Russell-Ocampo cycler 4.3.1.-5 (low-energy 4-synodic, near-Hohmann)

russell-ocampo-4.3.1-5 · source: literature · validation: V0

Signature

Bodies: E-M
Sequence (canonical): E-E-M-M
Sense: outbound
Period: 8.540 yr (4 × E-M synodic)
4 x 2.135 = 8.54 yr. Russell 2004 Table 3.7 lists complete cycle times: 3399 d ≈ 9.30 yr; the discrepancy is the partial second-cycle data Russell tabulates.
Priority date: 2003-02-09

V∞ at encounters

E (#1): 3.10 km/s
Russell 2004 Table 3.4 row 4.3.1.-5: 'Earth v_inf (km/s): 3.1'. Russell notes (§3.8): 'Cycler 4.3.1.-5 has remarkably low energy requirements at Earth and Mars. ... At Earth, the cycler has a v_inf of 3.10 km/s compared to the Hohman value of 2.84 km/s'.
M (#2): 2.50 km/s
Russell 2004 Table 3.4 row 4.3.1.-5: 'Mars v_inf (km/s): 2.5'. Russell §3.8: 'at Mars the cycler has a v_inf of 2.53 km/s compared to the Hohman value of 2.57 km/s.'

Orbit elements (heliocentric)

Semi-major axis a: — AU
Eccentricity e: —
Perihelion: — AU
Aphelion: 1.505 AU
Inclination: 0.00°

Russell 2004 Table 3.4 Aphelion Ratio 0.99: 'The Aphelion Ratio is 0.992, thus the cycler doesn't quite reach Mars in the simplified model.' This is technically a near-ballistic cycler in the simplified model (the small ΔV makes it ballistic in the true model where Mars's perihelion is closer).

Legs

E → M: 268 d, 0 revs
Russell 2004 Table 3.4 row 4.3.1.-5: 'Earth->Mars (or aphelion) Time (days): 268'.

Primary citation

Russell, R. P. & Ocampo, C. A. (2005). Geometric Analysis of Free-Return Trajectories Following a Gravity-Assisted Flyby. Journal of Spacecraft and Rockets, Vol. 42, No. 1, pp. 138-151.

DOI: 10.2514/1.5571

URL: https://arc.aiaa.org/doi/abs/10.2514/1.5571

Russell-Ocampo's first peer-reviewed publication of the 24 ballistic cycler set. The conference precursor (Russell/Ocampo AAS 03-145) is older but unpublished in archival form.

Corroborating sources

Russell, R. P. & Ocampo, C. A. (2004). A Systematic Method for Constructing Earth-Mars Cyclers Using Free-Return Trajectories. Journal of Guidance, Control, and Dynamics, Vol. 27, No. 3, pp. 321-335. DOI: 10.2514/1.1011
Citation per Wikipedia Mars Cycler article [8]. Russell's dissertation expands the catalogue.
Russell, R. P. (2004). Global Search and Optimization for Free-Return Earth-Mars Cyclers. Ph.D. dissertation, UT Austin. · link
Table 3.4 row '4.3.1.-5' is the canonical source for the parameters here. Table 3.7 has the full flyby velocity data for one cycle.

Notes

Russell describes this cycler (§3.8) as having "remarkably low energy requirements at Earth and Mars" because "the generic return portion of this cycler is very near a Hohman transfer". The aphelion ratio of 0.992 means it just barely doesn't reach Mars's circular orbit in the simplified model, so it's TECHNICALLY classed as "near-ballistic" in Russell's taxonomy — but in the real ephemeris model with Mars's eccentric orbit it crosses Mars's orbit at perihelion and is genuinely ballistic. This is one of the lowest-V_inf E-M cyclers known, distinct from the other Russell-Ocampo entries above and worth keeping in the seed catalogue as a counter-example to "low-V_inf cyclers require Venus". Russell 2004 Table 3.4 classifies this cycler under the wider ARMIN=0.9 / TRMIN=0.85 "ballistic" net rather than the strict AR>=1.0 AND TR>=1.0 criterion. Strictly, this cycler is near-ballistic: AR=0.99, TR=1.55; the gravity-assist deflection at Mars (aphelion just under Mars's circular-orbit radius) is short of fully ballistic and requires a small powered nudge. The `trajectory_regime: ballistic` field is retained because Russell and the cycler literature group it with the ballistic family; consumers doing powered-flyby DV accounting should still compute the residual.

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: Russell 2004 dissertation §3.8: "At Earth, the cycler has a v_inf of 3.10 km/s compared to the Hohman value of 2.84 km/s". Table 3.4 rounds to 3.1 km/s.
vinf_kms_at_encounters[1].vinf_kms: Russell 2004 §3.8: "at Mars the cycler has a v_inf of 2.53 km/s compared to the Hohman value of 2.57 km/s." Table 3.4 rounds to 2.5.
legs[0].tof_days: Russell 2004 Table 3.4 row 4.3.1.-5: 268 d.
aphelion_au: Russell 2004 §3.8: "The Aphelion Ratio is 0.992, thus the cycler doesn't quite reach Mars in the simplified model."