-129): 141 ballistic 3-synodic cyclers with generic transit legs. Many rows share the same (V_inf E, V_inf M, t_out, aphel) parameters and differ only in trailing leg phasing arguments (Russell line 5494 calls these "subtle differences"). ~37 distinct (V_inf, ToF, aphel) groups. 6 individually catalogued as `russell-ch4-3.64gGg3`, `-3.77Gh3`, `-3.78Gg3`, `-5.30gGf3`, `-5.66Gfh3`, `-9.94Gg3` (the bolded promising members per dissertation line 5510). - Table 4.12 (page 132): 28 ballistic 3-synodic cyclers with full-rev transit legs. Asymmetric inbound/outbound transit times. 3 individually catalogued as `russell-ch4-3.66gfF3`, `-5.30ggF3`, `-5.75ggF3`. Russell also bolds 3.77ghF (V_inf 3.77/4.71, t_out=170 t_in=200, aphel 1.63, TR=1.16) which is not individually catalogued here. - Table 4.13 (page 134): 28 NEAR-ballistic 3-synodic cyclers (TR reduced from 1.00 to 0.95). 1 individually catalogued as `russell-ch4-6.44Gg3`. The famous Aldrin cycler 6.399G1 falls in this class with TR=0.91 but is documented separately in the catalogue under `aldrin-classic-em-k1-outbound` (entry 1). For ingest of additional individual members, follow Russell's Chapter 5 parent-cycler list (Table 5.5, dissertation lines 7506-7549) which selects 77 of the 202 simple-model cyclers as having at least one launch window with ΔV ≤ 300 m/s in the realistic ephemeris model. Appendix C lists detailed reproducible cycler data for those 77. Russell's text explicitly cross-references several cyclers to the SnLm broad-class space (dissertation lines 5476, 7416, 8008): - 4.991gG2 = McConaghy "S1L1" (= entry 2 mcconaghy-2006-em-k2 under McConaghy's convention) - 5.658xxx family ≈ low realistic-ephemeris-ΔV cyclers (Russell's "consistently low ΔV requirements" remark, line 7420) - 6.399G1 = the Aldrin cycler (= entry 1) Discrepancy log for the McConaghy mapping: - McConaghy 2006 reports V_inf E = 4.7, V_inf M = 5.0, ToF 153 d - Russell 2004 Table 4.9 row 1 reports V_inf E = 4.99, V_inf M = 5.10, ToF 150 d. Cycler code "4.991gG2" — the "4.991" prefix matches Russell's simple-model V_inf E. - Both characterise the same trajectory; the discrepancy reflects circular-coplanar (Russell) vs realistic-ephemeris (McConaghy) optimisation. Wide M7 tolerances are needed to collapse the two entries.

Source quotes (per-field provenance)

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

name
Russell 2004 dissertation Chapter 4 Tables 4.9-4.13 cumulatively; see also Table 4.14 summary (line 5662) which gives the per-class counts: 2-syn generic ballistic = 5, 3-syn generic ballistic = 141, 3-syn full-rev ballistic = 28, 3-syn generic near-ballistic = 27, 3-syn full-rev near-ballistic = 1.
notes
Russell 2004 dissertation §4.9 (Chapter Conclusions, line 5697- 5715): "In total, all values of v∞ at Earth are examined from 2.5→10 km/s at intervals of 0.0025 km/s. At each value, every feasible permutation of all half-rev, full-rev, and generic returns is investigated. Of the trillions of combinations examined, nearly two million minimax problems are posed and solved. There are thirty-three previously documented and 170 previously undocumented promising cyclers found".